From 5a477707eb6bdd97fd054380ad46b9a24b6dfcab Mon Sep 17 00:00:00 2001 From: krakhit Date: Sun, 29 Oct 2023 10:15:31 +0000 Subject: [PATCH] deploy: 493c138a074ec3a45e026acca0fd5e78f4cc9c7b --- introfhe.html | 4 ++++ print.html | 4 ++++ searchindex.js | 2 +- searchindex.json | 2 +- 4 files changed, 10 insertions(+), 2 deletions(-) diff --git a/introfhe.html b/introfhe.html index 421a23b..53b0cab 100644 --- a/introfhe.html +++ b/introfhe.html @@ -188,6 +188,7 @@

Inroductory

  • Sunscreen - intro to fhe for engineers
  • Survey on FHE and applications
  • Computing on encrypted data: Nigel Smart
    • +
  • Hands on FHE

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    Inroductory

  • Sunscreen - intro to fhe for engineers
  • Survey on FHE and applications
  • Computing on encrypted data: Nigel Smart
    • +
  • Hands on FHE

    • Applications

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These hands-on workshops, tutorials, and projects are designed to help learners apply their understanding of ZK proofs in real-world situations, making them an invaluable resource for anyone looking to further their expertise in this field. What you will find here: Code-to-Learn Applications","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Hands-On ZK/Cryptography","id":"107","title":"Hands-On ZK/Cryptography"},"108":{"body":"A beginners intro to coding Zero knowledge Proofs Babysnark do do dodo dodo typescript zk zero knowledge with Bellman Cryptohack - hands on cryptography Hands on ZK - ZK learning group Intro to zk: do it yourself circuits Zk Sudoku - Python Arnacube implementations DAPP fron scratch - Vivian Plasencia Zordle - Zk wordle Mental Poker: Part 1 Mental poker: Part 2 0xparc learning groups - covering cricom and halo2 Plonkathon 0xparc Constructing ZK SNARK circuits - DSL Zk calculator Social Applied ZK projects on Ethereum Uncloak courses Proofs args and zk study group implementations Cryptopals challenges Starkware101 Verifiable AES code: lambdaclass Merkle patricia tree: lambdaclass Haskell: Introduction Practical Cryptography for Devs: Nakov Transforming code into arithmetic circuits Differential fuzzing Zkvm step by step Zk smart contract tutorial optimizing pairing based cryptography, montgomery arithmetic in rust In assembly code Pairing over BLS12-381 Part 1 : Fields Part 2 : Curves Part 3 : Pairing An overview of ZKtooling and proof systems right now: Sep 2023","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » General","id":"108","title":"General"},"109":{"body":"Berkeley RDI ZKP-Web3 hackathon Zk hack puzzles Ingonyama ZK CTF-May 2023","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Challenges and hackathons","id":"109","title":"Challenges and hackathons"},"11":{"body":"","breadcrumbs":"Glossary » J","id":"11","title":"J"},"110":{"body":"The Rust book rust book with interactive quizzes The Rust book course Rust guide books Comprehensive rust by google Print and keep nearby - cheats.rs Tutorials Idiomatic Rust - For beauty over brawn Uncloak Study group Awesome rust cryptographic libraries Awesome rust -- general Rust Algorithms Rustlings Rust learning Rust crash course Data engg with rust Circomscribe - learn circom","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Rust learning resources for ZK/cryptography","id":"110","title":"Rust learning resources for ZK/cryptography"},"111":{"body":"code Benchmarking with Rust Flamegraphs code code:flamegraphs from hierarchical data Criterion Criterion introduction The benchmark game Zkalc zkBench Benchmarks","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Benchmarking tools","id":"111","title":"Benchmarking tools"},"112":{"body":"Our collection of mathematical papers, protocols, and code on ZK proofs is a comprehensive resource for researchers, developers, and students in the field of cryptography. These materials provide a deep understanding of the theories, implementations, and practical applications of zero-knowledge proofs, serving as a valuable reference for anyone interested in this cutting-edge technology. What you will find here: Protocols, Papers, Code Implementation, Resources","breadcrumbs":"Zero Knowledge Proofs » Protocols » Protocols --- UNDER CONSTRUCTION","id":"112","title":"Protocols --- UNDER CONSTRUCTION"},"113":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » SNARK Protocols","id":"113","title":"SNARK Protocols"},"114":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » STARK Protocols","id":"114","title":"STARK Protocols"},"115":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Lookup Protocols","id":"115","title":"Lookup Protocols"},"116":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Folding Scheme Protocols","id":"116","title":"Folding Scheme Protocols"},"117":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Other Protocols","id":"117","title":"Other Protocols"},"118":{"body":"Protocols Paper Implementation Resources Universal Transparent Pinocchio - 2013 →📝 ❌ ❌ TinyRAM - 2013 →📝 ❌ ❌ vnTinyRAM - 2014 →📝 Mike Hearn ✅ ❌ Geppetto - 2015 →📝 ❌ ❌ Buffet - 2015 →📝 ❌ ❌ Groth -2016 →📝 ConsenSys-gnark [1] arkworks-rs [2] Groth16 Malleability - Geometry [1] Proof of forgery [2] Groth16 aggregation proposal [3] Groth - Talk [4] Deep into bellman library - Star Li [5] Lookups for groth16? [6.1] ultragroth [6.2] ❌ ❌ Ligero - 2017 →📝 ✅ ✅ ZoKrates - 2018 →📝 ZoKrates Proving hash preimage with Zokrates - Decentriq [1] Efficient ECC in Zokrates- Decentriq [2] xjSNARK - 2018 →📝 ❌ ❌ Hyrax - 2018 →📝 Sonic - 2019 →📝 Benthams Gaze ✅ ❌ Plonk - 2019 →📝 heliaxdev [1] kobigurk [2] ZK-Garage [3] dusk-network [4] Jellyfish (Includes Plookup) [5] Plonk high level summary [1] Talk: Ariel Gabizon [2] Talk: Zac Williamson [3] Understanding Plonk - Vitalik [4] From AIRs to RAPs - how PLONK-style arithmetization works [5] Custom gates on plonk -Do whatever [7] Plonk Cafe [8] Plonk: Anatomy of a proof generation: Scroll [9] Resource: Plonk by hand -1 Metastate [10.1] Resource: Plonk by hand -2 Metastate [10.2] Resource: Plonk by hand -3 Metastate [10.3] Resource: Plonk and Plookup Metastate [10.4] Turboplonk [11] Custom gates in plonk [12] Plonk: Thomas Piellard [13] ZKP intro to Plonk - Star Li [14] Multi set checks in Plonk and Plookup: Gabizon [15] Plonk - Kimchi: Mina Protocol [16.1] Kimchi [16.2] Plonk not a monad tutorial [17] ✅ ❌ Redshift - 2019 →📝 Redhsift Summary Spartan - 2019 →📝 Microsoft Halo - 2019 →📝 ✅ ✅ MIRAGE - 2020 →📝 ✅ ❌ Marlin - 2020 →📝 arkworks-rs Doc: Pre lunar and not updated to Aleo/testnet3 [1] Thesis [2] Eurocrypt 2020: Talk video [3] ZK summit - Talk: Pratyush [4] Sin7y tech review: blog [5] Marlin and Me [6] Fractal -2020 →📝 scipr-lab/libiop Fractal - talk [1] Demystifying Fractal 1 -Metastate [2.1] Demystifying Fractal 2 - Metastate [2.2] Lunar - 2020 →📝 ZK study club video SuperSonic - 2020 →📝 Demystifying supersonic 1 -Metastate [1.1] Demystifying supersonic 2- Metastate [1.2] ✅ ✅ Darlin - 2021 →📝 Plonkup -2021 →📝 HorizenOfficial/ginger-lib SnarkPack -2021 →📝 Efficient Aggregation FFlonk -2021 →📝 Brakedown - 2021 →📝 Gemini - 2022 →📝 Elastic SNARKs for diverse environments Hyperplonk - 2022 →📝 EspressoSystems Hyperplonk - benedikt Bunz [1] Delendum [2] Hardware friendliness of MLE-Sumcheck [3] Hardware-optimizations for SumCheck-Binyi Chen [4] Testudo: Groth+Spartan - 2023 →📝 cryptonetlab Jolt - 2023 →📝 Introducing Lasso and Jolt","breadcrumbs":"Zero Knowledge Proofs » Protocols » SNARK Protocols » SNARK Protocols","id":"118","title":"SNARK Protocols"},"119":{"body":"Protocols Paper Implementation Resources Universal Transparent zkSTARK -2018 →📝 Winterfell [1] Ministark [2] Cairo [3] Guide for Ministark ✅ ✅ Aurora - 2019 →📝 Thesis Spooner ✅ ✅ Zilch - 2021 →📝 TrustworthyComputing ✅ ✅ Plonky - 2021 →📝 mir-protocol Plonky: Fast recursive arguments based on Plonk and Halo [1] Plonky: Adding zero Knowledge to Plonk and Halo [2] Plonky2 - 2021 →📝 mir-protocol Orion -2022 →📝 sunblaze-ucb IACR -talk","breadcrumbs":"Zero Knowledge Proofs » Protocols » STARK Protocols » STARK Protocols","id":"119","title":"STARK Protocols"},"12":{"body":"","breadcrumbs":"Glossary » K","id":"12","title":"K"},"120":{"body":"Protocols Paper Implementation Resources Universal Transparent Plookup -2020 →📝 Jellyfish Plookup in action -Talk [1] Plonk and Plookup - Metastate [2] Plonk and Plookup - Khovratovich [3] Mina Protocol[4]](https://o1-labs.github.io/proof-systems/introduction.html)AES with lookup : Daira Hopwood [5] Lookup tables - Ariel Gabizon [6] Caulk - 2022 →📝 caulk-crypto [1] Caulk+ [2] Flookup - 2022 →📝 Baloo - 2022 →📝 CQ - 2022 →📝 Geometry CqLin - 2023 →📝 Lasso - 2023 →📝 Introducing Lasso and Jolt","breadcrumbs":"Zero Knowledge Proofs » Protocols » Lookup Protocols » Lookup Protocols","id":"120","title":"Lookup Protocols"},"121":{"body":"Protocols Paper Implementation Resources Universal Transparent Nova - 2021 →📝 microsoft Srinath Setty - Talk [1] Srinath Setty - Video [2] IACR talk slides [3] IVC:Nova lambdaclass [4] Nova - zkstudy club talk [5] zkstudy club video [6] Supernova - 2022 →📝 jules Champagne supernova: lambdaclass Hypernova - 2023 →📝 CCS: Customizable constraint systems for succinct arguments Sangria - 2023 →📝 Blog Protostar - 2023 →📝 Deep dive into Protostar paper & protocol - Binyi Chen Protogalaxy - 2023 →📝 CycleFold - 2023 →📝","breadcrumbs":"Zero Knowledge Proofs » Protocols » Folding Scheme Protocols » Folding Scheme Protocols","id":"121","title":"Folding Scheme Protocols"},"122":{"body":"Protocols Paper Implementation Resources Universal Transparent vRAM - 2018 →📝 ✅ ❌ Bulletproof - 2018 →📝 Dalek [1] Lovesh [2] ZKP using Bullet proofs - Lovesh Harchandani [1] Notes [2] ✅ ✅ Virgo - 2020 →📝 sunblaze-ucb ✅ ✅ Sigma Protocols →📝 sigmastate Sigma Protocols for the Working Programmer","breadcrumbs":"Zero Knowledge Proofs » Protocols » Other Protocols » Other Protocols","id":"122","title":"Other Protocols"},"123":{"body":"The resources on the mathematics behind ZK proofs delve into the complex theories and mathematical concepts that underpin this innovative technology. These resources are intended for those with a strong background in mathematics, or those looking to deepen their understanding of the mathematical foundations of zero-knowledge proofs and their applications. What will you find here: Atoms and building blocks of a ZKP","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Mathematics","id":"123","title":"Mathematics"},"124":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite Fields","id":"124","title":"Finite Fields"},"125":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Elliptic curves","id":"125","title":"Elliptic curves"},"126":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » FFT","id":"126","title":"FFT"},"127":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » MSM","id":"127","title":"MSM"},"128":{"body":"Number theory explained from first principles An introduction to the theory of finite fields MIT lectures -FInite Field arithmetic Finite field arithmetic Doche Lange Aztec emulated field and group operations","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Finite fields","id":"128","title":"Finite fields"},"129":{"body":"A Fast Large-Integer Extended GCD Algorithm and Hardware Design for Verifiable Delay Functions and Modular Inversion Optimized Binary GCD for Modular Inversion Library of Algorithms Modular Multiplication and Hardware implementations - Review Evaluation of large integer multiplications in hardware - Review Hardware friendly modular mult Montgomery REDC using positive inverse mod r Low latency multipliers and cryptographic puzzles optimizing pairing based cryptography, montgomery arithmetic in rust","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Modular arithmetic","id":"129","title":"Modular arithmetic"},"13":{"body":"Ligero - Ligero is a Zero Knowledge Proof system designed specifically for blockchain applications, offering low computational and storage requirements for verification.","breadcrumbs":"Glossary » L","id":"13","title":"L"},"130":{"body":"The Matrix cookbook Ideal Class Groups","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Related Math","id":"130","title":"Related Math"},"131":{"body":"Finite fields and polynomials Schwarz - Zippel Lemma Curious History of Schwarz-Zippel lemma","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Polynomials","id":"131","title":"Polynomials"},"132":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Cryptographic primitives","id":"132","title":"Cryptographic primitives"},"133":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Elliptic curves","id":"133","title":"Elliptic curves"},"134":{"body":"ECC cryptobook Cures over finite fields - Lectures Elliptic curves Chapter 4 Washington Elliptic Curves: MIT lectures Corbellini - ECC ECC primer Silverman - ECC talk Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms Solinas - Efficient Arithmetic on Koblitz Curves Koblitz curve cryptosystems Elliptic Curve Cryptosystems (Koblitz Curves) Algorithm to Find Elliptic curves with a subgroup of a given size Elliptic curves number theory and cryptography Elliptic curve Arithmetic Curve addition - Doche-Lange Elliptic Curve Arithmetic Exponentiation -Doche Lange Elliptic curves of characteristic 2 or 3 - John Cook Addition/Doubling formulae Visualize Elliptic curves j invariant of a curve subgroup checks in BLS12 Complete addition formulae : Bernstein - Lange Complete addition formulae for prime order curves FPGA implementation of complete formulae with Montgomery multiplier Survey of Elliptic curves for Proof systems Edwards curves Twisted Edwards curves Subgroup checks for BLS12 Cofactor explained: Elliptic curves dirty little secret Applications of Riemann Roch theorem in cryptography - Borgeaud Quaternion algebras and Isogeny based cryptography","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » General","id":"134","title":"General"},"135":{"body":"Pairings for beginners - Craig Costello Pairings - Vitalik Buterin Pairing friendly curves Pairing implementation revisited Groth_Sahai proofs are not scary Bilinear pairings in cryptography - Dennis Meffert Pairings and poly commitments - David Wong Circom pairing Code Pairings or bilinear maps optimizing emulated pairings Estimating the bit security of pairing friendly curves optimizing pairing based cryptography, montgomery arithmetic in rust","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Pairings","id":"135","title":"Pairings"},"136":{"body":"BLS12-381 For The Rest Of Us BN254 for the rest of us Benchmarking pairing-friendly elliptic curves libraries ecgfp5 - Pornin: Goldilocks ed448 blog John Cook A deep dive into ed25519 Pasta curves -Electric coin Developers guide to constructing application specific curves","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Specific curves","id":"136","title":"Specific curves"},"137":{"body":"ZK hashes- General ZKP friendly hash functions: SOK Whats the deal with hashes: zk hack Sponge functions: paper S box properties Hash Functions Monolith for ZK Applicationss STARK friendly hash functions Merkling What is a merkle tree Merkle trees Sparse Merkle trees Merkle Commitment scheme Merkle trees and proof of inclusion why you should not sort your Merkle Leaves Fiat Shamir Merlin: Fiat-Shamir magic generator How to Fiat Shamir Serving up ZKP Frozen Heart vulnerability in Girault proof of knowledge in Bulletproofs in Plonk Hashes Keccak: Sponge and Duplex constructions SHA256 Halo2 16 bit lookup implementation Poseidon POSEIDON: A New Hash Function for Zero-Knowledge Proof Systems some documentation Encryption With Poseidon: Dima Khovratovich SAFE A tool box for Poseidon API SAFE: Faster and simple hashing with ZKP Encoding of long objects in Poseidon - Dmitry Khovratovich Talk Grassi Plonky2: Poseidon gate Penumbra: Poseidon Decaf377 Poseidon Implementations code: filecoin Poseidon in Filecoin - Dmitry Khovratovich code: Ingonyama (python) code: Dusk network code: Dust netowrk - Poseidon merkle code: Triplewz - GO Rescue Rescue-Prime: a Standard Specification (SoK) Observations on Rescue Poseidon vs Rescye MIMC MiMc Mimc7 in Plonk - Custom gates Mimc Roy slides Reinforced concrete Reinforced concrete implementation Plonkup reinforced concrete zkstudyclub Code: Luke Pearson Sinsemilla Sinsemilla: A circuit-efficient, lookup-based collision-resistant hash function ZCash protocol specification BLAKE Blake code Tip5 Tip5 code Hash to Curve Hash to Curve Hash to secp256k1 curve Optimized BLS signatures on EVM Hash Bounties Algebraic Hash bounties","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Hash functions » Hash functions","id":"137","title":"Hash functions"},"138":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Verifiable Delay functions » Verifiable Delay functions","id":"138","title":"Verifiable Delay functions"},"139":{"body":"All about Verifiable Delay Functions (VDF's) - VDFresearch","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Verifiable Delay functions » General","id":"139","title":"General"},"14":{"body":"Marlin - Marlin is a Zero Knowledge Proof system that leverages recursive composition to construct large-scale Zero Knowledge Proofs with low proof sizes and verification times. Merkle Tree - A tree data structure in cryptography that enables efficient verification of the integrity and membership of data elements. Multi-party Computation (MPC) - A cryptographic protocol that enables multiple parties to jointly compute a function over their private inputs while preserving the privacy of those inputs, allowing them to collectively obtain the desired result without revealing individual data to each other.","breadcrumbs":"Glossary » M","id":"14","title":"M"},"140":{"body":"General Arithmetic Circuits: A survey Complexity Zoo Arithmetization schemes for snarks Grobner basis used in circuits Circomscribe - learn circom R1CS constraint system Daira Hopwood - Efficient R1CS circuits: Video Quadratic Arithmetic programs R1CS 0 to H - Vitalik Buterin Aleo - Basics of R1CS Zero Knowledge Proofs: How Cryptographers can prove anything Alex Pinto - Constraint system for snarks Alex Pinto - How to build QAP Alex Pinto - Vanishing polynomial for QAP QAP from zero to hero: Vitalik R1CS workshop - Mir Plonkish arithmetization Refer to Plonk AIR Arithmetization AIR to RAPs - Gabizon AIR-Multivariate Sumcheck - W.Borgeaud AIR assembly Bobbin Threadbare Customizable Constraint system CCS CCS: Customizable constraint systems for succinct arguments A multivariate AIR using Superspartan- Borgeaud","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Arithmetization » Arithmetization","id":"140","title":"Arithmetization"},"141":{"body":"General Overview of commitment schemes: Justin Drakes Comparison of Commitment Schemes review of polynomial commmitments KZG KZG commitments KZG - Suyash Polynomial commitments - Dankrad Feist How to use KZG in proofs Fast KZG proofs Amortized KZG - Feist Khovratovich Multiplying a vector by a Toeplitz matrix PCS multiproofs - Feist New sharding design with tight beacon and shard block integration - Dankrad Feist Protodanksharding - FAQ Vitalik Universal verification equation for data availability sampling KZG friendly curves: El Housseini KZG in practice: Scroll Vector Commitments Verkle Trie - Dankrad Feist Aggregatable vector sub commitments Catalano-Fiore VC Inner product Arguments (IPA) Inner product arguments - Dankrad Feist IPA by hand - arnacube IPA commitment scheme Lambdaclass Lattice based commitment Schemes Vortex SLAP Blog","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Commitment Schemes » Commitment Schemes","id":"141","title":"Commitment Schemes"},"142":{"body":"( needs sorting )","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Secure Multi Party Computation » Secure Multi Party Computation","id":"142","title":"Secure Multi Party Computation"},"143":{"body":"An Introduction to Secret-Sharing-Based Secure Multiparty Computation - Daniel Escudero Yau;s garbled circuits: MPC A gentle introduction to YAU's Garbled circuits Setup ceremonies - Pruden & Matlala Collaborative zk-Snarks a Multi-Prover Zero-Knowledge Proof System Trinocchio: Privacy-Preserving Outsourcing by Distributed Verifiable Computation Zero-Knowledge Proofs on Secret-Shared Data via Fully Linear PCPs Prio: Private, Robust, and Scalable Computation of Aggregate Statistics ATLAS (Goyal, CMU) Efficient and Scalable MPC in the Honest Majority Setting","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Secure Multi Party Computation » General","id":"143","title":"General"},"144":{"body":"( To add papers: Work in progress )","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Proving Methods","id":"144","title":"Proving Methods"},"145":{"body":"Unreasonable power of sumcheck - Thaler Justin Thaler Lecture Intro to Sumcheck protocol -oxsage Inuition behind sumcheck - Wong Sumcheck argument and applications Proving AIR with MultiLinear Sumcheck - Borgeaud","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Sumcheck Protocol","id":"145","title":"Sumcheck Protocol"},"146":{"body":"STARK paper DEEP - FRI Proximity Gaps for Reed-Solomon Codes FRI hackernoon FRI properties FRI erasure code fraud proof Barycentric low deg check - Dankrad Feist Low Degree Testing","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Low degree Testing/FRI","id":"146","title":"Low degree Testing/FRI"},"147":{"body":"A brief history of lookup arguments","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Lookup arguments","id":"147","title":"Lookup arguments"},"148":{"body":"Snarkpack: practical snark aggregation blog talk talk","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Aggregations and recursions","id":"148","title":"Aggregations and recursions"},"149":{"body":"Resource: Awesome Folding How to build a snark that is out of this world - Nat Bunner An incomplete guide to FOlding schemes - Lisa","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Folding and accumulation schemes","id":"149","title":"Folding and accumulation schemes"},"15":{"body":"Non-interactive Proof - A Zero Knowledge Proof where the prover generates a single proof without any interaction with the verifier. NTT (Number Theoretic Transform) - A mathematical technique used for efficient polynomial multiplication and fast Fourier transforms in various applications such as signal processing, error correction codes, and cryptography.","breadcrumbs":"Glossary » N","id":"15","title":"N"},"150":{"body":"Succinct Proofs and Linear Algebra","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » General","id":"150","title":"General"},"151":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Computational Primitives","id":"151","title":"Computational Primitives"},"152":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Hardware acceleration","id":"152","title":"Hardware acceleration"},"153":{"body":"Measuring Snark performance frontends-backends and future - Thaler SNark security and peformance - Thaler Decentralized Speed: Advances in Zero Knowledge Proofs Hardware Acceleration for Zero Knowledge Proofs HW acc review - 0xmonia","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Need for hardware acceleration or not?","id":"153","title":"Need for hardware acceleration or not?"},"154":{"body":"Zprize","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Competitions","id":"154","title":"Competitions"},"155":{"body":"PipeZK Algorithms for modern Hardware","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » General HW resources and guides","id":"155","title":"General HW resources and guides"},"156":{"body":"Pantheon of ZKP frameworks - Celer Network ZK Harness ZK Benchmarking -Delendum ZKalc","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Benchmarks of ZKP primitives","id":"156","title":"Benchmarks of ZKP primitives"},"157":{"body":"TEE for CPU and GPU Nvidia TEE for blockchain applications","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » TEE and confidential computing","id":"157","title":"TEE and confidential computing"},"158":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Discrete Fourier Transforms","id":"158","title":"Discrete Fourier Transforms"},"159":{"body":"FFT - Vitalik Reed-Solomon code: Vitalik FFT Notes The Fast Fourier Transform in a Finite Field - Pollard Number Theoretic Transform (NTT): Introduction Gentle intro to NTT 1 (includes rings) Gentle intro to NTT2 (includes rings) Efficient primes for NTT - Goldilocks Goldilocks in nuFHE Goldilocks NTT trick - Solberg Elliptic Curve Fast Fourier Transform (ECFFT) Part I: Fast Polynomial Algorithms over all Finite Fields: Eli Ben-Sasson et.al Talk -zk study club ECFFT algorithm Rust Implementation -Wboregaud Rust ECFFT BN254- Wboregeaud ECFFT-2 Ben-Sasson et.al FFT - Ferror Moreno thesis Zcash FFT FFT for polynomial multiplication A quick barycentric evaluation tutorial - Vitalik Barycentric interpolation - Math Oxford Walsh Hadamard Transform - Borgeaud FFT on finite fields intro","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Algorithms and methods","id":"159","title":"Algorithms and methods"},"16":{"body":"","breadcrumbs":"Glossary » O","id":"16","title":"O"},"160":{"body":"Thesis: BUNTTERFLY: A Flexible Hardware Generator for the Number Theoretic Transform - Jason Vranek CycloneNTT NTL: a library for NTT Zprize 2022","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Implementations","id":"160","title":"Implementations"},"161":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Multi scalar multiplications","id":"161","title":"Multi scalar multiplications"},"162":{"body":"Fast Multi-scalar Multiplication Methods on Elliptic Curves with Precomputation Strategy Using Montgomery Trick Faster batch forgery identification See section 4 for MSM, bucket method Pippenger's exponentiation algorithm - Bernstein Efficient multi-exponentiation implementation in Python Multi-scalar multiplication: state of the art & new ideas with Gus Gutoski Improved Fast exponentiations - Bodo Moller Fast exponentiation with precomputation - Brickell Gordon et al Matter labs -ALgorithms Ryah Henry - Thesis Efficient Multi exponentiation: Bucket method - Bootle","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Algorithms and methods","id":"162","title":"Algorithms and methods"},"163":{"body":"pipezk MSM with FPGA -Connor Masterson thesis PipeMSM EdMSM CycloneMSM Cuzk Zprize MSM implementations","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Implementations","id":"163","title":"Implementations"},"164":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Fully Homomorphic Encryption","id":"164","title":"Fully Homomorphic Encryption"},"165":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Articles","id":"165","title":"Articles"},"166":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes","id":"166","title":"Schemes"},"167":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Libraries","id":"167","title":"Libraries"},"168":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics","id":"168","title":"Mathematics"},"169":{"body":"What you will find here: Blogs, Articles, PDFs, Videos, Notes","breadcrumbs":"Fully Homomorphic Encryption » Articles » Articles","id":"169","title":"Articles"},"17":{"body":"Pairing-Based Cryptography - A cryptographic approach that leverages mathematical pairings to perform various operations and enable advanced cryptographic protocols. Perfect Zero Knowledge - A level of security provided by a Zero Knowledge proof where the verifier gains no additional knowledge about the secret information being proved, except for the validity of the statement. Plonk - Plonk (Permutation-based SNARK) is a Zero Knowledge Proof system that utilizes permutation arguments to achieve succinctness and efficiency. Privacy - The state of being free from unauthorized intrusion, surveillance, or disclosure of personal or sensitive information. Proof Of Knowledge - A cryptographic concept where a prover demonstrates possession of certain information or knowledge to a verifier without revealing the actual information. Prover - The entity in a Zero Knowledge Proof protocol that possesses knowledge of a secret and aims to prove its knowledge to the verifier. Pseudorandom Function - A pseudorandom function (PRF) is a deterministic function that takes an input and produces an output that appears random, even though it is generated by a deterministic algorithm, making it indistinguishable from a truly random function for practical purposes.","breadcrumbs":"Glossary » P","id":"17","title":"P"},"170":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Articles » UNDER CONSTRUCTION 👷","id":"170","title":"UNDER CONSTRUCTION 👷"},"171":{"body":"Encrypted search using FHE Exploring FHE: Vitalik Sunscreen - intro to fhe for engineers Survey on FHE and applications Computing on encrypted data: Nigel Smart","breadcrumbs":"Fully Homomorphic Encryption » Articles » Inroductory","id":"171","title":"Inroductory"},"172":{"body":"ML and FHE Solving LLM Privacy with FHE How Snarks fall short for FHE fhevm fhEVM - Morten Dahl","breadcrumbs":"Fully Homomorphic Encryption » Articles » Applications","id":"172","title":"Applications"},"173":{"body":"FPT: a Fixed-Point Accelerator for Torus Fully Homomorphic Encryption","breadcrumbs":"Fully Homomorphic Encryption » Articles » Implementations","id":"173","title":"Implementations"},"174":{"body":"Security of FHE Schemes Lattice based attacks On concrete hardness of LWE","breadcrumbs":"Fully Homomorphic Encryption » Articles » Security","id":"174","title":"Security"},"175":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » Schemes","id":"175","title":"Schemes"},"176":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » UNDER CONSTRUCTION 👷","id":"176","title":"UNDER CONSTRUCTION 👷"},"177":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » BGV","id":"177","title":"BGV"},"178":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » BFV","id":"178","title":"BFV"},"179":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » CKKS","id":"179","title":"CKKS"},"18":{"body":"QAP (Quadratic Arithmetic Programs) - QAP is a method to represent arithmetic circuits as quadratic polynomials, commonly used in Zero Knowledge Proof systems for efficient proof generation and verification.","breadcrumbs":"Glossary » Q","id":"18","title":"Q"},"180":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » FHEW","id":"180","title":"FHEW"},"181":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » TFHE","id":"181","title":"TFHE"},"182":{"body":"Part 1: Ciphertext types Part 2: Encoding and linear ops part 3: key switching and levelled multiplications Part 4: programmable bootstrapping","breadcrumbs":"Fully Homomorphic Encryption » Schemes » Deep dive: ZAMA AI - Ilaria Chilloti","id":"182","title":"Deep dive: ZAMA AI - Ilaria Chilloti"},"183":{"body":"A curated list of Homomorphic Encryption libraries, and what schemes they use.","breadcrumbs":"Fully Homomorphic Encryption » Libraries » Libraries","id":"183","title":"Libraries"},"184":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Libraries » UNDER CONSTRUCTION 👷","id":"184","title":"UNDER CONSTRUCTION 👷"},"185":{"body":"Libraries Scheme Resources Microsoft SEAL BFV BGV PALISADE BFV FHEW TFHE IBM FHE BGV IBM HElib BGV CKKS Sunscreen - levelled bootstrap BFV Introduction OpenFHE BFV BGV CKKS FHEW TFHE OpenFHE.com TenSEAL - Openmined BFV CKKS Zama AI - Concrete - Python compiler TFHE Zama AI - TFHE-rs - Rust library TFHE Google - FHE TFHE","breadcrumbs":"Fully Homomorphic Encryption » Libraries » Libraries","id":"185","title":"Libraries"},"186":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » Mathematics","id":"186","title":"Mathematics"},"187":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » UNDER CONSTRUCTION 👷","id":"187","title":"UNDER CONSTRUCTION 👷"},"188":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » LWE","id":"188","title":"LWE"},"189":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » FFT","id":"189","title":"FFT"},"19":{"body":"R1CS (Rank-1 Constraint Systems) - R1CS is a mathematical framework used in Zero Knowledge Proof systems to represent computational problems as sets of constraints. Redshift - Redshift is a Zero Knowledge Proof system designed for blockchain applications, offering scalability, efficiency, and post-quantum security. Ring Signature - A cryptographic digital signature scheme that allows a user to sign a message on behalf of a group (or ring) of potential signers, while maintaining the privacy of the actual signer's identity within the group.","breadcrumbs":"Glossary » R","id":"19","title":"R"},"190":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » NTT","id":"190","title":"NTT"},"2":{"body":"ASIC (Application-Specific Integrated Circuit) - A specialized integrated circuit designed for a specific application or function, offering optimized performance and efficiency by implementing dedicated hardware tailored to that specific task. Authentication - The process of verifying the identity of a user, device, or system to ensure that it is genuine and authorized to access certain resources or information. Aurora - Aurora is a Zero Knowledge Proof system that combines zk-SNARKs and Bulletproofs to achieve compact proofs for general-purpose computations. AuroraLight - AuroraLight is an improvement over Aurora that achieves faster prover times and smaller proof sizes while maintaining its generality and security properties.","breadcrumbs":"Glossary » A","id":"2","title":"A"},"20":{"body":"Security - The protection of hardware, software, and data from unauthorized access, theft, damage, or disruption, aiming to maintain confidentiality and integrity. Side-channel Attacks - Attacks that exploit unintended information leakage, such as timing, power consumption, or electromagnetic radiation, to infer secret information. Statistical Zero Knowledge - A level of security offered by a Zero Knowledge proof where the verifier cannot distinguish between a valid proof and a false proof, except with an extremely low probability. Sonic - Sonic (Scalable, Non-Interactive, and Compact) is a Zero Knowledge Proof system that offers scalability and efficiency for verifying large computations. Soundness - The property of a Zero Knowledge Proof protocol that ensures an honest prover cannot convince a verifier of an incorrect statement. Spartan - Spartan is a Zero Knowledge Proof system that achieves transparency, scalability, and post-quantum security without requiring a trusted setup. Supersonic - Supersonic is a Zero Knowledge Proof system that provides high-performance and efficient verification of arithmetic circuits and boolean satisfiability.","breadcrumbs":"Glossary » S","id":"20","title":"S"},"21":{"body":"Trusted Execution - The execution of a program or process in a secure and isolated environment, protecting it from tampering and unauthorized access. Trusted Setup - The process of generating initial parameters for a Zero Knowledge Proof protocol, ensuring that they do not reveal any secret information.","breadcrumbs":"Glossary » T","id":"21","title":"T"},"22":{"body":"","breadcrumbs":"Glossary » U","id":"22","title":"U"},"23":{"body":"Verifier - The entity in a Zero Knowledge Proof protocol that challenges the prover's claim and verifies the validity of the proof without gaining knowledge of the secret.","breadcrumbs":"Glossary » V","id":"23","title":"V"},"24":{"body":"Witness Indistinguishable Proof - A cryptographic proof that guarantees that given two valid proofs for the same statement, it is computationally infeasible for an adversary to distinguish which proof corresponds to the true witness.","breadcrumbs":"Glossary » W","id":"24","title":"W"},"25":{"body":"","breadcrumbs":"Glossary » X","id":"25","title":"X"},"26":{"body":"","breadcrumbs":"Glossary » Y","id":"26","title":"Y"},"27":{"body":"Zero Knowledge Proof - A cryptographic protocol where a prover can demonstrate knowledge of a secret without revealing the secret itself, convincing the verifier of its validity. Zero Knowledge Property - The property of a Zero Knowledge Proof protocol that assures the verifier learns no additional information about the secret beyond its validity. Zk-rollups - zk-rollups, short for Zero-Knowledge Rollups, are Layer 2 scaling solutions for blockchain networks that utilize zero-knowledge proofs to aggregate and validate multiple transactions off-chain, improving scalability and reducing transaction fees while maintaining the security and trustlessness of the underlying blockchain. zk-STARKs - Zero-Knowledge Scalable Transparent Arguments of Knowledge (zk-STARKs) are Zero Knowledge Proofs that achieve transparency and scalability without a trusted setup. zk-SNARKs - Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (zk-SNARKs) are Zero Knowledge Proofs that provide succinctness and non-interactivity. ZPU - A Zero Knowledge Processing Unit (ZPU) is an application-specific integrated circuit (ASIC) designed to accelerate zero-knowledge proof computations and enhance the efficiency of cryptographic protocols.","breadcrumbs":"Glossary » Z","id":"27","title":"Z"},"28":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Zero Knowledge Proofs","id":"28","title":"Zero Knowledge Proofs"},"29":{"body":"Our curated resources consist of carefully selected, links, linktrees and other almanacs like \"Ingopedia\" . These resources are aimed at helping users access high-quality information in a quick and efficient manner.","breadcrumbs":"Zero Knowledge Proofs » Curated Resources","id":"29","title":"Curated Resources"},"3":{"body":"Bulletproofs - Bulletproofs are a non-interactive Zero Knowledge Proof construction that enables efficient verification of range proofs and arithmetic circuits.","breadcrumbs":"Glossary » B","id":"3","title":"B"},"30":{"body":"Our Video lecture series on ZK proofs offers in-depth and engaging presentations that cover the fundamentals and advanced topics of zero-knowledge proofs. These lectures are designed to educate and inform a wide range of audiences, and will contain series of videos on ZKP's various concepts.","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series","id":"30","title":"Video Lecture Series"},"31":{"body":"ZK Introductory ZKSNARKS STARKS Applications Our articles on ZK proofs are comprehensive and educational pieces that delve into the intricacies of zero-knowledge proofs. They consist of blogs, articles, PDFs, and notes. These articles aim to provide a clear understanding of this cutting-edge technology, its used-case applications, its vulnerabilities and its significance.","breadcrumbs":"Zero Knowledge Proofs » Articles","id":"31","title":"Articles"},"32":{"body":"Our hands-on approach to learning ZK proofs provides interactive and practical training experiences that allow participants to build their skills and knowledge in an engaging way. These hands-on workshops, tutorials, and projects are designed to help learners apply their understanding of ZK proofs in real-world situations, making them an invaluable resource for anyone looking to further their expertise in this field.","breadcrumbs":"Zero Knowledge Proofs » Hands on ZK","id":"32","title":"Hands on ZK"},"33":{"body":"Our collection of mathematical papers, protocols, and code on ZK proofs is a comprehensive resource for researchers, developers, and students in the field of cryptography. These materials provide a deep understanding of the theories, implementations, and practical applications of zero-knowledge proofs, serving as a valuable reference for anyone interested in this cutting-edge technology.","breadcrumbs":"Zero Knowledge Proofs » Protocols","id":"33","title":"Protocols"},"34":{"body":"The resources on the mathematics behind ZK proofs delve into the complex theories and mathematical concepts that underpin this intive technology. These resources are intended for those with a strong background in mathematics, or those looking to deepen their understanding of the mathematical foundations of zero-knowledge proofs and their applications.","breadcrumbs":"Zero Knowledge Proofs » Mathematics","id":"34","title":"Mathematics"},"35":{"body":"Our curated resources consist of carefully selected, links, linktrees and other almanacs like \"Ingopedia\". These resources are aimed at helping users access high-quality information in a quick and efficient manner. What you will find here: Links, Linktrees, Almanacs","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » Curated Resources","id":"35","title":"Curated Resources"},"36":{"body":"A collection of links and Almanacs breaking down ZKPs and related topics. zkProof Standards - Resource ZK Mesh - resource Zero Knowledge Fm Curated list of ZKP implementations Awesome - Matter labs - ZK proofs Awesome - Mikerah - Privacy on Blockchains Awesome - Worldcoin - ZK Machine Learning Resource: Awesome_Plonk Resource: Awesome Folding ZK research 0x ZK canon DAO canon NFT canon Crypto Canon Moonmath manual ZKP knowledge base: Delendum ZKP beginner resources Proofs Arguments and Zero Knowledge - Justin Thaler Discord group Awesome ZKEVM Awesome lattice FPGA's","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » References","id":"36","title":"References"},"37":{"body":"A collection of libraries where you can create a ZKP. Rust Cryptographic libraries Arkworks Lambdaworks by Lambdaclass Gnark: in Golang Circom: creating zk circuits Circom tutorials by 0xparc Halo 2 - library Awesome: Halo2 Halo2 club Latest development in Halo2 Guide to Halo2 source code ZK MOOC halo2 circuit building Building and testing with halo2 workshop slides Anatomy of proof generation by Scroll (KZG) version Halo2 workshop by 0xparc lookup args in Halo2 circuit development in halo2 Icemelon circuit development tutorial Halo2 tutorial: ZK natives Getting started with halo2 Axiom Halo2 app and wasm 1 Halo2 app and wasm 2 Halo2 review Automated analysis of halo2 circuits halo2 circuitry tutorial Zokrates Crrl: Cryptography research library - Thomas Pornin Bellman (not updated) libsnark in C++ Snarky frontend Cairo Cairo resource","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » Libraries","id":"37","title":"Libraries"},"38":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » HW libraries","id":"38","title":"HW libraries"},"39":{"body":"ICICLE Danksharding application SPPARK","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » GPU","id":"39","title":"GPU"},"4":{"body":"Cryptography - The practice and study of secure communication techniques, including encryption, decryption, and various cryptographic protocols. Completeness - The property of a Zero Knowledge Proof protocol that guarantees an honest prover can convince a verifier of a correct statement. Commitment Scheme - A cryptographic protocol that enables a party to commit to a value without revealing it and later prove the committed value's consistency. Computational Zero Knowledge - The lowest level of security among the three types of Zero Knowledge proofs, ensuring that an efficient computational algorithm cannot distinguish between valid and invalid proofs within a reasonable amount of time.","breadcrumbs":"Glossary » C","id":"4","title":"C"},"40":{"body":"BLAZE Blaze developer walkthrough","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » FPGA","id":"40","title":"FPGA"},"41":{"body":"Our Video lecture series on ZK proofs offers in-depth and engaging presentations that cover the fundamentals and advanced topics of zero-knowledge proofs. These lectures are designed to educate and inform a wide range of audiences, and will contain series of videos on ZKP's various concepts. What you will find here: Video playlists of Podcasts, Lectures, and University/Professional Classes","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Lecture Series","id":"41","title":"Lecture Series"},"42":{"body":"University and proffesional level courses on ZK. ZKMOOC - 2023 ZK BIU school - 2019 Cryptography 2018 MIT Modern ZK cryptography 0xparc","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » ZK courses","id":"42","title":"ZK courses"},"43":{"body":"Podcasts and lecture playlists on various ZKP related topics. ZK whiteboard Sessions ZK hack ZK summit Zk study club ZK privacy in cosmos ZK podcast ZK Sessions RISC0 architecture RISC0 Study club Modular arithmetic visually PLONK by David Wong Ingonyama: Moon math club a16z summer seminars ZK Hack: Thaler study group ZKP workshop 2022 ZK Shanghai 2023","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Discussions/Seminars","id":"43","title":"Discussions/Seminars"},"44":{"body":"Advanced University and proffesional level courses on ZK. Meta complexity bootcamp - Simons Institute Foundations of probabilistic proofs - Chiesa Probabilistically checkable and interactive proofs - Chisea Algebraic error correcting codes - Stanford ZKP composition and recursion - Wong Introduction to Elliptic curves BIU winter school Bilinear pairings in cryptography BIU winter school: Advances in MPC Foundations of Block chains - Tim Roughgarden BLockchain and money MIT 2018 DEFI MOOC Fuzzing workshop optimizations for fast algorithms bootcamp","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Advanced Courses/Topics","id":"44","title":"Advanced Courses/Topics"},"45":{"body":"Our articles on ZK proofs are comprehensive and educational pieces that delve into the intricacies of zero-knowledge proofs. They consist of blogs, articles, PDFs, and notes. These articles aim to provide a clear understanding of this cutting-edge technology, its used-case applications, its vulnerabilities and its significance. What you will find here: Blogs, Articles, PDFs, Notes","breadcrumbs":"Zero Knowledge Proofs » Articles » Articles","id":"45","title":"Articles"},"46":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory","id":"46","title":"ZK Introductory"},"47":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » ZKSNARKS","id":"47","title":"ZKSNARKS"},"48":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » STARKS","id":"48","title":"STARKS"},"49":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications","id":"49","title":"Applications"},"5":{"body":"","breadcrumbs":"Glossary » D","id":"5","title":"D"},"50":{"body":"Understanding ZK from beginner to advanced on a surface level.","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » ZK Introductory","id":"50","title":"ZK Introductory"},"51":{"body":"Amit Sahai explaining ZK to people of all ages - video Nico's ZK Jargon Decoder ) KU Lueven: Intro to ZK part 1 Interactive_proofs and Zk The incredible Machine - Aviv Zohar What is a ZKP system - Alin Tomescu A friendly intro to ZKP Life cycle of a ZKP","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Beginner","id":"51","title":"Beginner"},"52":{"body":"An introduction to how zk snarks are possible - Vitalik Zk blog Math survival kit for zk developers - lambdaclass Understanding polynomials Intro to ZK in block chain and economics A journey into ZKP - David Wong","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Intermediate","id":"52","title":"Intermediate"},"53":{"body":"An incomplete guide to zk: why zk matters Why and how Zero knowledge works zk Snarks a gentle introduction The math behind ZkSNARK - video De-mystifying Zk proofs -workshop An evolution of ZKP - Sarah Meiklejohn Zk_primer_1 M.Green Zk_primer_2 M.Green Zero Knowledge: A tutorial by Oded Goldreich Cryptographic Protocls: lectures Using zkSnarks for privacy: Vitalik STARK vs SNARK SNARK vs STARK vs Bulletproofs ZKp from Information theoretic Proof systems 1 - Yuval Ishai ZKP from Information theoretic Proof systems 2 - Yuval Ishai ZKP - Modular approach -Yuval Ishai Misconceptions in ZK-Snarks - Thaler Introduction to range proofs","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Advanced","id":"53","title":"Advanced"},"54":{"body":"Check out blogs, papers, pieces, and videos published by the Ingonyama Team","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Ingonyama Blogs","id":"54","title":"Ingonyama Blogs"},"55":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Fast Danksharding Video & Slides","id":"55","title":"Fast Danksharding Video & Slides"},"56":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Recap: ZK Capture the Flag","id":"56","title":"Recap: ZK Capture the Flag"},"57":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Introducing Blaze: ZK Acceleration for FPGA","id":"57","title":"Introducing Blaze: ZK Acceleration for FPGA"},"58":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Hardware Review: GPUs , FPGAs and Zero Knowledge Proofs","id":"58","title":"Hardware Review: GPUs , FPGAs and Zero Knowledge Proofs"},"59":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » RISC Zero Prover Protocol & Analysis","id":"59","title":"RISC Zero Prover Protocol & Analysis"},"6":{"body":"","breadcrumbs":"Glossary » E","id":"6","title":"E"},"60":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » ZK Hardware Table Stakes part 1 -MSM","id":"60","title":"ZK Hardware Table Stakes part 1 -MSM"},"61":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Unleashing Secure AI","id":"61","title":"Unleashing Secure AI"},"62":{"body":"Medium Link Fast-Danksharding Implementation","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Fast Danksharding using ICICLE","id":"62","title":"Fast Danksharding using ICICLE"},"63":{"body":"Medium Link ICICLE - GPU Library","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Introducing ICICLE: An Open-Source GPU Library for Zero Knowledge Acceleration","id":"63","title":"Introducing ICICLE: An Open-Source GPU Library for Zero Knowledge Acceleration"},"64":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » A Brief History of Lookup Arguments","id":"64","title":"A Brief History of Lookup Arguments"},"65":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » How Zero-Knowledge Proofs Will Change Gaming Forever","id":"65","title":"How Zero-Knowledge Proofs Will Change Gaming Forever"},"66":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Intro to ECNTT from Starkware Sessions 2023","id":"66","title":"Intro to ECNTT from Starkware Sessions 2023"},"67":{"body":"YouTube Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Deep Dive into the Sumcheck Protocol with Justin Thaler","id":"67","title":"Deep Dive into the Sumcheck Protocol with Justin Thaler"},"68":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Multi-Precision Fast Modular Multiplication","id":"68","title":"Multi-Precision Fast Modular Multiplication"},"69":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Hardware-friendliness of HyperPlonk","id":"69","title":"Hardware-friendliness of HyperPlonk"},"7":{"body":"Fiat-Shamir Heuristic - A technique used to transform an interactive Zero Knowledge Proof into a non-interactive form by simulating the verifier's challenges. FPGA (Field-Programmable Gate Array) - A reconfigurable integrated circuit that can be programmed and reprogrammed to perform a wide range of tasks, offering flexibility and customization for various applications without requiring a fixed design. Fractal - Fractal is a non-interactive Zero Knowledge Proof system that allows for scalable and efficient verification of statements in a distributed setting.","breadcrumbs":"Glossary » F","id":"7","title":"F"},"70":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Zero Knowledge Proofs and the Metaverse","id":"70","title":"Zero Knowledge Proofs and the Metaverse"},"71":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » The Z Games: Pushing ZK Provers to the Extreme","id":"71","title":"The Z Games: Pushing ZK Provers to the Extreme"},"72":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Goldilocks NTT Trick","id":"72","title":"Goldilocks NTT Trick"},"73":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Down the Rabbit Hole: Optimizing AWS F1 Direct Memory Access (DMA)","id":"73","title":"Down the Rabbit Hole: Optimizing AWS F1 Direct Memory Access (DMA)"},"74":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Sparkworks - Native Hardware Acceleration in Arkworks","id":"74","title":"Sparkworks - Native Hardware Acceleration in Arkworks"},"75":{"body":"Medium Link Paper: https://github.com/ingonyama-zk/papers/blob/main/Winograd_fft.pdf","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » NTT Mini: Exploring Winograd’s Heuristic for Faster NTT","id":"75","title":"NTT Mini: Exploring Winograd’s Heuristic for Faster NTT"},"76":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Marlin & Me: A Deep Dive into the Heart of the Marlin ZK Protocol","id":"76","title":"Marlin & Me: A Deep Dive into the Heart of the Marlin ZK Protocol"},"77":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Bridging the Multichain Universe with Zero Knowledge Proofs","id":"77","title":"Bridging the Multichain Universe with Zero Knowledge Proofs"},"78":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Systemization of Knowledge: ZK-Friendly Hash Functions","id":"78","title":"Systemization of Knowledge: ZK-Friendly Hash Functions"},"79":{"body":"HackerNoon Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » HackerNoon: Using Cloud-ZK for Developing ZKP Acceleration in the Cloud","id":"79","title":"HackerNoon: Using Cloud-ZK for Developing ZKP Acceleration in the Cloud"},"8":{"body":"Groth16 - Groth16 is a non-interactive Zero Knowledge Proof system that utilizes elliptic curve pairings to achieve succinctness and efficient verification.","breadcrumbs":"Glossary » G","id":"8","title":"G"},"80":{"body":"Medium Link Repository Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Cloud-ZK: A Toolkit for Developing ZKP Acceleration in the Cloud","id":"80","title":"Cloud-ZK: A Toolkit for Developing ZKP Acceleration in the Cloud"},"81":{"body":"HackerNoon Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » HackerNoon: Lowering the Barrier of Entry to Zero Knowledge Proofs","id":"81","title":"HackerNoon: Lowering the Barrier of Entry to Zero Knowledge Proofs"},"82":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » A Mathematical Theory of Danksharding","id":"82","title":"A Mathematical Theory of Danksharding"},"83":{"body":"Medium Link and Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » PipeMSM: Hardware Acceleration for Multi-Scalar Multiplication","id":"83","title":"PipeMSM: Hardware Acceleration for Multi-Scalar Multiplication"},"84":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Fast Modular Multiplication","id":"84","title":"Fast Modular Multiplication"},"85":{"body":"Medium Links","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Ingopedia: A Repo for all things ZK","id":"85","title":"Ingopedia: A Repo for all things ZK"},"86":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Poseidon-Hash Repository","id":"86","title":"Poseidon-Hash Repository"},"87":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Polygon’s zkEVM Fun Facts","id":"87","title":"Polygon’s zkEVM Fun Facts"},"88":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Introducing Ingonyama","id":"88","title":"Introducing Ingonyama"},"89":{"body":"A collection of resources explainig ZKSnarks.","breadcrumbs":"Zero Knowledge Proofs » Articles » ZKSNARKS » ZKSNARKS","id":"89","title":"ZKSNARKS"},"9":{"body":"Homomorphic Encryption - A form of encryption that allows mathematical operations to be performed on encrypted data without decrypting it. 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This is a community-driven effort to compile a comprehensive collection of resources and information related to Zero Knowledge Proofs. Our goal is to provide a one-stop-shop for anyone interested in learning about ZKPs, from beginners to experts. We invite the community to help us keep Ingopedia up-to-date and relevant. If you have any suggestions or contributions, please feel free to submit them through the appropriate channels. We believe that the power of the community lies in collaboration and sharing knowledge, so we encourage everyone to get involved. To keep this book organized, we ask that you use the designated sections for your contributions. If you have a new resource to share, please add it to the appropriate section. If you are unsure where to add your contribution, feel free to reach out to the moderators for guidance. Thank you for being a part of our ZKP community and helping us build a valuable resource for all. Note: The branch master contains the src files for the ingopedia mdbook. Each page from the deployment page has a editable button that allows one to edit the markdown file of the specific page. The old Ingopedia is still available in the branch main, we are planning to continue in the mdbook format. Suggestions are welcome. Nerdy Lion","breadcrumbs":"Community Guidelines » Community Guidelines","id":"0","title":"Community Guidelines"},"1":{"body":"A B C D E F G H I J K L M N O P Q R S T U V W X Y Z","breadcrumbs":"Glossary » Glossary","id":"1","title":"Glossary"},"10":{"body":"Interactive Proof - A Zero Knowledge Proof where the prover and verifier engage in multiple rounds of communication to establish the validity of the proof.","breadcrumbs":"Glossary » I","id":"10","title":"I"},"100":{"body":"Vulnerabilities in ZK bridges Primer on Cross chain bridges and how to break them: Niv Yehezkel Block chain bridges: Introduction Introduction to validating bridges and L2 protocols - Patrick McCory zkEVMOS - Bridges and Interoperability Bridging the blockchain multiverse with ZKP Navigating privacy on Blockchains - Wei Dai Having a safe CEX: proof of solvency and beyond","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » ZK bridges","id":"100","title":"ZK bridges"},"101":{"body":"Accelerating client side ZK with webGPU","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » Client side","id":"101","title":"Client side"},"102":{"body":"An Introduction to ZKML zkMNIST awesome-zkml Checks and balances ZK and ML - Elena Burger DO Language models possess Knowledge soundness - Tarun Chitra verifying twitter algorithmic integrity with zkml - Daniel Kang How ZK snarks bring transparency to private ML models with zkml - Daniel Kang Bridging AI/ML and web3 with ZKPs Exploring ZKML Verified execution of GPT,BERT,CLIP","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » ZKML","id":"102","title":"ZKML"},"103":{"body":"Dark Forest - the zk SNARK game Cairo Games Vol2: Solns Blockchain games and game mechanics Crypto gaming - A practical thesis The strongest Crypto gaming thesis ZKP for gaming: Mina","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » ZK Gaming","id":"103","title":"ZK Gaming"},"104":{"body":"Filecoin Filecoin primer Economics specs Proof system Filecoin snark audit Proof of space Proof of Replication: Depth Robust Graphs SDR blog mining task overview task definitions PoRep circuit blog Precommit 2","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » Ecosystem with ZK applications","id":"104","title":"Ecosystem with ZK applications"},"105":{"body":"Private search engine","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » other applications","id":"105","title":"other applications"},"106":{"body":"Potential vulnerabilities and security in ZK systems ZK bug tracker by0xparc bug tracker intro Vulnerabilities in zk systems Vulnerability in Fiat-Shamir Frozen heart vulnerability: Bulletproof Frozen heart vulnerability: Plonk Hertzbleed attack: sidechannel paper Stress testing Zk systems: Zk docs Specialized ZKP vulnerabilities security of zkp projects: same but different ZK programmability and security Vulnerabilities in private delegated computations Vulnerability in Nova - David Wong Algebraic attacks on ZK hash functions Feldman Secret sharing attacks Threshold signature pitfalls VSS forgery Boomerang values in ZK GPUz.zip Sidechannel attacks on GPUs","breadcrumbs":"Zero Knowledge Proofs » Articles » Vulnerabilities » Security and Vulnerabilities","id":"106","title":"Security and Vulnerabilities"},"107":{"body":"Our hands-on approach to learning ZK proofs provides interactive and practical training experiences that allow participants to build their skills and knowledge in an engaging way. These hands-on workshops, tutorials, and projects are designed to help learners apply their understanding of ZK proofs in real-world situations, making them an invaluable resource for anyone looking to further their expertise in this field. What you will find here: Code-to-Learn Applications","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Hands-On ZK/Cryptography","id":"107","title":"Hands-On ZK/Cryptography"},"108":{"body":"A beginners intro to coding Zero knowledge Proofs Babysnark do do dodo dodo typescript zk zero knowledge with Bellman Cryptohack - hands on cryptography Hands on ZK - ZK learning group Intro to zk: do it yourself circuits Zk Sudoku - Python Arnacube implementations DAPP fron scratch - Vivian Plasencia Zordle - Zk wordle Mental Poker: Part 1 Mental poker: Part 2 0xparc learning groups - covering cricom and halo2 Plonkathon 0xparc Constructing ZK SNARK circuits - DSL Zk calculator Social Applied ZK projects on Ethereum Uncloak courses Proofs args and zk study group implementations Cryptopals challenges Starkware101 Verifiable AES code: lambdaclass Merkle patricia tree: lambdaclass Haskell: Introduction Practical Cryptography for Devs: Nakov Transforming code into arithmetic circuits Differential fuzzing Zkvm step by step Zk smart contract tutorial optimizing pairing based cryptography, montgomery arithmetic in rust In assembly code Pairing over BLS12-381 Part 1 : Fields Part 2 : Curves Part 3 : Pairing An overview of ZKtooling and proof systems right now: Sep 2023","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » General","id":"108","title":"General"},"109":{"body":"Berkeley RDI ZKP-Web3 hackathon Zk hack puzzles Ingonyama ZK CTF-May 2023","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Challenges and hackathons","id":"109","title":"Challenges and hackathons"},"11":{"body":"","breadcrumbs":"Glossary » J","id":"11","title":"J"},"110":{"body":"The Rust book rust book with interactive quizzes The Rust book course Rust guide books Comprehensive rust by google Print and keep nearby - cheats.rs Tutorials Idiomatic Rust - For beauty over brawn Uncloak Study group Awesome rust cryptographic libraries Awesome rust -- general Rust Algorithms Rustlings Rust learning Rust crash course Data engg with rust Circomscribe - learn circom","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Rust learning resources for ZK/cryptography","id":"110","title":"Rust learning resources for ZK/cryptography"},"111":{"body":"code Benchmarking with Rust Flamegraphs code code:flamegraphs from hierarchical data Criterion Criterion introduction The benchmark game Zkalc zkBench Benchmarks","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Benchmarking tools","id":"111","title":"Benchmarking tools"},"112":{"body":"Our collection of mathematical papers, protocols, and code on ZK proofs is a comprehensive resource for researchers, developers, and students in the field of cryptography. These materials provide a deep understanding of the theories, implementations, and practical applications of zero-knowledge proofs, serving as a valuable reference for anyone interested in this cutting-edge technology. What you will find here: Protocols, Papers, Code Implementation, Resources","breadcrumbs":"Zero Knowledge Proofs » Protocols » Protocols --- UNDER CONSTRUCTION","id":"112","title":"Protocols --- UNDER CONSTRUCTION"},"113":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » SNARK Protocols","id":"113","title":"SNARK Protocols"},"114":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » STARK Protocols","id":"114","title":"STARK Protocols"},"115":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Lookup Protocols","id":"115","title":"Lookup Protocols"},"116":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Folding Scheme Protocols","id":"116","title":"Folding Scheme Protocols"},"117":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Other Protocols","id":"117","title":"Other Protocols"},"118":{"body":"Protocols Paper Implementation Resources Universal Transparent Pinocchio - 2013 →📝 ❌ ❌ TinyRAM - 2013 →📝 ❌ ❌ vnTinyRAM - 2014 →📝 Mike Hearn ✅ ❌ Geppetto - 2015 →📝 ❌ ❌ Buffet - 2015 →📝 ❌ ❌ Groth -2016 →📝 ConsenSys-gnark [1] arkworks-rs [2] Groth16 Malleability - Geometry [1] Proof of forgery [2] Groth16 aggregation proposal [3] Groth - Talk [4] Deep into bellman library - Star Li [5] Lookups for groth16? [6.1] ultragroth [6.2] ❌ ❌ Ligero - 2017 →📝 ✅ ✅ ZoKrates - 2018 →📝 ZoKrates Proving hash preimage with Zokrates - Decentriq [1] Efficient ECC in Zokrates- Decentriq [2] xjSNARK - 2018 →📝 ❌ ❌ Hyrax - 2018 →📝 Sonic - 2019 →📝 Benthams Gaze ✅ ❌ Plonk - 2019 →📝 heliaxdev [1] kobigurk [2] ZK-Garage [3] dusk-network [4] Jellyfish (Includes Plookup) [5] Plonk high level summary [1] Talk: Ariel Gabizon [2] Talk: Zac Williamson [3] Understanding Plonk - Vitalik [4] From AIRs to RAPs - how PLONK-style arithmetization works [5] Custom gates on plonk -Do whatever [7] Plonk Cafe [8] Plonk: Anatomy of a proof generation: Scroll [9] Resource: Plonk by hand -1 Metastate [10.1] Resource: Plonk by hand -2 Metastate [10.2] Resource: Plonk by hand -3 Metastate [10.3] Resource: Plonk and Plookup Metastate [10.4] Turboplonk [11] Custom gates in plonk [12] Plonk: Thomas Piellard [13] ZKP intro to Plonk - Star Li [14] Multi set checks in Plonk and Plookup: Gabizon [15] Plonk - Kimchi: Mina Protocol [16.1] Kimchi [16.2] Plonk not a monad tutorial [17] ✅ ❌ Redshift - 2019 →📝 Redhsift Summary Spartan - 2019 →📝 Microsoft Halo - 2019 →📝 ✅ ✅ MIRAGE - 2020 →📝 ✅ ❌ Marlin - 2020 →📝 arkworks-rs Doc: Pre lunar and not updated to Aleo/testnet3 [1] Thesis [2] Eurocrypt 2020: Talk video [3] ZK summit - Talk: Pratyush [4] Sin7y tech review: blog [5] Marlin and Me [6] Fractal -2020 →📝 scipr-lab/libiop Fractal - talk [1] Demystifying Fractal 1 -Metastate [2.1] Demystifying Fractal 2 - Metastate [2.2] Lunar - 2020 →📝 ZK study club video SuperSonic - 2020 →📝 Demystifying supersonic 1 -Metastate [1.1] Demystifying supersonic 2- Metastate [1.2] ✅ ✅ Darlin - 2021 →📝 Plonkup -2021 →📝 HorizenOfficial/ginger-lib SnarkPack -2021 →📝 Efficient Aggregation FFlonk -2021 →📝 Brakedown - 2021 →📝 Gemini - 2022 →📝 Elastic SNARKs for diverse environments Hyperplonk - 2022 →📝 EspressoSystems Hyperplonk - benedikt Bunz [1] Delendum [2] Hardware friendliness of MLE-Sumcheck [3] Hardware-optimizations for SumCheck-Binyi Chen [4] Testudo: Groth+Spartan - 2023 →📝 cryptonetlab Jolt - 2023 →📝 Introducing Lasso and Jolt","breadcrumbs":"Zero Knowledge Proofs » Protocols » SNARK Protocols » SNARK Protocols","id":"118","title":"SNARK Protocols"},"119":{"body":"Protocols Paper Implementation Resources Universal Transparent zkSTARK -2018 →📝 Winterfell [1] Ministark [2] Cairo [3] Guide for Ministark ✅ ✅ Aurora - 2019 →📝 Thesis Spooner ✅ ✅ Zilch - 2021 →📝 TrustworthyComputing ✅ ✅ Plonky - 2021 →📝 mir-protocol Plonky: Fast recursive arguments based on Plonk and Halo [1] Plonky: Adding zero Knowledge to Plonk and Halo [2] Plonky2 - 2021 →📝 mir-protocol Orion -2022 →📝 sunblaze-ucb IACR -talk","breadcrumbs":"Zero Knowledge Proofs » Protocols » STARK Protocols » STARK Protocols","id":"119","title":"STARK Protocols"},"12":{"body":"","breadcrumbs":"Glossary » K","id":"12","title":"K"},"120":{"body":"Protocols Paper Implementation Resources Universal Transparent Plookup -2020 →📝 Jellyfish Plookup in action -Talk [1] Plonk and Plookup - Metastate [2] Plonk and Plookup - Khovratovich [3] Mina Protocol[4]](https://o1-labs.github.io/proof-systems/introduction.html)AES with lookup : Daira Hopwood [5] Lookup tables - Ariel Gabizon [6] Caulk - 2022 →📝 caulk-crypto [1] Caulk+ [2] Flookup - 2022 →📝 Baloo - 2022 →📝 CQ - 2022 →📝 Geometry CqLin - 2023 →📝 Lasso - 2023 →📝 Introducing Lasso and Jolt","breadcrumbs":"Zero Knowledge Proofs » Protocols » Lookup Protocols » Lookup Protocols","id":"120","title":"Lookup Protocols"},"121":{"body":"Protocols Paper Implementation Resources Universal Transparent Nova - 2021 →📝 microsoft Srinath Setty - Talk [1] Srinath Setty - Video [2] IACR talk slides [3] IVC:Nova lambdaclass [4] Nova - zkstudy club talk [5] zkstudy club video [6] Supernova - 2022 →📝 jules Champagne supernova: lambdaclass Hypernova - 2023 →📝 CCS: Customizable constraint systems for succinct arguments Sangria - 2023 →📝 Blog Protostar - 2023 →📝 Deep dive into Protostar paper & protocol - Binyi Chen Protogalaxy - 2023 →📝 CycleFold - 2023 →📝","breadcrumbs":"Zero Knowledge Proofs » Protocols » Folding Scheme Protocols » Folding Scheme Protocols","id":"121","title":"Folding Scheme Protocols"},"122":{"body":"Protocols Paper Implementation Resources Universal Transparent vRAM - 2018 →📝 ✅ ❌ Bulletproof - 2018 →📝 Dalek [1] Lovesh [2] ZKP using Bullet proofs - Lovesh Harchandani [1] Notes [2] ✅ ✅ Virgo - 2020 →📝 sunblaze-ucb ✅ ✅ Sigma Protocols →📝 sigmastate Sigma Protocols for the Working Programmer","breadcrumbs":"Zero Knowledge Proofs » Protocols » Other Protocols » Other Protocols","id":"122","title":"Other Protocols"},"123":{"body":"The resources on the mathematics behind ZK proofs delve into the complex theories and mathematical concepts that underpin this innovative technology. These resources are intended for those with a strong background in mathematics, or those looking to deepen their understanding of the mathematical foundations of zero-knowledge proofs and their applications. What will you find here: Atoms and building blocks of a ZKP","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Mathematics","id":"123","title":"Mathematics"},"124":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite Fields","id":"124","title":"Finite Fields"},"125":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Elliptic curves","id":"125","title":"Elliptic curves"},"126":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » FFT","id":"126","title":"FFT"},"127":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » MSM","id":"127","title":"MSM"},"128":{"body":"Number theory explained from first principles An introduction to the theory of finite fields MIT lectures -FInite Field arithmetic Finite field arithmetic Doche Lange Aztec emulated field and group operations","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Finite fields","id":"128","title":"Finite fields"},"129":{"body":"A Fast Large-Integer Extended GCD Algorithm and Hardware Design for Verifiable Delay Functions and Modular Inversion Optimized Binary GCD for Modular Inversion Library of Algorithms Modular Multiplication and Hardware implementations - Review Evaluation of large integer multiplications in hardware - Review Hardware friendly modular mult Montgomery REDC using positive inverse mod r Low latency multipliers and cryptographic puzzles optimizing pairing based cryptography, montgomery arithmetic in rust","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Modular arithmetic","id":"129","title":"Modular arithmetic"},"13":{"body":"Ligero - Ligero is a Zero Knowledge Proof system designed specifically for blockchain applications, offering low computational and storage requirements for verification.","breadcrumbs":"Glossary » L","id":"13","title":"L"},"130":{"body":"The Matrix cookbook Ideal Class Groups","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Related Math","id":"130","title":"Related Math"},"131":{"body":"Finite fields and polynomials Schwarz - Zippel Lemma Curious History of Schwarz-Zippel lemma","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Polynomials","id":"131","title":"Polynomials"},"132":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Cryptographic primitives","id":"132","title":"Cryptographic primitives"},"133":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Elliptic curves","id":"133","title":"Elliptic curves"},"134":{"body":"ECC cryptobook Cures over finite fields - Lectures Elliptic curves Chapter 4 Washington Elliptic Curves: MIT lectures Corbellini - ECC ECC primer Silverman - ECC talk Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms Solinas - Efficient Arithmetic on Koblitz Curves Koblitz curve cryptosystems Elliptic Curve Cryptosystems (Koblitz Curves) Algorithm to Find Elliptic curves with a subgroup of a given size Elliptic curves number theory and cryptography Elliptic curve Arithmetic Curve addition - Doche-Lange Elliptic Curve Arithmetic Exponentiation -Doche Lange Elliptic curves of characteristic 2 or 3 - John Cook Addition/Doubling formulae Visualize Elliptic curves j invariant of a curve subgroup checks in BLS12 Complete addition formulae : Bernstein - Lange Complete addition formulae for prime order curves FPGA implementation of complete formulae with Montgomery multiplier Survey of Elliptic curves for Proof systems Edwards curves Twisted Edwards curves Subgroup checks for BLS12 Cofactor explained: Elliptic curves dirty little secret Applications of Riemann Roch theorem in cryptography - Borgeaud Quaternion algebras and Isogeny based cryptography","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » General","id":"134","title":"General"},"135":{"body":"Pairings for beginners - Craig Costello Pairings - Vitalik Buterin Pairing friendly curves Pairing implementation revisited Groth_Sahai proofs are not scary Bilinear pairings in cryptography - Dennis Meffert Pairings and poly commitments - David Wong Circom pairing Code Pairings or bilinear maps optimizing emulated pairings Estimating the bit security of pairing friendly curves optimizing pairing based cryptography, montgomery arithmetic in rust","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Pairings","id":"135","title":"Pairings"},"136":{"body":"BLS12-381 For The Rest Of Us BN254 for the rest of us Benchmarking pairing-friendly elliptic curves libraries ecgfp5 - Pornin: Goldilocks ed448 blog John Cook A deep dive into ed25519 Pasta curves -Electric coin Developers guide to constructing application specific curves","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Specific curves","id":"136","title":"Specific curves"},"137":{"body":"ZK hashes- General ZKP friendly hash functions: SOK Whats the deal with hashes: zk hack Sponge functions: paper S box properties Hash Functions Monolith for ZK Applicationss STARK friendly hash functions Merkling What is a merkle tree Merkle trees Sparse Merkle trees Merkle Commitment scheme Merkle trees and proof of inclusion why you should not sort your Merkle Leaves Fiat Shamir Merlin: Fiat-Shamir magic generator How to Fiat Shamir Serving up ZKP Frozen Heart vulnerability in Girault proof of knowledge in Bulletproofs in Plonk Hashes Keccak: Sponge and Duplex constructions SHA256 Halo2 16 bit lookup implementation Poseidon POSEIDON: A New Hash Function for Zero-Knowledge Proof Systems some documentation Encryption With Poseidon: Dima Khovratovich SAFE A tool box for Poseidon API SAFE: Faster and simple hashing with ZKP Encoding of long objects in Poseidon - Dmitry Khovratovich Talk Grassi Plonky2: Poseidon gate Penumbra: Poseidon Decaf377 Poseidon Implementations code: filecoin Poseidon in Filecoin - Dmitry Khovratovich code: Ingonyama (python) code: Dusk network code: Dust netowrk - Poseidon merkle code: Triplewz - GO Rescue Rescue-Prime: a Standard Specification (SoK) Observations on Rescue Poseidon vs Rescye MIMC MiMc Mimc7 in Plonk - Custom gates Mimc Roy slides Reinforced concrete Reinforced concrete implementation Plonkup reinforced concrete zkstudyclub Code: Luke Pearson Sinsemilla Sinsemilla: A circuit-efficient, lookup-based collision-resistant hash function ZCash protocol specification BLAKE Blake code Tip5 Tip5 code Hash to Curve Hash to Curve Hash to secp256k1 curve Optimized BLS signatures on EVM Hash Bounties Algebraic Hash bounties","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Hash functions » Hash functions","id":"137","title":"Hash functions"},"138":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Verifiable Delay functions » Verifiable Delay functions","id":"138","title":"Verifiable Delay functions"},"139":{"body":"All about Verifiable Delay Functions (VDF's) - VDFresearch","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Verifiable Delay functions » General","id":"139","title":"General"},"14":{"body":"Marlin - Marlin is a Zero Knowledge Proof system that leverages recursive composition to construct large-scale Zero Knowledge Proofs with low proof sizes and verification times. Merkle Tree - A tree data structure in cryptography that enables efficient verification of the integrity and membership of data elements. Multi-party Computation (MPC) - A cryptographic protocol that enables multiple parties to jointly compute a function over their private inputs while preserving the privacy of those inputs, allowing them to collectively obtain the desired result without revealing individual data to each other.","breadcrumbs":"Glossary » M","id":"14","title":"M"},"140":{"body":"General Arithmetic Circuits: A survey Complexity Zoo Arithmetization schemes for snarks Grobner basis used in circuits Circomscribe - learn circom R1CS constraint system Daira Hopwood - Efficient R1CS circuits: Video Quadratic Arithmetic programs R1CS 0 to H - Vitalik Buterin Aleo - Basics of R1CS Zero Knowledge Proofs: How Cryptographers can prove anything Alex Pinto - Constraint system for snarks Alex Pinto - How to build QAP Alex Pinto - Vanishing polynomial for QAP QAP from zero to hero: Vitalik R1CS workshop - Mir Plonkish arithmetization Refer to Plonk AIR Arithmetization AIR to RAPs - Gabizon AIR-Multivariate Sumcheck - W.Borgeaud AIR assembly Bobbin Threadbare Customizable Constraint system CCS CCS: Customizable constraint systems for succinct arguments A multivariate AIR using Superspartan- Borgeaud","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Arithmetization » Arithmetization","id":"140","title":"Arithmetization"},"141":{"body":"General Overview of commitment schemes: Justin Drakes Comparison of Commitment Schemes review of polynomial commmitments KZG KZG commitments KZG - Suyash Polynomial commitments - Dankrad Feist How to use KZG in proofs Fast KZG proofs Amortized KZG - Feist Khovratovich Multiplying a vector by a Toeplitz matrix PCS multiproofs - Feist New sharding design with tight beacon and shard block integration - Dankrad Feist Protodanksharding - FAQ Vitalik Universal verification equation for data availability sampling KZG friendly curves: El Housseini KZG in practice: Scroll Vector Commitments Verkle Trie - Dankrad Feist Aggregatable vector sub commitments Catalano-Fiore VC Inner product Arguments (IPA) Inner product arguments - Dankrad Feist IPA by hand - arnacube IPA commitment scheme Lambdaclass Lattice based commitment Schemes Vortex SLAP Blog","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Commitment Schemes » Commitment Schemes","id":"141","title":"Commitment Schemes"},"142":{"body":"( needs sorting )","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Secure Multi Party Computation » Secure Multi Party Computation","id":"142","title":"Secure Multi Party Computation"},"143":{"body":"An Introduction to Secret-Sharing-Based Secure Multiparty Computation - Daniel Escudero Yau;s garbled circuits: MPC A gentle introduction to YAU's Garbled circuits Setup ceremonies - Pruden & Matlala Collaborative zk-Snarks a Multi-Prover Zero-Knowledge Proof System Trinocchio: Privacy-Preserving Outsourcing by Distributed Verifiable Computation Zero-Knowledge Proofs on Secret-Shared Data via Fully Linear PCPs Prio: Private, Robust, and Scalable Computation of Aggregate Statistics ATLAS (Goyal, CMU) Efficient and Scalable MPC in the Honest Majority Setting","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Secure Multi Party Computation » General","id":"143","title":"General"},"144":{"body":"( To add papers: Work in progress )","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Proving Methods","id":"144","title":"Proving Methods"},"145":{"body":"Unreasonable power of sumcheck - Thaler Justin Thaler Lecture Intro to Sumcheck protocol -oxsage Inuition behind sumcheck - Wong Sumcheck argument and applications Proving AIR with MultiLinear Sumcheck - Borgeaud","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Sumcheck Protocol","id":"145","title":"Sumcheck Protocol"},"146":{"body":"STARK paper DEEP - FRI Proximity Gaps for Reed-Solomon Codes FRI hackernoon FRI properties FRI erasure code fraud proof Barycentric low deg check - Dankrad Feist Low Degree Testing","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Low degree Testing/FRI","id":"146","title":"Low degree Testing/FRI"},"147":{"body":"A brief history of lookup arguments","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Lookup arguments","id":"147","title":"Lookup arguments"},"148":{"body":"Snarkpack: practical snark aggregation blog talk talk","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Aggregations and recursions","id":"148","title":"Aggregations and recursions"},"149":{"body":"Resource: Awesome Folding How to build a snark that is out of this world - Nat Bunner An incomplete guide to FOlding schemes - Lisa","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Folding and accumulation schemes","id":"149","title":"Folding and accumulation schemes"},"15":{"body":"Non-interactive Proof - A Zero Knowledge Proof where the prover generates a single proof without any interaction with the verifier. NTT (Number Theoretic Transform) - A mathematical technique used for efficient polynomial multiplication and fast Fourier transforms in various applications such as signal processing, error correction codes, and cryptography.","breadcrumbs":"Glossary » N","id":"15","title":"N"},"150":{"body":"Succinct Proofs and Linear Algebra","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » General","id":"150","title":"General"},"151":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Computational Primitives","id":"151","title":"Computational Primitives"},"152":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Hardware acceleration","id":"152","title":"Hardware acceleration"},"153":{"body":"Measuring Snark performance frontends-backends and future - Thaler SNark security and peformance - Thaler Decentralized Speed: Advances in Zero Knowledge Proofs Hardware Acceleration for Zero Knowledge Proofs HW acc review - 0xmonia","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Need for hardware acceleration or not?","id":"153","title":"Need for hardware acceleration or not?"},"154":{"body":"Zprize","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Competitions","id":"154","title":"Competitions"},"155":{"body":"PipeZK Algorithms for modern Hardware","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » General HW resources and guides","id":"155","title":"General HW resources and guides"},"156":{"body":"Pantheon of ZKP frameworks - Celer Network ZK Harness ZK Benchmarking -Delendum ZKalc","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Benchmarks of ZKP primitives","id":"156","title":"Benchmarks of ZKP primitives"},"157":{"body":"TEE for CPU and GPU Nvidia TEE for blockchain applications","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » TEE and confidential computing","id":"157","title":"TEE and confidential computing"},"158":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Discrete Fourier Transforms","id":"158","title":"Discrete Fourier Transforms"},"159":{"body":"FFT - Vitalik Reed-Solomon code: Vitalik FFT Notes The Fast Fourier Transform in a Finite Field - Pollard Number Theoretic Transform (NTT): Introduction Gentle intro to NTT 1 (includes rings) Gentle intro to NTT2 (includes rings) Efficient primes for NTT - Goldilocks Goldilocks in nuFHE Goldilocks NTT trick - Solberg Elliptic Curve Fast Fourier Transform (ECFFT) Part I: Fast Polynomial Algorithms over all Finite Fields: Eli Ben-Sasson et.al Talk -zk study club ECFFT algorithm Rust Implementation -Wboregaud Rust ECFFT BN254- Wboregeaud ECFFT-2 Ben-Sasson et.al FFT - Ferror Moreno thesis Zcash FFT FFT for polynomial multiplication A quick barycentric evaluation tutorial - Vitalik Barycentric interpolation - Math Oxford Walsh Hadamard Transform - Borgeaud FFT on finite fields intro","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Algorithms and methods","id":"159","title":"Algorithms and methods"},"16":{"body":"","breadcrumbs":"Glossary » O","id":"16","title":"O"},"160":{"body":"Thesis: BUNTTERFLY: A Flexible Hardware Generator for the Number Theoretic Transform - Jason Vranek CycloneNTT NTL: a library for NTT Zprize 2022","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Implementations","id":"160","title":"Implementations"},"161":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Multi scalar multiplications","id":"161","title":"Multi scalar multiplications"},"162":{"body":"Fast Multi-scalar Multiplication Methods on Elliptic Curves with Precomputation Strategy Using Montgomery Trick Faster batch forgery identification See section 4 for MSM, bucket method Pippenger's exponentiation algorithm - Bernstein Efficient multi-exponentiation implementation in Python Multi-scalar multiplication: state of the art & new ideas with Gus Gutoski Improved Fast exponentiations - Bodo Moller Fast exponentiation with precomputation - Brickell Gordon et al Matter labs -ALgorithms Ryah Henry - Thesis Efficient Multi exponentiation: Bucket method - Bootle","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Algorithms and methods","id":"162","title":"Algorithms and methods"},"163":{"body":"pipezk MSM with FPGA -Connor Masterson thesis PipeMSM EdMSM CycloneMSM Cuzk Zprize MSM implementations","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Implementations","id":"163","title":"Implementations"},"164":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Fully Homomorphic Encryption","id":"164","title":"Fully Homomorphic Encryption"},"165":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Articles","id":"165","title":"Articles"},"166":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes","id":"166","title":"Schemes"},"167":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Libraries","id":"167","title":"Libraries"},"168":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics","id":"168","title":"Mathematics"},"169":{"body":"What you will find here: Blogs, Articles, PDFs, Videos, Notes","breadcrumbs":"Fully Homomorphic Encryption » Articles » Articles","id":"169","title":"Articles"},"17":{"body":"Pairing-Based Cryptography - A cryptographic approach that leverages mathematical pairings to perform various operations and enable advanced cryptographic protocols. Perfect Zero Knowledge - A level of security provided by a Zero Knowledge proof where the verifier gains no additional knowledge about the secret information being proved, except for the validity of the statement. Plonk - Plonk (Permutation-based SNARK) is a Zero Knowledge Proof system that utilizes permutation arguments to achieve succinctness and efficiency. Privacy - The state of being free from unauthorized intrusion, surveillance, or disclosure of personal or sensitive information. Proof Of Knowledge - A cryptographic concept where a prover demonstrates possession of certain information or knowledge to a verifier without revealing the actual information. Prover - The entity in a Zero Knowledge Proof protocol that possesses knowledge of a secret and aims to prove its knowledge to the verifier. Pseudorandom Function - A pseudorandom function (PRF) is a deterministic function that takes an input and produces an output that appears random, even though it is generated by a deterministic algorithm, making it indistinguishable from a truly random function for practical purposes.","breadcrumbs":"Glossary » P","id":"17","title":"P"},"170":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Articles » UNDER CONSTRUCTION 👷","id":"170","title":"UNDER CONSTRUCTION 👷"},"171":{"body":"Encrypted search using FHE Exploring FHE: Vitalik Sunscreen - intro to fhe for engineers Survey on FHE and applications Computing on encrypted data: Nigel Smart Hands on FHE","breadcrumbs":"Fully Homomorphic Encryption » Articles » Inroductory","id":"171","title":"Inroductory"},"172":{"body":"ML and FHE Solving LLM Privacy with FHE How Snarks fall short for FHE fhevm fhEVM - Morten Dahl","breadcrumbs":"Fully Homomorphic Encryption » Articles » Applications","id":"172","title":"Applications"},"173":{"body":"FPT: a Fixed-Point Accelerator for Torus Fully Homomorphic Encryption cuHE for GPU FHE","breadcrumbs":"Fully Homomorphic Encryption » Articles » Implementations","id":"173","title":"Implementations"},"174":{"body":"Security of FHE Schemes Lattice based attacks On concrete hardness of LWE Security of HE on AN On security of multivariate RLWE","breadcrumbs":"Fully Homomorphic Encryption » Articles » Security","id":"174","title":"Security"},"175":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » Schemes","id":"175","title":"Schemes"},"176":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » UNDER CONSTRUCTION 👷","id":"176","title":"UNDER CONSTRUCTION 👷"},"177":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » BGV","id":"177","title":"BGV"},"178":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » BFV","id":"178","title":"BFV"},"179":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » CKKS","id":"179","title":"CKKS"},"18":{"body":"QAP (Quadratic Arithmetic Programs) - QAP is a method to represent arithmetic circuits as quadratic polynomials, commonly used in Zero Knowledge Proof systems for efficient proof generation and verification.","breadcrumbs":"Glossary » Q","id":"18","title":"Q"},"180":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » FHEW","id":"180","title":"FHEW"},"181":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » TFHE","id":"181","title":"TFHE"},"182":{"body":"Part 1: Ciphertext types Part 2: Encoding and linear ops part 3: key switching and levelled multiplications Part 4: programmable bootstrapping","breadcrumbs":"Fully Homomorphic Encryption » Schemes » Deep dive: ZAMA AI - Ilaria Chilloti","id":"182","title":"Deep dive: ZAMA AI - Ilaria Chilloti"},"183":{"body":"A curated list of Homomorphic Encryption libraries, and what schemes they use.","breadcrumbs":"Fully Homomorphic Encryption » Libraries » Libraries","id":"183","title":"Libraries"},"184":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Libraries » UNDER CONSTRUCTION 👷","id":"184","title":"UNDER CONSTRUCTION 👷"},"185":{"body":"Libraries Scheme Resources Microsoft SEAL BFV BGV PALISADE BFV FHEW TFHE IBM FHE BGV IBM HElib BGV CKKS Sunscreen - levelled bootstrap BFV Introduction OpenFHE BFV BGV CKKS FHEW TFHE OpenFHE.com TenSEAL - Openmined BFV CKKS Zama AI - Concrete - Python compiler TFHE Zama AI - TFHE-rs - Rust library TFHE Google - FHE TFHE","breadcrumbs":"Fully Homomorphic Encryption » Libraries » Libraries","id":"185","title":"Libraries"},"186":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » Mathematics","id":"186","title":"Mathematics"},"187":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » UNDER CONSTRUCTION 👷","id":"187","title":"UNDER CONSTRUCTION 👷"},"188":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » LWE","id":"188","title":"LWE"},"189":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » FFT","id":"189","title":"FFT"},"19":{"body":"R1CS (Rank-1 Constraint Systems) - R1CS is a mathematical framework used in Zero Knowledge Proof systems to represent computational problems as sets of constraints. Redshift - Redshift is a Zero Knowledge Proof system designed for blockchain applications, offering scalability, efficiency, and post-quantum security. Ring Signature - A cryptographic digital signature scheme that allows a user to sign a message on behalf of a group (or ring) of potential signers, while maintaining the privacy of the actual signer's identity within the group.","breadcrumbs":"Glossary » R","id":"19","title":"R"},"190":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » NTT","id":"190","title":"NTT"},"2":{"body":"ASIC (Application-Specific Integrated Circuit) - A specialized integrated circuit designed for a specific application or function, offering optimized performance and efficiency by implementing dedicated hardware tailored to that specific task. Authentication - The process of verifying the identity of a user, device, or system to ensure that it is genuine and authorized to access certain resources or information. Aurora - Aurora is a Zero Knowledge Proof system that combines zk-SNARKs and Bulletproofs to achieve compact proofs for general-purpose computations. AuroraLight - AuroraLight is an improvement over Aurora that achieves faster prover times and smaller proof sizes while maintaining its generality and security properties.","breadcrumbs":"Glossary » A","id":"2","title":"A"},"20":{"body":"Security - The protection of hardware, software, and data from unauthorized access, theft, damage, or disruption, aiming to maintain confidentiality and integrity. Side-channel Attacks - Attacks that exploit unintended information leakage, such as timing, power consumption, or electromagnetic radiation, to infer secret information. Statistical Zero Knowledge - A level of security offered by a Zero Knowledge proof where the verifier cannot distinguish between a valid proof and a false proof, except with an extremely low probability. Sonic - Sonic (Scalable, Non-Interactive, and Compact) is a Zero Knowledge Proof system that offers scalability and efficiency for verifying large computations. Soundness - The property of a Zero Knowledge Proof protocol that ensures an honest prover cannot convince a verifier of an incorrect statement. Spartan - Spartan is a Zero Knowledge Proof system that achieves transparency, scalability, and post-quantum security without requiring a trusted setup. Supersonic - Supersonic is a Zero Knowledge Proof system that provides high-performance and efficient verification of arithmetic circuits and boolean satisfiability.","breadcrumbs":"Glossary » S","id":"20","title":"S"},"21":{"body":"Trusted Execution - The execution of a program or process in a secure and isolated environment, protecting it from tampering and unauthorized access. Trusted Setup - The process of generating initial parameters for a Zero Knowledge Proof protocol, ensuring that they do not reveal any secret information.","breadcrumbs":"Glossary » T","id":"21","title":"T"},"22":{"body":"","breadcrumbs":"Glossary » U","id":"22","title":"U"},"23":{"body":"Verifier - The entity in a Zero Knowledge Proof protocol that challenges the prover's claim and verifies the validity of the proof without gaining knowledge of the secret.","breadcrumbs":"Glossary » V","id":"23","title":"V"},"24":{"body":"Witness Indistinguishable Proof - A cryptographic proof that guarantees that given two valid proofs for the same statement, it is computationally infeasible for an adversary to distinguish which proof corresponds to the true witness.","breadcrumbs":"Glossary » W","id":"24","title":"W"},"25":{"body":"","breadcrumbs":"Glossary » X","id":"25","title":"X"},"26":{"body":"","breadcrumbs":"Glossary » Y","id":"26","title":"Y"},"27":{"body":"Zero Knowledge Proof - A cryptographic protocol where a prover can demonstrate knowledge of a secret without revealing the secret itself, convincing the verifier of its validity. Zero Knowledge Property - The property of a Zero Knowledge Proof protocol that assures the verifier learns no additional information about the secret beyond its validity. Zk-rollups - zk-rollups, short for Zero-Knowledge Rollups, are Layer 2 scaling solutions for blockchain networks that utilize zero-knowledge proofs to aggregate and validate multiple transactions off-chain, improving scalability and reducing transaction fees while maintaining the security and trustlessness of the underlying blockchain. zk-STARKs - Zero-Knowledge Scalable Transparent Arguments of Knowledge (zk-STARKs) are Zero Knowledge Proofs that achieve transparency and scalability without a trusted setup. zk-SNARKs - Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (zk-SNARKs) are Zero Knowledge Proofs that provide succinctness and non-interactivity. ZPU - A Zero Knowledge Processing Unit (ZPU) is an application-specific integrated circuit (ASIC) designed to accelerate zero-knowledge proof computations and enhance the efficiency of cryptographic protocols.","breadcrumbs":"Glossary » Z","id":"27","title":"Z"},"28":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Zero Knowledge Proofs","id":"28","title":"Zero Knowledge Proofs"},"29":{"body":"Our curated resources consist of carefully selected, links, linktrees and other almanacs like \"Ingopedia\" . These resources are aimed at helping users access high-quality information in a quick and efficient manner.","breadcrumbs":"Zero Knowledge Proofs » Curated Resources","id":"29","title":"Curated Resources"},"3":{"body":"Bulletproofs - Bulletproofs are a non-interactive Zero Knowledge Proof construction that enables efficient verification of range proofs and arithmetic circuits.","breadcrumbs":"Glossary » B","id":"3","title":"B"},"30":{"body":"Our Video lecture series on ZK proofs offers in-depth and engaging presentations that cover the fundamentals and advanced topics of zero-knowledge proofs. These lectures are designed to educate and inform a wide range of audiences, and will contain series of videos on ZKP's various concepts.","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series","id":"30","title":"Video Lecture Series"},"31":{"body":"ZK Introductory ZKSNARKS STARKS Applications Our articles on ZK proofs are comprehensive and educational pieces that delve into the intricacies of zero-knowledge proofs. They consist of blogs, articles, PDFs, and notes. These articles aim to provide a clear understanding of this cutting-edge technology, its used-case applications, its vulnerabilities and its significance.","breadcrumbs":"Zero Knowledge Proofs » Articles","id":"31","title":"Articles"},"32":{"body":"Our hands-on approach to learning ZK proofs provides interactive and practical training experiences that allow participants to build their skills and knowledge in an engaging way. These hands-on workshops, tutorials, and projects are designed to help learners apply their understanding of ZK proofs in real-world situations, making them an invaluable resource for anyone looking to further their expertise in this field.","breadcrumbs":"Zero Knowledge Proofs » Hands on ZK","id":"32","title":"Hands on ZK"},"33":{"body":"Our collection of mathematical papers, protocols, and code on ZK proofs is a comprehensive resource for researchers, developers, and students in the field of cryptography. These materials provide a deep understanding of the theories, implementations, and practical applications of zero-knowledge proofs, serving as a valuable reference for anyone interested in this cutting-edge technology.","breadcrumbs":"Zero Knowledge Proofs » Protocols","id":"33","title":"Protocols"},"34":{"body":"The resources on the mathematics behind ZK proofs delve into the complex theories and mathematical concepts that underpin this intive technology. These resources are intended for those with a strong background in mathematics, or those looking to deepen their understanding of the mathematical foundations of zero-knowledge proofs and their applications.","breadcrumbs":"Zero Knowledge Proofs » Mathematics","id":"34","title":"Mathematics"},"35":{"body":"Our curated resources consist of carefully selected, links, linktrees and other almanacs like \"Ingopedia\". These resources are aimed at helping users access high-quality information in a quick and efficient manner. What you will find here: Links, Linktrees, Almanacs","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » Curated Resources","id":"35","title":"Curated Resources"},"36":{"body":"A collection of links and Almanacs breaking down ZKPs and related topics. zkProof Standards - Resource ZK Mesh - resource Zero Knowledge Fm Curated list of ZKP implementations Awesome - Matter labs - ZK proofs Awesome - Mikerah - Privacy on Blockchains Awesome - Worldcoin - ZK Machine Learning Resource: Awesome_Plonk Resource: Awesome Folding ZK research 0x ZK canon DAO canon NFT canon Crypto Canon Moonmath manual ZKP knowledge base: Delendum ZKP beginner resources Proofs Arguments and Zero Knowledge - Justin Thaler Discord group Awesome ZKEVM Awesome lattice FPGA's","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » References","id":"36","title":"References"},"37":{"body":"A collection of libraries where you can create a ZKP. Rust Cryptographic libraries Arkworks Lambdaworks by Lambdaclass Gnark: in Golang Circom: creating zk circuits Circom tutorials by 0xparc Halo 2 - library Awesome: Halo2 Halo2 club Latest development in Halo2 Guide to Halo2 source code ZK MOOC halo2 circuit building Building and testing with halo2 workshop slides Anatomy of proof generation by Scroll (KZG) version Halo2 workshop by 0xparc lookup args in Halo2 circuit development in halo2 Icemelon circuit development tutorial Halo2 tutorial: ZK natives Getting started with halo2 Axiom Halo2 app and wasm 1 Halo2 app and wasm 2 Halo2 review Automated analysis of halo2 circuits halo2 circuitry tutorial Zokrates Crrl: Cryptography research library - Thomas Pornin Bellman (not updated) libsnark in C++ Snarky frontend Cairo Cairo resource","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » Libraries","id":"37","title":"Libraries"},"38":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » HW libraries","id":"38","title":"HW libraries"},"39":{"body":"ICICLE Danksharding application SPPARK","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » GPU","id":"39","title":"GPU"},"4":{"body":"Cryptography - The practice and study of secure communication techniques, including encryption, decryption, and various cryptographic protocols. Completeness - The property of a Zero Knowledge Proof protocol that guarantees an honest prover can convince a verifier of a correct statement. Commitment Scheme - A cryptographic protocol that enables a party to commit to a value without revealing it and later prove the committed value's consistency. Computational Zero Knowledge - The lowest level of security among the three types of Zero Knowledge proofs, ensuring that an efficient computational algorithm cannot distinguish between valid and invalid proofs within a reasonable amount of time.","breadcrumbs":"Glossary » C","id":"4","title":"C"},"40":{"body":"BLAZE Blaze developer walkthrough","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » FPGA","id":"40","title":"FPGA"},"41":{"body":"Our Video lecture series on ZK proofs offers in-depth and engaging presentations that cover the fundamentals and advanced topics of zero-knowledge proofs. These lectures are designed to educate and inform a wide range of audiences, and will contain series of videos on ZKP's various concepts. What you will find here: Video playlists of Podcasts, Lectures, and University/Professional Classes","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Lecture Series","id":"41","title":"Lecture Series"},"42":{"body":"University and proffesional level courses on ZK. ZKMOOC - 2023 ZK BIU school - 2019 Cryptography 2018 MIT Modern ZK cryptography 0xparc","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » ZK courses","id":"42","title":"ZK courses"},"43":{"body":"Podcasts and lecture playlists on various ZKP related topics. ZK whiteboard Sessions ZK hack ZK summit Zk study club ZK privacy in cosmos ZK podcast ZK Sessions RISC0 architecture RISC0 Study club Modular arithmetic visually PLONK by David Wong Ingonyama: Moon math club a16z summer seminars ZK Hack: Thaler study group ZKP workshop 2022 ZK Shanghai 2023","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Discussions/Seminars","id":"43","title":"Discussions/Seminars"},"44":{"body":"Advanced University and proffesional level courses on ZK. Meta complexity bootcamp - Simons Institute Foundations of probabilistic proofs - Chiesa Probabilistically checkable and interactive proofs - Chisea Algebraic error correcting codes - Stanford ZKP composition and recursion - Wong Introduction to Elliptic curves BIU winter school Bilinear pairings in cryptography BIU winter school: Advances in MPC Foundations of Block chains - Tim Roughgarden BLockchain and money MIT 2018 DEFI MOOC Fuzzing workshop optimizations for fast algorithms bootcamp","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Advanced Courses/Topics","id":"44","title":"Advanced Courses/Topics"},"45":{"body":"Our articles on ZK proofs are comprehensive and educational pieces that delve into the intricacies of zero-knowledge proofs. They consist of blogs, articles, PDFs, and notes. These articles aim to provide a clear understanding of this cutting-edge technology, its used-case applications, its vulnerabilities and its significance. What you will find here: Blogs, Articles, PDFs, Notes","breadcrumbs":"Zero Knowledge Proofs » Articles » Articles","id":"45","title":"Articles"},"46":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory","id":"46","title":"ZK Introductory"},"47":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » ZKSNARKS","id":"47","title":"ZKSNARKS"},"48":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » STARKS","id":"48","title":"STARKS"},"49":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications","id":"49","title":"Applications"},"5":{"body":"","breadcrumbs":"Glossary » D","id":"5","title":"D"},"50":{"body":"Understanding ZK from beginner to advanced on a surface level.","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » ZK Introductory","id":"50","title":"ZK Introductory"},"51":{"body":"Amit Sahai explaining ZK to people of all ages - video Nico's ZK Jargon Decoder ) KU Lueven: Intro to ZK part 1 Interactive_proofs and Zk The incredible Machine - Aviv Zohar What is a ZKP system - Alin Tomescu A friendly intro to ZKP Life cycle of a ZKP","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Beginner","id":"51","title":"Beginner"},"52":{"body":"An introduction to how zk snarks are possible - Vitalik Zk blog Math survival kit for zk developers - lambdaclass Understanding polynomials Intro to ZK in block chain and economics A journey into ZKP - David Wong","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Intermediate","id":"52","title":"Intermediate"},"53":{"body":"An incomplete guide to zk: why zk matters Why and how Zero knowledge works zk Snarks a gentle introduction The math behind ZkSNARK - video De-mystifying Zk proofs -workshop An evolution of ZKP - Sarah Meiklejohn Zk_primer_1 M.Green Zk_primer_2 M.Green Zero Knowledge: A tutorial by Oded Goldreich Cryptographic Protocls: lectures Using zkSnarks for privacy: Vitalik STARK vs SNARK SNARK vs STARK vs Bulletproofs ZKp from Information theoretic Proof systems 1 - Yuval Ishai ZKP from Information theoretic Proof systems 2 - Yuval Ishai ZKP - Modular approach -Yuval Ishai Misconceptions in ZK-Snarks - Thaler Introduction to range proofs","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Advanced","id":"53","title":"Advanced"},"54":{"body":"Check out blogs, papers, pieces, and videos published by the Ingonyama Team","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Ingonyama Blogs","id":"54","title":"Ingonyama Blogs"},"55":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Fast Danksharding Video & Slides","id":"55","title":"Fast Danksharding Video & Slides"},"56":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Recap: ZK Capture the Flag","id":"56","title":"Recap: ZK Capture the Flag"},"57":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Introducing Blaze: ZK Acceleration for FPGA","id":"57","title":"Introducing Blaze: ZK Acceleration for FPGA"},"58":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Hardware Review: GPUs , FPGAs and Zero Knowledge Proofs","id":"58","title":"Hardware Review: GPUs , FPGAs and Zero Knowledge Proofs"},"59":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » RISC Zero Prover Protocol & Analysis","id":"59","title":"RISC Zero Prover Protocol & Analysis"},"6":{"body":"","breadcrumbs":"Glossary » E","id":"6","title":"E"},"60":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » ZK Hardware Table Stakes part 1 -MSM","id":"60","title":"ZK Hardware Table Stakes part 1 -MSM"},"61":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Unleashing Secure AI","id":"61","title":"Unleashing Secure AI"},"62":{"body":"Medium Link Fast-Danksharding Implementation","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Fast Danksharding using ICICLE","id":"62","title":"Fast Danksharding using ICICLE"},"63":{"body":"Medium Link ICICLE - GPU Library","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Introducing ICICLE: An Open-Source GPU Library for Zero Knowledge Acceleration","id":"63","title":"Introducing ICICLE: An Open-Source GPU Library for Zero Knowledge Acceleration"},"64":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » A Brief History of Lookup Arguments","id":"64","title":"A Brief History of Lookup Arguments"},"65":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » How Zero-Knowledge Proofs Will Change Gaming Forever","id":"65","title":"How Zero-Knowledge Proofs Will Change Gaming Forever"},"66":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Intro to ECNTT from Starkware Sessions 2023","id":"66","title":"Intro to ECNTT from Starkware Sessions 2023"},"67":{"body":"YouTube Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Deep Dive into the Sumcheck Protocol with Justin Thaler","id":"67","title":"Deep Dive into the Sumcheck Protocol with Justin Thaler"},"68":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Multi-Precision Fast Modular Multiplication","id":"68","title":"Multi-Precision Fast Modular Multiplication"},"69":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Hardware-friendliness of HyperPlonk","id":"69","title":"Hardware-friendliness of HyperPlonk"},"7":{"body":"Fiat-Shamir Heuristic - 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FPGA (Field-Programmable Gate Array) - A reconfigurable integrated circuit that can be programmed and reprogrammed to perform a wide range of tasks, offering flexibility and customization for various applications without requiring a fixed design. 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What you will find here: Code-to-Learn Applications","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Hands-On ZK/Cryptography","id":"107","title":"Hands-On ZK/Cryptography"},"108":{"body":"A beginners intro to coding Zero knowledge Proofs Babysnark do do dodo dodo typescript zk zero knowledge with Bellman Cryptohack - hands on cryptography Hands on ZK - ZK learning group Intro to zk: do it yourself circuits Zk Sudoku - Python Arnacube implementations DAPP fron scratch - Vivian Plasencia Zordle - Zk wordle Mental Poker: Part 1 Mental poker: Part 2 0xparc learning groups - covering cricom and halo2 Plonkathon 0xparc Constructing ZK SNARK circuits - DSL Zk calculator Social Applied ZK projects on Ethereum Uncloak courses Proofs args and zk study group implementations Cryptopals challenges Starkware101 Verifiable AES code: lambdaclass Merkle patricia tree: lambdaclass Haskell: Introduction Practical Cryptography for Devs: Nakov Transforming code into arithmetic circuits Differential fuzzing Zkvm step by step Zk smart contract tutorial optimizing pairing based cryptography, montgomery arithmetic in rust In assembly code Pairing over BLS12-381 Part 1 : Fields Part 2 : Curves Part 3 : Pairing An overview of ZKtooling and proof systems right now: Sep 2023","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » General","id":"108","title":"General"},"109":{"body":"Berkeley RDI ZKP-Web3 hackathon Zk hack puzzles Ingonyama ZK CTF-May 2023","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Challenges and hackathons","id":"109","title":"Challenges and hackathons"},"11":{"body":"","breadcrumbs":"Glossary » J","id":"11","title":"J"},"110":{"body":"The Rust book rust book with interactive quizzes The Rust book course Rust guide books Comprehensive rust by google Print and keep nearby - cheats.rs Tutorials Idiomatic Rust - For beauty over brawn Uncloak Study group Awesome rust cryptographic libraries Awesome rust -- general Rust Algorithms Rustlings Rust learning Rust crash course Data engg with rust Circomscribe - learn circom","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Rust learning resources for ZK/cryptography","id":"110","title":"Rust learning resources for ZK/cryptography"},"111":{"body":"code Benchmarking with Rust Flamegraphs code code:flamegraphs from hierarchical data Criterion Criterion introduction The benchmark game Zkalc zkBench Benchmarks","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Benchmarking tools","id":"111","title":"Benchmarking tools"},"112":{"body":"Our collection of mathematical papers, protocols, and code on ZK proofs is a comprehensive resource for researchers, developers, and students in the field of cryptography. These materials provide a deep understanding of the theories, implementations, and practical applications of zero-knowledge proofs, serving as a valuable reference for anyone interested in this cutting-edge technology. What you will find here: Protocols, Papers, Code Implementation, Resources","breadcrumbs":"Zero Knowledge Proofs » Protocols » Protocols --- UNDER CONSTRUCTION","id":"112","title":"Protocols --- UNDER CONSTRUCTION"},"113":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » SNARK Protocols","id":"113","title":"SNARK Protocols"},"114":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » STARK Protocols","id":"114","title":"STARK Protocols"},"115":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Lookup Protocols","id":"115","title":"Lookup Protocols"},"116":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Folding Scheme Protocols","id":"116","title":"Folding Scheme Protocols"},"117":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Other Protocols","id":"117","title":"Other Protocols"},"118":{"body":"Protocols Paper Implementation Resources Universal Transparent Pinocchio - 2013 →📝 ❌ ❌ TinyRAM - 2013 →📝 ❌ ❌ vnTinyRAM - 2014 →📝 Mike Hearn ✅ ❌ Geppetto - 2015 →📝 ❌ ❌ Buffet - 2015 →📝 ❌ ❌ Groth -2016 →📝 ConsenSys-gnark [1] arkworks-rs [2] Groth16 Malleability - Geometry [1] Proof of forgery [2] Groth16 aggregation proposal [3] Groth - Talk [4] Deep into bellman library - Star Li [5] Lookups for groth16? [6.1] ultragroth [6.2] ❌ ❌ Ligero - 2017 →📝 ✅ ✅ ZoKrates - 2018 →📝 ZoKrates Proving hash preimage with Zokrates - Decentriq [1] Efficient ECC in Zokrates- Decentriq [2] xjSNARK - 2018 →📝 ❌ ❌ Hyrax - 2018 →📝 Sonic - 2019 →📝 Benthams Gaze ✅ ❌ Plonk - 2019 →📝 heliaxdev [1] kobigurk [2] ZK-Garage [3] dusk-network [4] Jellyfish (Includes Plookup) [5] Plonk high level summary [1] Talk: Ariel Gabizon [2] Talk: Zac Williamson [3] Understanding Plonk - Vitalik [4] From AIRs to RAPs - how PLONK-style arithmetization works [5] Custom gates on plonk -Do whatever [7] Plonk Cafe [8] Plonk: Anatomy of a proof generation: Scroll [9] Resource: Plonk by hand -1 Metastate [10.1] Resource: Plonk by hand -2 Metastate [10.2] Resource: Plonk by hand -3 Metastate [10.3] Resource: Plonk and Plookup Metastate [10.4] Turboplonk [11] Custom gates in plonk [12] Plonk: Thomas Piellard [13] ZKP intro to Plonk - Star Li [14] Multi set checks in Plonk and Plookup: Gabizon [15] Plonk - Kimchi: Mina Protocol [16.1] Kimchi [16.2] Plonk not a monad tutorial [17] ✅ ❌ Redshift - 2019 →📝 Redhsift Summary Spartan - 2019 →📝 Microsoft Halo - 2019 →📝 ✅ ✅ MIRAGE - 2020 →📝 ✅ ❌ Marlin - 2020 →📝 arkworks-rs Doc: Pre lunar and not updated to Aleo/testnet3 [1] Thesis [2] Eurocrypt 2020: Talk video [3] ZK summit - Talk: Pratyush [4] Sin7y tech review: blog [5] Marlin and Me [6] Fractal -2020 →📝 scipr-lab/libiop Fractal - talk [1] Demystifying Fractal 1 -Metastate [2.1] Demystifying Fractal 2 - Metastate [2.2] Lunar - 2020 →📝 ZK study club video SuperSonic - 2020 →📝 Demystifying supersonic 1 -Metastate [1.1] Demystifying supersonic 2- Metastate [1.2] ✅ ✅ Darlin - 2021 →📝 Plonkup -2021 →📝 HorizenOfficial/ginger-lib SnarkPack -2021 →📝 Efficient Aggregation FFlonk -2021 →📝 Brakedown - 2021 →📝 Gemini - 2022 →📝 Elastic SNARKs for diverse environments Hyperplonk - 2022 →📝 EspressoSystems Hyperplonk - benedikt Bunz [1] Delendum [2] Hardware friendliness of MLE-Sumcheck [3] Hardware-optimizations for SumCheck-Binyi Chen [4] Testudo: Groth+Spartan - 2023 →📝 cryptonetlab Jolt - 2023 →📝 Introducing Lasso and Jolt","breadcrumbs":"Zero Knowledge Proofs » Protocols » SNARK Protocols » SNARK Protocols","id":"118","title":"SNARK Protocols"},"119":{"body":"Protocols Paper Implementation Resources Universal Transparent zkSTARK -2018 →📝 Winterfell [1] Ministark [2] Cairo [3] Guide for Ministark ✅ ✅ Aurora - 2019 →📝 Thesis Spooner ✅ ✅ Zilch - 2021 →📝 TrustworthyComputing ✅ ✅ Plonky - 2021 →📝 mir-protocol Plonky: Fast recursive arguments based on Plonk and Halo [1] Plonky: Adding zero Knowledge to Plonk and Halo [2] Plonky2 - 2021 →📝 mir-protocol Orion -2022 →📝 sunblaze-ucb IACR -talk","breadcrumbs":"Zero Knowledge Proofs » Protocols » STARK Protocols » STARK Protocols","id":"119","title":"STARK Protocols"},"12":{"body":"","breadcrumbs":"Glossary » K","id":"12","title":"K"},"120":{"body":"Protocols Paper Implementation Resources Universal Transparent Plookup -2020 →📝 Jellyfish Plookup in action -Talk [1] Plonk and Plookup - Metastate [2] Plonk and Plookup - Khovratovich [3] Mina Protocol[4]](https://o1-labs.github.io/proof-systems/introduction.html)AES with lookup : Daira Hopwood [5] Lookup tables - Ariel Gabizon [6] Caulk - 2022 →📝 caulk-crypto [1] Caulk+ [2] Flookup - 2022 →📝 Baloo - 2022 →📝 CQ - 2022 →📝 Geometry CqLin - 2023 →📝 Lasso - 2023 →📝 Introducing Lasso and Jolt","breadcrumbs":"Zero Knowledge Proofs » Protocols » Lookup Protocols » Lookup Protocols","id":"120","title":"Lookup Protocols"},"121":{"body":"Protocols Paper Implementation Resources Universal Transparent Nova - 2021 →📝 microsoft Srinath Setty - Talk [1] Srinath Setty - Video [2] IACR talk slides [3] IVC:Nova lambdaclass [4] Nova - zkstudy club talk [5] zkstudy club video [6] Supernova - 2022 →📝 jules Champagne supernova: lambdaclass Hypernova - 2023 →📝 CCS: Customizable constraint systems for succinct arguments Sangria - 2023 →📝 Blog Protostar - 2023 →📝 Deep dive into Protostar paper & protocol - Binyi Chen Protogalaxy - 2023 →📝 CycleFold - 2023 →📝","breadcrumbs":"Zero Knowledge Proofs » Protocols » Folding Scheme Protocols » Folding Scheme Protocols","id":"121","title":"Folding Scheme Protocols"},"122":{"body":"Protocols Paper Implementation Resources Universal Transparent vRAM - 2018 →📝 ✅ ❌ Bulletproof - 2018 →📝 Dalek [1] Lovesh [2] ZKP using Bullet proofs - Lovesh Harchandani [1] Notes [2] ✅ ✅ Virgo - 2020 →📝 sunblaze-ucb ✅ ✅ Sigma Protocols →📝 sigmastate Sigma Protocols for the Working Programmer","breadcrumbs":"Zero Knowledge Proofs » Protocols » Other Protocols » Other Protocols","id":"122","title":"Other Protocols"},"123":{"body":"The resources on the mathematics behind ZK proofs delve into the complex theories and mathematical concepts that underpin this innovative technology. These resources are intended for those with a strong background in mathematics, or those looking to deepen their understanding of the mathematical foundations of zero-knowledge proofs and their applications. What will you find here: Atoms and building blocks of a ZKP","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Mathematics","id":"123","title":"Mathematics"},"124":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite Fields","id":"124","title":"Finite Fields"},"125":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Elliptic curves","id":"125","title":"Elliptic curves"},"126":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » FFT","id":"126","title":"FFT"},"127":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » MSM","id":"127","title":"MSM"},"128":{"body":"Number theory explained from first principles An introduction to the theory of finite fields MIT lectures -FInite Field arithmetic Finite field arithmetic Doche Lange Aztec emulated field and group operations","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Finite fields","id":"128","title":"Finite fields"},"129":{"body":"A Fast Large-Integer Extended GCD Algorithm and Hardware Design for Verifiable Delay Functions and Modular Inversion Optimized Binary GCD for Modular Inversion Library of Algorithms Modular Multiplication and Hardware implementations - Review Evaluation of large integer multiplications in hardware - Review Hardware friendly modular mult Montgomery REDC using positive inverse mod r Low latency multipliers and cryptographic puzzles optimizing pairing based cryptography, montgomery arithmetic in rust","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Modular arithmetic","id":"129","title":"Modular arithmetic"},"13":{"body":"Ligero - Ligero is a Zero Knowledge Proof system designed specifically for blockchain applications, offering low computational and storage requirements for verification.","breadcrumbs":"Glossary » L","id":"13","title":"L"},"130":{"body":"The Matrix cookbook Ideal Class Groups","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Related Math","id":"130","title":"Related Math"},"131":{"body":"Finite fields and polynomials Schwarz - Zippel Lemma Curious History of Schwarz-Zippel lemma","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Polynomials","id":"131","title":"Polynomials"},"132":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Cryptographic primitives","id":"132","title":"Cryptographic primitives"},"133":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Elliptic curves","id":"133","title":"Elliptic curves"},"134":{"body":"ECC cryptobook Cures over finite fields - Lectures Elliptic curves Chapter 4 Washington Elliptic Curves: MIT lectures Corbellini - ECC ECC primer Silverman - ECC talk Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms Solinas - Efficient Arithmetic on Koblitz Curves Koblitz curve cryptosystems Elliptic Curve Cryptosystems (Koblitz Curves) Algorithm to Find Elliptic curves with a subgroup of a given size Elliptic curves number theory and cryptography Elliptic curve Arithmetic Curve addition - Doche-Lange Elliptic Curve Arithmetic Exponentiation -Doche Lange Elliptic curves of characteristic 2 or 3 - John Cook Addition/Doubling formulae Visualize Elliptic curves j invariant of a curve subgroup checks in BLS12 Complete addition formulae : Bernstein - Lange Complete addition formulae for prime order curves FPGA implementation of complete formulae with Montgomery multiplier Survey of Elliptic curves for Proof systems Edwards curves Twisted Edwards curves Subgroup checks for BLS12 Cofactor explained: Elliptic curves dirty little secret Applications of Riemann Roch theorem in cryptography - Borgeaud Quaternion algebras and Isogeny based cryptography","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » General","id":"134","title":"General"},"135":{"body":"Pairings for beginners - Craig Costello Pairings - Vitalik Buterin Pairing friendly curves Pairing implementation revisited Groth_Sahai proofs are not scary Bilinear pairings in cryptography - Dennis Meffert Pairings and poly commitments - David Wong Circom pairing Code Pairings or bilinear maps optimizing emulated pairings Estimating the bit security of pairing friendly curves optimizing pairing based cryptography, montgomery arithmetic in rust","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Pairings","id":"135","title":"Pairings"},"136":{"body":"BLS12-381 For The Rest Of Us BN254 for the rest of us Benchmarking pairing-friendly elliptic curves libraries ecgfp5 - Pornin: Goldilocks ed448 blog John Cook A deep dive into ed25519 Pasta curves -Electric coin Developers guide to constructing application specific curves","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Specific curves","id":"136","title":"Specific curves"},"137":{"body":"ZK hashes- General ZKP friendly hash functions: SOK Whats the deal with hashes: zk hack Sponge functions: paper S box properties Hash Functions Monolith for ZK Applicationss STARK friendly hash functions Merkling What is a merkle tree Merkle trees Sparse Merkle trees Merkle Commitment scheme Merkle trees and proof of inclusion why you should not sort your Merkle Leaves Fiat Shamir Merlin: Fiat-Shamir magic generator How to Fiat Shamir Serving up ZKP Frozen Heart vulnerability in Girault proof of knowledge in Bulletproofs in Plonk Hashes Keccak: Sponge and Duplex constructions SHA256 Halo2 16 bit lookup implementation Poseidon POSEIDON: A New Hash Function for Zero-Knowledge Proof Systems some documentation Encryption With Poseidon: Dima Khovratovich SAFE A tool box for Poseidon API SAFE: Faster and simple hashing with ZKP Encoding of long objects in Poseidon - Dmitry Khovratovich Talk Grassi Plonky2: Poseidon gate Penumbra: Poseidon Decaf377 Poseidon Implementations code: filecoin Poseidon in Filecoin - Dmitry Khovratovich code: Ingonyama (python) code: Dusk network code: Dust netowrk - Poseidon merkle code: Triplewz - GO Rescue Rescue-Prime: a Standard Specification (SoK) Observations on Rescue Poseidon vs Rescye MIMC MiMc Mimc7 in Plonk - Custom gates Mimc Roy slides Reinforced concrete Reinforced concrete implementation Plonkup reinforced concrete zkstudyclub Code: Luke Pearson Sinsemilla Sinsemilla: A circuit-efficient, lookup-based collision-resistant hash function ZCash protocol specification BLAKE Blake code Tip5 Tip5 code Hash to Curve Hash to Curve Hash to secp256k1 curve Optimized BLS signatures on EVM Hash Bounties Algebraic Hash bounties","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Hash functions » Hash functions","id":"137","title":"Hash functions"},"138":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Verifiable Delay functions » Verifiable Delay functions","id":"138","title":"Verifiable Delay functions"},"139":{"body":"All about Verifiable Delay Functions (VDF's) - VDFresearch","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Verifiable Delay functions » General","id":"139","title":"General"},"14":{"body":"Marlin - Marlin is a Zero Knowledge Proof system that leverages recursive composition to construct large-scale Zero Knowledge Proofs with low proof sizes and verification times. Merkle Tree - A tree data structure in cryptography that enables efficient verification of the integrity and membership of data elements. Multi-party Computation (MPC) - A cryptographic protocol that enables multiple parties to jointly compute a function over their private inputs while preserving the privacy of those inputs, allowing them to collectively obtain the desired result without revealing individual data to each other.","breadcrumbs":"Glossary » M","id":"14","title":"M"},"140":{"body":"General Arithmetic Circuits: A survey Complexity Zoo Arithmetization schemes for snarks Grobner basis used in circuits Circomscribe - learn circom R1CS constraint system Daira Hopwood - Efficient R1CS circuits: Video Quadratic Arithmetic programs R1CS 0 to H - Vitalik Buterin Aleo - Basics of R1CS Zero Knowledge Proofs: How Cryptographers can prove anything Alex Pinto - Constraint system for snarks Alex Pinto - How to build QAP Alex Pinto - Vanishing polynomial for QAP QAP from zero to hero: Vitalik R1CS workshop - Mir Plonkish arithmetization Refer to Plonk AIR Arithmetization AIR to RAPs - Gabizon AIR-Multivariate Sumcheck - W.Borgeaud AIR assembly Bobbin Threadbare Customizable Constraint system CCS CCS: Customizable constraint systems for succinct arguments A multivariate AIR using Superspartan- Borgeaud","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Arithmetization » Arithmetization","id":"140","title":"Arithmetization"},"141":{"body":"General Overview of commitment schemes: Justin Drakes Comparison of Commitment Schemes review of polynomial commmitments KZG KZG commitments KZG - Suyash Polynomial commitments - Dankrad Feist How to use KZG in proofs Fast KZG proofs Amortized KZG - Feist Khovratovich Multiplying a vector by a Toeplitz matrix PCS multiproofs - Feist New sharding design with tight beacon and shard block integration - Dankrad Feist Protodanksharding - FAQ Vitalik Universal verification equation for data availability sampling KZG friendly curves: El Housseini KZG in practice: Scroll Vector Commitments Verkle Trie - Dankrad Feist Aggregatable vector sub commitments Catalano-Fiore VC Inner product Arguments (IPA) Inner product arguments - Dankrad Feist IPA by hand - arnacube IPA commitment scheme Lambdaclass Lattice based commitment Schemes Vortex SLAP Blog","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Commitment Schemes » Commitment Schemes","id":"141","title":"Commitment Schemes"},"142":{"body":"( needs sorting )","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Secure Multi Party Computation » Secure Multi Party Computation","id":"142","title":"Secure Multi Party Computation"},"143":{"body":"An Introduction to Secret-Sharing-Based Secure Multiparty Computation - Daniel Escudero Yau;s garbled circuits: MPC A gentle introduction to YAU's Garbled circuits Setup ceremonies - Pruden & Matlala Collaborative zk-Snarks a Multi-Prover Zero-Knowledge Proof System Trinocchio: Privacy-Preserving Outsourcing by Distributed Verifiable Computation Zero-Knowledge Proofs on Secret-Shared Data via Fully Linear PCPs Prio: Private, Robust, and Scalable Computation of Aggregate Statistics ATLAS (Goyal, CMU) Efficient and Scalable MPC in the Honest Majority Setting","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Secure Multi Party Computation » General","id":"143","title":"General"},"144":{"body":"( To add papers: Work in progress )","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Proving Methods","id":"144","title":"Proving Methods"},"145":{"body":"Unreasonable power of sumcheck - Thaler Justin Thaler Lecture Intro to Sumcheck protocol -oxsage Inuition behind sumcheck - Wong Sumcheck argument and applications Proving AIR with MultiLinear Sumcheck - Borgeaud","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Sumcheck Protocol","id":"145","title":"Sumcheck Protocol"},"146":{"body":"STARK paper DEEP - FRI Proximity Gaps for Reed-Solomon Codes FRI hackernoon FRI properties FRI erasure code fraud proof Barycentric low deg check - Dankrad Feist Low Degree Testing","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Low degree Testing/FRI","id":"146","title":"Low degree Testing/FRI"},"147":{"body":"A brief history of lookup arguments","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Lookup arguments","id":"147","title":"Lookup arguments"},"148":{"body":"Snarkpack: practical snark aggregation blog talk talk","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Aggregations and recursions","id":"148","title":"Aggregations and recursions"},"149":{"body":"Resource: Awesome Folding How to build a snark that is out of this world - Nat Bunner An incomplete guide to FOlding schemes - Lisa","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Folding and accumulation schemes","id":"149","title":"Folding and accumulation schemes"},"15":{"body":"Non-interactive Proof - A Zero Knowledge Proof where the prover generates a single proof without any interaction with the verifier. NTT (Number Theoretic Transform) - A mathematical technique used for efficient polynomial multiplication and fast Fourier transforms in various applications such as signal processing, error correction codes, and cryptography.","breadcrumbs":"Glossary » N","id":"15","title":"N"},"150":{"body":"Succinct Proofs and Linear Algebra","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » General","id":"150","title":"General"},"151":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Computational Primitives","id":"151","title":"Computational Primitives"},"152":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Hardware acceleration","id":"152","title":"Hardware acceleration"},"153":{"body":"Measuring Snark performance frontends-backends and future - Thaler SNark security and peformance - Thaler Decentralized Speed: Advances in Zero Knowledge Proofs Hardware Acceleration for Zero Knowledge Proofs HW acc review - 0xmonia","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Need for hardware acceleration or not?","id":"153","title":"Need for hardware acceleration or not?"},"154":{"body":"Zprize","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Competitions","id":"154","title":"Competitions"},"155":{"body":"PipeZK Algorithms for modern Hardware","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » General HW resources and guides","id":"155","title":"General HW resources and guides"},"156":{"body":"Pantheon of ZKP frameworks - Celer Network ZK Harness ZK Benchmarking -Delendum ZKalc","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Benchmarks of ZKP primitives","id":"156","title":"Benchmarks of ZKP primitives"},"157":{"body":"TEE for CPU and GPU Nvidia TEE for blockchain applications","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » TEE and confidential computing","id":"157","title":"TEE and confidential computing"},"158":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Discrete Fourier Transforms","id":"158","title":"Discrete Fourier Transforms"},"159":{"body":"FFT - Vitalik Reed-Solomon code: Vitalik FFT Notes The Fast Fourier Transform in a Finite Field - Pollard Number Theoretic Transform (NTT): Introduction Gentle intro to NTT 1 (includes rings) Gentle intro to NTT2 (includes rings) Efficient primes for NTT - Goldilocks Goldilocks in nuFHE Goldilocks NTT trick - Solberg Elliptic Curve Fast Fourier Transform (ECFFT) Part I: Fast Polynomial Algorithms over all Finite Fields: Eli Ben-Sasson et.al Talk -zk study club ECFFT algorithm Rust Implementation -Wboregaud Rust ECFFT BN254- Wboregeaud ECFFT-2 Ben-Sasson et.al FFT - Ferror Moreno thesis Zcash FFT FFT for polynomial multiplication A quick barycentric evaluation tutorial - Vitalik Barycentric interpolation - Math Oxford Walsh Hadamard Transform - Borgeaud FFT on finite fields intro","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Algorithms and methods","id":"159","title":"Algorithms and methods"},"16":{"body":"","breadcrumbs":"Glossary » O","id":"16","title":"O"},"160":{"body":"Thesis: BUNTTERFLY: A Flexible Hardware Generator for the Number Theoretic Transform - Jason Vranek CycloneNTT NTL: a library for NTT Zprize 2022","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Implementations","id":"160","title":"Implementations"},"161":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Multi scalar multiplications","id":"161","title":"Multi scalar multiplications"},"162":{"body":"Fast Multi-scalar Multiplication Methods on Elliptic Curves with Precomputation Strategy Using Montgomery Trick Faster batch forgery identification See section 4 for MSM, bucket method Pippenger's exponentiation algorithm - Bernstein Efficient multi-exponentiation implementation in Python Multi-scalar multiplication: state of the art & new ideas with Gus Gutoski Improved Fast exponentiations - Bodo Moller Fast exponentiation with precomputation - Brickell Gordon et al Matter labs -ALgorithms Ryah Henry - Thesis Efficient Multi exponentiation: Bucket method - Bootle","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Algorithms and methods","id":"162","title":"Algorithms and methods"},"163":{"body":"pipezk MSM with FPGA -Connor Masterson thesis PipeMSM EdMSM CycloneMSM Cuzk Zprize MSM implementations","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Implementations","id":"163","title":"Implementations"},"164":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Fully Homomorphic Encryption","id":"164","title":"Fully Homomorphic Encryption"},"165":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Articles","id":"165","title":"Articles"},"166":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes","id":"166","title":"Schemes"},"167":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Libraries","id":"167","title":"Libraries"},"168":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics","id":"168","title":"Mathematics"},"169":{"body":"What you will find here: Blogs, Articles, PDFs, Videos, Notes","breadcrumbs":"Fully Homomorphic Encryption » Articles » Articles","id":"169","title":"Articles"},"17":{"body":"Pairing-Based Cryptography - A cryptographic approach that leverages mathematical pairings to perform various operations and enable advanced cryptographic protocols. Perfect Zero Knowledge - A level of security provided by a Zero Knowledge proof where the verifier gains no additional knowledge about the secret information being proved, except for the validity of the statement. Plonk - Plonk (Permutation-based SNARK) is a Zero Knowledge Proof system that utilizes permutation arguments to achieve succinctness and efficiency. Privacy - The state of being free from unauthorized intrusion, surveillance, or disclosure of personal or sensitive information. Proof Of Knowledge - A cryptographic concept where a prover demonstrates possession of certain information or knowledge to a verifier without revealing the actual information. Prover - The entity in a Zero Knowledge Proof protocol that possesses knowledge of a secret and aims to prove its knowledge to the verifier. Pseudorandom Function - A pseudorandom function (PRF) is a deterministic function that takes an input and produces an output that appears random, even though it is generated by a deterministic algorithm, making it indistinguishable from a truly random function for practical purposes.","breadcrumbs":"Glossary » P","id":"17","title":"P"},"170":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Articles » UNDER CONSTRUCTION 👷","id":"170","title":"UNDER CONSTRUCTION 👷"},"171":{"body":"Encrypted search using FHE Exploring FHE: Vitalik Sunscreen - intro to fhe for engineers Survey on FHE and applications Computing on encrypted data: Nigel Smart","breadcrumbs":"Fully Homomorphic Encryption » Articles » Inroductory","id":"171","title":"Inroductory"},"172":{"body":"ML and FHE Solving LLM Privacy with FHE How Snarks fall short for FHE fhevm fhEVM - Morten Dahl","breadcrumbs":"Fully Homomorphic Encryption » Articles » Applications","id":"172","title":"Applications"},"173":{"body":"FPT: a Fixed-Point Accelerator for Torus Fully Homomorphic Encryption","breadcrumbs":"Fully Homomorphic Encryption » Articles » Implementations","id":"173","title":"Implementations"},"174":{"body":"Security of FHE Schemes Lattice based attacks On concrete hardness of LWE","breadcrumbs":"Fully Homomorphic Encryption » Articles » Security","id":"174","title":"Security"},"175":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » Schemes","id":"175","title":"Schemes"},"176":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » UNDER CONSTRUCTION 👷","id":"176","title":"UNDER CONSTRUCTION 👷"},"177":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » BGV","id":"177","title":"BGV"},"178":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » BFV","id":"178","title":"BFV"},"179":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » CKKS","id":"179","title":"CKKS"},"18":{"body":"QAP (Quadratic Arithmetic Programs) - QAP is a method to represent arithmetic circuits as quadratic polynomials, commonly used in Zero Knowledge Proof systems for efficient proof generation and verification.","breadcrumbs":"Glossary » Q","id":"18","title":"Q"},"180":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » FHEW","id":"180","title":"FHEW"},"181":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » TFHE","id":"181","title":"TFHE"},"182":{"body":"Part 1: Ciphertext types Part 2: Encoding and linear ops part 3: key switching and levelled multiplications Part 4: programmable bootstrapping","breadcrumbs":"Fully Homomorphic Encryption » Schemes » Deep dive: ZAMA AI - Ilaria Chilloti","id":"182","title":"Deep dive: ZAMA AI - Ilaria Chilloti"},"183":{"body":"A curated list of Homomorphic Encryption libraries, and what schemes they use.","breadcrumbs":"Fully Homomorphic Encryption » Libraries » Libraries","id":"183","title":"Libraries"},"184":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Libraries » UNDER CONSTRUCTION 👷","id":"184","title":"UNDER CONSTRUCTION 👷"},"185":{"body":"Libraries Scheme Resources Microsoft SEAL BFV BGV PALISADE BFV FHEW TFHE IBM FHE BGV IBM HElib BGV CKKS Sunscreen - levelled bootstrap BFV Introduction OpenFHE BFV BGV CKKS FHEW TFHE OpenFHE.com TenSEAL - Openmined BFV CKKS Zama AI - Concrete - Python compiler TFHE Zama AI - TFHE-rs - Rust library TFHE Google - FHE TFHE","breadcrumbs":"Fully Homomorphic Encryption » Libraries » Libraries","id":"185","title":"Libraries"},"186":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » Mathematics","id":"186","title":"Mathematics"},"187":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » UNDER CONSTRUCTION 👷","id":"187","title":"UNDER CONSTRUCTION 👷"},"188":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » LWE","id":"188","title":"LWE"},"189":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » FFT","id":"189","title":"FFT"},"19":{"body":"R1CS (Rank-1 Constraint Systems) - R1CS is a mathematical framework used in Zero Knowledge Proof systems to represent computational problems as sets of constraints. Redshift - Redshift is a Zero Knowledge Proof system designed for blockchain applications, offering scalability, efficiency, and post-quantum security. Ring Signature - A cryptographic digital signature scheme that allows a user to sign a message on behalf of a group (or ring) of potential signers, while maintaining the privacy of the actual signer's identity within the group.","breadcrumbs":"Glossary » R","id":"19","title":"R"},"190":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » NTT","id":"190","title":"NTT"},"2":{"body":"ASIC (Application-Specific Integrated Circuit) - A specialized integrated circuit designed for a specific application or function, offering optimized performance and efficiency by implementing dedicated hardware tailored to that specific task. Authentication - The process of verifying the identity of a user, device, or system to ensure that it is genuine and authorized to access certain resources or information. Aurora - Aurora is a Zero Knowledge Proof system that combines zk-SNARKs and Bulletproofs to achieve compact proofs for general-purpose computations. AuroraLight - AuroraLight is an improvement over Aurora that achieves faster prover times and smaller proof sizes while maintaining its generality and security properties.","breadcrumbs":"Glossary » A","id":"2","title":"A"},"20":{"body":"Security - The protection of hardware, software, and data from unauthorized access, theft, damage, or disruption, aiming to maintain confidentiality and integrity. Side-channel Attacks - Attacks that exploit unintended information leakage, such as timing, power consumption, or electromagnetic radiation, to infer secret information. Statistical Zero Knowledge - A level of security offered by a Zero Knowledge proof where the verifier cannot distinguish between a valid proof and a false proof, except with an extremely low probability. Sonic - Sonic (Scalable, Non-Interactive, and Compact) is a Zero Knowledge Proof system that offers scalability and efficiency for verifying large computations. Soundness - The property of a Zero Knowledge Proof protocol that ensures an honest prover cannot convince a verifier of an incorrect statement. Spartan - Spartan is a Zero Knowledge Proof system that achieves transparency, scalability, and post-quantum security without requiring a trusted setup. Supersonic - Supersonic is a Zero Knowledge Proof system that provides high-performance and efficient verification of arithmetic circuits and boolean satisfiability.","breadcrumbs":"Glossary » S","id":"20","title":"S"},"21":{"body":"Trusted Execution - The execution of a program or process in a secure and isolated environment, protecting it from tampering and unauthorized access. Trusted Setup - The process of generating initial parameters for a Zero Knowledge Proof protocol, ensuring that they do not reveal any secret information.","breadcrumbs":"Glossary » T","id":"21","title":"T"},"22":{"body":"","breadcrumbs":"Glossary » U","id":"22","title":"U"},"23":{"body":"Verifier - The entity in a Zero Knowledge Proof protocol that challenges the prover's claim and verifies the validity of the proof without gaining knowledge of the secret.","breadcrumbs":"Glossary » V","id":"23","title":"V"},"24":{"body":"Witness Indistinguishable Proof - A cryptographic proof that guarantees that given two valid proofs for the same statement, it is computationally infeasible for an adversary to distinguish which proof corresponds to the true witness.","breadcrumbs":"Glossary » W","id":"24","title":"W"},"25":{"body":"","breadcrumbs":"Glossary » X","id":"25","title":"X"},"26":{"body":"","breadcrumbs":"Glossary » Y","id":"26","title":"Y"},"27":{"body":"Zero Knowledge Proof - A cryptographic protocol where a prover can demonstrate knowledge of a secret without revealing the secret itself, convincing the verifier of its validity. Zero Knowledge Property - The property of a Zero Knowledge Proof protocol that assures the verifier learns no additional information about the secret beyond its validity. Zk-rollups - zk-rollups, short for Zero-Knowledge Rollups, are Layer 2 scaling solutions for blockchain networks that utilize zero-knowledge proofs to aggregate and validate multiple transactions off-chain, improving scalability and reducing transaction fees while maintaining the security and trustlessness of the underlying blockchain. zk-STARKs - Zero-Knowledge Scalable Transparent Arguments of Knowledge (zk-STARKs) are Zero Knowledge Proofs that achieve transparency and scalability without a trusted setup. zk-SNARKs - Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (zk-SNARKs) are Zero Knowledge Proofs that provide succinctness and non-interactivity. ZPU - A Zero Knowledge Processing Unit (ZPU) is an application-specific integrated circuit (ASIC) designed to accelerate zero-knowledge proof computations and enhance the efficiency of cryptographic protocols.","breadcrumbs":"Glossary » Z","id":"27","title":"Z"},"28":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Zero Knowledge Proofs","id":"28","title":"Zero Knowledge Proofs"},"29":{"body":"Our curated resources consist of carefully selected, links, linktrees and other almanacs like \"Ingopedia\" . These resources are aimed at helping users access high-quality information in a quick and efficient manner.","breadcrumbs":"Zero Knowledge Proofs » Curated Resources","id":"29","title":"Curated Resources"},"3":{"body":"Bulletproofs - Bulletproofs are a non-interactive Zero Knowledge Proof construction that enables efficient verification of range proofs and arithmetic circuits.","breadcrumbs":"Glossary » B","id":"3","title":"B"},"30":{"body":"Our Video lecture series on ZK proofs offers in-depth and engaging presentations that cover the fundamentals and advanced topics of zero-knowledge proofs. These lectures are designed to educate and inform a wide range of audiences, and will contain series of videos on ZKP's various concepts.","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series","id":"30","title":"Video Lecture Series"},"31":{"body":"ZK Introductory ZKSNARKS STARKS Applications Our articles on ZK proofs are comprehensive and educational pieces that delve into the intricacies of zero-knowledge proofs. They consist of blogs, articles, PDFs, and notes. These articles aim to provide a clear understanding of this cutting-edge technology, its used-case applications, its vulnerabilities and its significance.","breadcrumbs":"Zero Knowledge Proofs » Articles","id":"31","title":"Articles"},"32":{"body":"Our hands-on approach to learning ZK proofs provides interactive and practical training experiences that allow participants to build their skills and knowledge in an engaging way. These hands-on workshops, tutorials, and projects are designed to help learners apply their understanding of ZK proofs in real-world situations, making them an invaluable resource for anyone looking to further their expertise in this field.","breadcrumbs":"Zero Knowledge Proofs » Hands on ZK","id":"32","title":"Hands on ZK"},"33":{"body":"Our collection of mathematical papers, protocols, and code on ZK proofs is a comprehensive resource for researchers, developers, and students in the field of cryptography. These materials provide a deep understanding of the theories, implementations, and practical applications of zero-knowledge proofs, serving as a valuable reference for anyone interested in this cutting-edge technology.","breadcrumbs":"Zero Knowledge Proofs » Protocols","id":"33","title":"Protocols"},"34":{"body":"The resources on the mathematics behind ZK proofs delve into the complex theories and mathematical concepts that underpin this intive technology. These resources are intended for those with a strong background in mathematics, or those looking to deepen their understanding of the mathematical foundations of zero-knowledge proofs and their applications.","breadcrumbs":"Zero Knowledge Proofs » Mathematics","id":"34","title":"Mathematics"},"35":{"body":"Our curated resources consist of carefully selected, links, linktrees and other almanacs like \"Ingopedia\". These resources are aimed at helping users access high-quality information in a quick and efficient manner. What you will find here: Links, Linktrees, Almanacs","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » Curated Resources","id":"35","title":"Curated Resources"},"36":{"body":"A collection of links and Almanacs breaking down ZKPs and related topics. zkProof Standards - Resource ZK Mesh - resource Zero Knowledge Fm Curated list of ZKP implementations Awesome - Matter labs - ZK proofs Awesome - Mikerah - Privacy on Blockchains Awesome - Worldcoin - ZK Machine Learning Resource: Awesome_Plonk Resource: Awesome Folding ZK research 0x ZK canon DAO canon NFT canon Crypto Canon Moonmath manual ZKP knowledge base: Delendum ZKP beginner resources Proofs Arguments and Zero Knowledge - Justin Thaler Discord group Awesome ZKEVM Awesome lattice FPGA's","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » References","id":"36","title":"References"},"37":{"body":"A collection of libraries where you can create a ZKP. Rust Cryptographic libraries Arkworks Lambdaworks by Lambdaclass Gnark: in Golang Circom: creating zk circuits Circom tutorials by 0xparc Halo 2 - library Awesome: Halo2 Halo2 club Latest development in Halo2 Guide to Halo2 source code ZK MOOC halo2 circuit building Building and testing with halo2 workshop slides Anatomy of proof generation by Scroll (KZG) version Halo2 workshop by 0xparc lookup args in Halo2 circuit development in halo2 Icemelon circuit development tutorial Halo2 tutorial: ZK natives Getting started with halo2 Axiom Halo2 app and wasm 1 Halo2 app and wasm 2 Halo2 review Automated analysis of halo2 circuits halo2 circuitry tutorial Zokrates Crrl: Cryptography research library - Thomas Pornin Bellman (not updated) libsnark in C++ Snarky frontend Cairo Cairo resource","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » Libraries","id":"37","title":"Libraries"},"38":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » HW libraries","id":"38","title":"HW libraries"},"39":{"body":"ICICLE Danksharding application SPPARK","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » GPU","id":"39","title":"GPU"},"4":{"body":"Cryptography - The practice and study of secure communication techniques, including encryption, decryption, and various cryptographic protocols. Completeness - The property of a Zero Knowledge Proof protocol that guarantees an honest prover can convince a verifier of a correct statement. Commitment Scheme - A cryptographic protocol that enables a party to commit to a value without revealing it and later prove the committed value's consistency. Computational Zero Knowledge - The lowest level of security among the three types of Zero Knowledge proofs, ensuring that an efficient computational algorithm cannot distinguish between valid and invalid proofs within a reasonable amount of time.","breadcrumbs":"Glossary » C","id":"4","title":"C"},"40":{"body":"BLAZE Blaze developer walkthrough","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » FPGA","id":"40","title":"FPGA"},"41":{"body":"Our Video lecture series on ZK proofs offers in-depth and engaging presentations that cover the fundamentals and advanced topics of zero-knowledge proofs. These lectures are designed to educate and inform a wide range of audiences, and will contain series of videos on ZKP's various concepts. What you will find here: Video playlists of Podcasts, Lectures, and University/Professional Classes","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Lecture Series","id":"41","title":"Lecture Series"},"42":{"body":"University and proffesional level courses on ZK. ZKMOOC - 2023 ZK BIU school - 2019 Cryptography 2018 MIT Modern ZK cryptography 0xparc","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » ZK courses","id":"42","title":"ZK courses"},"43":{"body":"Podcasts and lecture playlists on various ZKP related topics. ZK whiteboard Sessions ZK hack ZK summit Zk study club ZK privacy in cosmos ZK podcast ZK Sessions RISC0 architecture RISC0 Study club Modular arithmetic visually PLONK by David Wong Ingonyama: Moon math club a16z summer seminars ZK Hack: Thaler study group ZKP workshop 2022 ZK Shanghai 2023","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Discussions/Seminars","id":"43","title":"Discussions/Seminars"},"44":{"body":"Advanced University and proffesional level courses on ZK. Meta complexity bootcamp - Simons Institute Foundations of probabilistic proofs - Chiesa Probabilistically checkable and interactive proofs - Chisea Algebraic error correcting codes - Stanford ZKP composition and recursion - Wong Introduction to Elliptic curves BIU winter school Bilinear pairings in cryptography BIU winter school: Advances in MPC Foundations of Block chains - Tim Roughgarden BLockchain and money MIT 2018 DEFI MOOC Fuzzing workshop optimizations for fast algorithms bootcamp","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Advanced Courses/Topics","id":"44","title":"Advanced Courses/Topics"},"45":{"body":"Our articles on ZK proofs are comprehensive and educational pieces that delve into the intricacies of zero-knowledge proofs. They consist of blogs, articles, PDFs, and notes. These articles aim to provide a clear understanding of this cutting-edge technology, its used-case applications, its vulnerabilities and its significance. What you will find here: Blogs, Articles, PDFs, Notes","breadcrumbs":"Zero Knowledge Proofs » Articles » Articles","id":"45","title":"Articles"},"46":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory","id":"46","title":"ZK Introductory"},"47":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » ZKSNARKS","id":"47","title":"ZKSNARKS"},"48":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » STARKS","id":"48","title":"STARKS"},"49":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications","id":"49","title":"Applications"},"5":{"body":"","breadcrumbs":"Glossary » D","id":"5","title":"D"},"50":{"body":"Understanding ZK from beginner to advanced on a surface level.","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » ZK Introductory","id":"50","title":"ZK Introductory"},"51":{"body":"Amit Sahai explaining ZK to people of all ages - video Nico's ZK Jargon Decoder ) KU Lueven: Intro to ZK part 1 Interactive_proofs and Zk The incredible Machine - Aviv Zohar What is a ZKP system - Alin Tomescu A friendly intro to ZKP Life cycle of a ZKP","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Beginner","id":"51","title":"Beginner"},"52":{"body":"An introduction to how zk snarks are possible - Vitalik Zk blog Math survival kit for zk developers - lambdaclass Understanding polynomials Intro to ZK in block chain and economics A journey into ZKP - David Wong","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Intermediate","id":"52","title":"Intermediate"},"53":{"body":"An incomplete guide to zk: why zk matters Why and how Zero knowledge works zk Snarks a gentle introduction The math behind ZkSNARK - video De-mystifying Zk proofs -workshop An evolution of ZKP - Sarah Meiklejohn Zk_primer_1 M.Green Zk_primer_2 M.Green Zero Knowledge: A tutorial by Oded Goldreich Cryptographic Protocls: lectures Using zkSnarks for privacy: Vitalik STARK vs SNARK SNARK vs STARK vs Bulletproofs ZKp from Information theoretic Proof systems 1 - Yuval Ishai ZKP from Information theoretic Proof systems 2 - Yuval Ishai ZKP - Modular approach -Yuval Ishai Misconceptions in ZK-Snarks - Thaler Introduction to range proofs","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Advanced","id":"53","title":"Advanced"},"54":{"body":"Check out blogs, papers, pieces, and videos published by the Ingonyama Team","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Ingonyama Blogs","id":"54","title":"Ingonyama Blogs"},"55":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Fast Danksharding Video & Slides","id":"55","title":"Fast Danksharding Video & Slides"},"56":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Recap: ZK Capture the Flag","id":"56","title":"Recap: ZK Capture the Flag"},"57":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Introducing Blaze: ZK Acceleration for FPGA","id":"57","title":"Introducing Blaze: ZK Acceleration for FPGA"},"58":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Hardware Review: GPUs , FPGAs and Zero Knowledge Proofs","id":"58","title":"Hardware Review: GPUs , FPGAs and Zero Knowledge Proofs"},"59":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » RISC Zero Prover Protocol & Analysis","id":"59","title":"RISC Zero Prover Protocol & Analysis"},"6":{"body":"","breadcrumbs":"Glossary » E","id":"6","title":"E"},"60":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » ZK Hardware Table Stakes part 1 -MSM","id":"60","title":"ZK Hardware Table Stakes part 1 -MSM"},"61":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Unleashing Secure AI","id":"61","title":"Unleashing Secure AI"},"62":{"body":"Medium Link Fast-Danksharding Implementation","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Fast Danksharding using ICICLE","id":"62","title":"Fast Danksharding using ICICLE"},"63":{"body":"Medium Link ICICLE - GPU Library","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Introducing ICICLE: An Open-Source GPU Library for Zero Knowledge Acceleration","id":"63","title":"Introducing ICICLE: An Open-Source GPU Library for Zero Knowledge Acceleration"},"64":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » A Brief History of Lookup Arguments","id":"64","title":"A Brief History of Lookup Arguments"},"65":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » How Zero-Knowledge Proofs Will Change Gaming Forever","id":"65","title":"How Zero-Knowledge Proofs Will Change Gaming Forever"},"66":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Intro to ECNTT from Starkware Sessions 2023","id":"66","title":"Intro to ECNTT from Starkware Sessions 2023"},"67":{"body":"YouTube Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Deep Dive into the Sumcheck Protocol with Justin Thaler","id":"67","title":"Deep Dive into the Sumcheck Protocol with Justin Thaler"},"68":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Multi-Precision Fast Modular Multiplication","id":"68","title":"Multi-Precision Fast Modular Multiplication"},"69":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Hardware-friendliness of HyperPlonk","id":"69","title":"Hardware-friendliness of HyperPlonk"},"7":{"body":"Fiat-Shamir Heuristic - A technique used to transform an interactive Zero Knowledge Proof into a non-interactive form by simulating the verifier's challenges. FPGA (Field-Programmable Gate Array) - A reconfigurable integrated circuit that can be programmed and reprogrammed to perform a wide range of tasks, offering flexibility and customization for various applications without requiring a fixed design. Fractal - Fractal is a non-interactive Zero Knowledge Proof system that allows for scalable and efficient verification of statements in a distributed setting.","breadcrumbs":"Glossary » F","id":"7","title":"F"},"70":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Zero Knowledge Proofs and the Metaverse","id":"70","title":"Zero Knowledge Proofs and the Metaverse"},"71":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » The Z Games: Pushing ZK Provers to the Extreme","id":"71","title":"The Z Games: Pushing ZK Provers to the Extreme"},"72":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Goldilocks NTT Trick","id":"72","title":"Goldilocks NTT Trick"},"73":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Down the Rabbit Hole: Optimizing AWS F1 Direct Memory Access (DMA)","id":"73","title":"Down the Rabbit Hole: Optimizing AWS F1 Direct Memory Access (DMA)"},"74":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Sparkworks - Native Hardware Acceleration in Arkworks","id":"74","title":"Sparkworks - Native Hardware Acceleration in Arkworks"},"75":{"body":"Medium Link Paper: https://github.com/ingonyama-zk/papers/blob/main/Winograd_fft.pdf","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » NTT Mini: Exploring Winograd’s Heuristic for Faster NTT","id":"75","title":"NTT Mini: Exploring Winograd’s Heuristic for Faster NTT"},"76":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Marlin & Me: A Deep Dive into the Heart of the Marlin ZK Protocol","id":"76","title":"Marlin & Me: A Deep Dive into the Heart of the Marlin ZK Protocol"},"77":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Bridging the Multichain Universe with Zero Knowledge Proofs","id":"77","title":"Bridging the Multichain Universe with Zero Knowledge Proofs"},"78":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Systemization of Knowledge: ZK-Friendly Hash Functions","id":"78","title":"Systemization of Knowledge: ZK-Friendly Hash Functions"},"79":{"body":"HackerNoon Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » HackerNoon: Using Cloud-ZK for Developing ZKP Acceleration in the Cloud","id":"79","title":"HackerNoon: Using Cloud-ZK for Developing ZKP Acceleration in the Cloud"},"8":{"body":"Groth16 - Groth16 is a non-interactive Zero Knowledge Proof system that utilizes elliptic curve pairings to achieve succinctness and efficient verification.","breadcrumbs":"Glossary » G","id":"8","title":"G"},"80":{"body":"Medium Link Repository Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Cloud-ZK: A Toolkit for Developing ZKP Acceleration in the Cloud","id":"80","title":"Cloud-ZK: A Toolkit for Developing ZKP Acceleration in the Cloud"},"81":{"body":"HackerNoon Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » HackerNoon: Lowering the Barrier of Entry to Zero Knowledge Proofs","id":"81","title":"HackerNoon: Lowering the Barrier of Entry to Zero Knowledge Proofs"},"82":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » A Mathematical Theory of Danksharding","id":"82","title":"A Mathematical Theory of Danksharding"},"83":{"body":"Medium Link and Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » PipeMSM: Hardware Acceleration for Multi-Scalar Multiplication","id":"83","title":"PipeMSM: Hardware Acceleration for Multi-Scalar Multiplication"},"84":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Fast Modular Multiplication","id":"84","title":"Fast Modular Multiplication"},"85":{"body":"Medium Links","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Ingopedia: A Repo for all things ZK","id":"85","title":"Ingopedia: A Repo for all things ZK"},"86":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Poseidon-Hash Repository","id":"86","title":"Poseidon-Hash Repository"},"87":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Polygon’s zkEVM Fun Facts","id":"87","title":"Polygon’s zkEVM Fun Facts"},"88":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Introducing Ingonyama","id":"88","title":"Introducing Ingonyama"},"89":{"body":"A collection of resources explainig ZKSnarks.","breadcrumbs":"Zero Knowledge Proofs » Articles » ZKSNARKS » ZKSNARKS","id":"89","title":"ZKSNARKS"},"9":{"body":"Homomorphic Encryption - A form of encryption that allows mathematical operations to be performed on encrypted data without decrypting it. 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This is a community-driven effort to compile a comprehensive collection of resources and information related to Zero Knowledge Proofs. Our goal is to provide a one-stop-shop for anyone interested in learning about ZKPs, from beginners to experts. We invite the community to help us keep Ingopedia up-to-date and relevant. If you have any suggestions or contributions, please feel free to submit them through the appropriate channels. We believe that the power of the community lies in collaboration and sharing knowledge, so we encourage everyone to get involved. To keep this book organized, we ask that you use the designated sections for your contributions. If you have a new resource to share, please add it to the appropriate section. If you are unsure where to add your contribution, feel free to reach out to the moderators for guidance. Thank you for being a part of our ZKP community and helping us build a valuable resource for all. Note: The branch master contains the src files for the ingopedia mdbook. Each page from the deployment page has a editable button that allows one to edit the markdown file of the specific page. The old Ingopedia is still available in the branch main, we are planning to continue in the mdbook format. Suggestions are welcome. Nerdy Lion","breadcrumbs":"Community Guidelines » Community Guidelines","id":"0","title":"Community Guidelines"},"1":{"body":"A B C D E F G H I J K L M N O P Q R S T U V W X Y Z","breadcrumbs":"Glossary » Glossary","id":"1","title":"Glossary"},"10":{"body":"Interactive Proof - A Zero Knowledge Proof where the prover and verifier engage in multiple rounds of communication to establish the validity of the proof.","breadcrumbs":"Glossary » I","id":"10","title":"I"},"100":{"body":"Vulnerabilities in ZK bridges Primer on Cross chain bridges and how to break them: Niv Yehezkel Block chain bridges: Introduction Introduction to validating bridges and L2 protocols - Patrick McCory zkEVMOS - Bridges and Interoperability Bridging the blockchain multiverse with ZKP Navigating privacy on Blockchains - Wei Dai Having a safe CEX: proof of solvency and beyond","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » ZK bridges","id":"100","title":"ZK bridges"},"101":{"body":"Accelerating client side ZK with webGPU","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » Client side","id":"101","title":"Client side"},"102":{"body":"An Introduction to ZKML zkMNIST awesome-zkml Checks and balances ZK and ML - Elena Burger DO Language models possess Knowledge soundness - Tarun Chitra verifying twitter algorithmic integrity with zkml - Daniel Kang How ZK snarks bring transparency to private ML models with zkml - Daniel Kang Bridging AI/ML and web3 with ZKPs Exploring ZKML Verified execution of GPT,BERT,CLIP","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » ZKML","id":"102","title":"ZKML"},"103":{"body":"Dark Forest - the zk SNARK game Cairo Games Vol2: Solns Blockchain games and game mechanics Crypto gaming - A practical thesis The strongest Crypto gaming thesis ZKP for gaming: Mina","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » ZK Gaming","id":"103","title":"ZK Gaming"},"104":{"body":"Filecoin Filecoin primer Economics specs Proof system Filecoin snark audit Proof of space Proof of Replication: Depth Robust Graphs SDR blog mining task overview task definitions PoRep circuit blog Precommit 2","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » Ecosystem with ZK applications","id":"104","title":"Ecosystem with ZK applications"},"105":{"body":"Private search engine","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications » other applications","id":"105","title":"other applications"},"106":{"body":"Potential vulnerabilities and security in ZK systems ZK bug tracker by0xparc bug tracker intro Vulnerabilities in zk systems Vulnerability in Fiat-Shamir Frozen heart vulnerability: Bulletproof Frozen heart vulnerability: Plonk Hertzbleed attack: sidechannel paper Stress testing Zk systems: Zk docs Specialized ZKP vulnerabilities security of zkp projects: same but different ZK programmability and security Vulnerabilities in private delegated computations Vulnerability in Nova - David Wong Algebraic attacks on ZK hash functions Feldman Secret sharing attacks Threshold signature pitfalls VSS forgery Boomerang values in ZK GPUz.zip Sidechannel attacks on GPUs","breadcrumbs":"Zero Knowledge Proofs » Articles » Vulnerabilities » Security and Vulnerabilities","id":"106","title":"Security and Vulnerabilities"},"107":{"body":"Our hands-on approach to learning ZK proofs provides interactive and practical training experiences that allow participants to build their skills and knowledge in an engaging way. These hands-on workshops, tutorials, and projects are designed to help learners apply their understanding of ZK proofs in real-world situations, making them an invaluable resource for anyone looking to further their expertise in this field. What you will find here: Code-to-Learn Applications","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Hands-On ZK/Cryptography","id":"107","title":"Hands-On ZK/Cryptography"},"108":{"body":"A beginners intro to coding Zero knowledge Proofs Babysnark do do dodo dodo typescript zk zero knowledge with Bellman Cryptohack - hands on cryptography Hands on ZK - ZK learning group Intro to zk: do it yourself circuits Zk Sudoku - Python Arnacube implementations DAPP fron scratch - Vivian Plasencia Zordle - Zk wordle Mental Poker: Part 1 Mental poker: Part 2 0xparc learning groups - covering cricom and halo2 Plonkathon 0xparc Constructing ZK SNARK circuits - DSL Zk calculator Social Applied ZK projects on Ethereum Uncloak courses Proofs args and zk study group implementations Cryptopals challenges Starkware101 Verifiable AES code: lambdaclass Merkle patricia tree: lambdaclass Haskell: Introduction Practical Cryptography for Devs: Nakov Transforming code into arithmetic circuits Differential fuzzing Zkvm step by step Zk smart contract tutorial optimizing pairing based cryptography, montgomery arithmetic in rust In assembly code Pairing over BLS12-381 Part 1 : Fields Part 2 : Curves Part 3 : Pairing An overview of ZKtooling and proof systems right now: Sep 2023","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » General","id":"108","title":"General"},"109":{"body":"Berkeley RDI ZKP-Web3 hackathon Zk hack puzzles Ingonyama ZK CTF-May 2023","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Challenges and hackathons","id":"109","title":"Challenges and hackathons"},"11":{"body":"","breadcrumbs":"Glossary » J","id":"11","title":"J"},"110":{"body":"The Rust book rust book with interactive quizzes The Rust book course Rust guide books Comprehensive rust by google Print and keep nearby - cheats.rs Tutorials Idiomatic Rust - For beauty over brawn Uncloak Study group Awesome rust cryptographic libraries Awesome rust -- general Rust Algorithms Rustlings Rust learning Rust crash course Data engg with rust Circomscribe - learn circom","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Rust learning resources for ZK/cryptography","id":"110","title":"Rust learning resources for ZK/cryptography"},"111":{"body":"code Benchmarking with Rust Flamegraphs code code:flamegraphs from hierarchical data Criterion Criterion introduction The benchmark game Zkalc zkBench Benchmarks","breadcrumbs":"Zero Knowledge Proofs » Hands-On ZK » Benchmarking tools","id":"111","title":"Benchmarking tools"},"112":{"body":"Our collection of mathematical papers, protocols, and code on ZK proofs is a comprehensive resource for researchers, developers, and students in the field of cryptography. These materials provide a deep understanding of the theories, implementations, and practical applications of zero-knowledge proofs, serving as a valuable reference for anyone interested in this cutting-edge technology. What you will find here: Protocols, Papers, Code Implementation, Resources","breadcrumbs":"Zero Knowledge Proofs » Protocols » Protocols --- UNDER CONSTRUCTION","id":"112","title":"Protocols --- UNDER CONSTRUCTION"},"113":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » SNARK Protocols","id":"113","title":"SNARK Protocols"},"114":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » STARK Protocols","id":"114","title":"STARK Protocols"},"115":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Lookup Protocols","id":"115","title":"Lookup Protocols"},"116":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Folding Scheme Protocols","id":"116","title":"Folding Scheme Protocols"},"117":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Protocols » Other Protocols","id":"117","title":"Other Protocols"},"118":{"body":"Protocols Paper Implementation Resources Universal Transparent Pinocchio - 2013 →📝 ❌ ❌ TinyRAM - 2013 →📝 ❌ ❌ vnTinyRAM - 2014 →📝 Mike Hearn ✅ ❌ Geppetto - 2015 →📝 ❌ ❌ Buffet - 2015 →📝 ❌ ❌ Groth -2016 →📝 ConsenSys-gnark [1] arkworks-rs [2] Groth16 Malleability - Geometry [1] Proof of forgery [2] Groth16 aggregation proposal [3] Groth - Talk [4] Deep into bellman library - Star Li [5] Lookups for groth16? [6.1] ultragroth [6.2] ❌ ❌ Ligero - 2017 →📝 ✅ ✅ ZoKrates - 2018 →📝 ZoKrates Proving hash preimage with Zokrates - Decentriq [1] Efficient ECC in Zokrates- Decentriq [2] xjSNARK - 2018 →📝 ❌ ❌ Hyrax - 2018 →📝 Sonic - 2019 →📝 Benthams Gaze ✅ ❌ Plonk - 2019 →📝 heliaxdev [1] kobigurk [2] ZK-Garage [3] dusk-network [4] Jellyfish (Includes Plookup) [5] Plonk high level summary [1] Talk: Ariel Gabizon [2] Talk: Zac Williamson [3] Understanding Plonk - Vitalik [4] From AIRs to RAPs - how PLONK-style arithmetization works [5] Custom gates on plonk -Do whatever [7] Plonk Cafe [8] Plonk: Anatomy of a proof generation: Scroll [9] Resource: Plonk by hand -1 Metastate [10.1] Resource: Plonk by hand -2 Metastate [10.2] Resource: Plonk by hand -3 Metastate [10.3] Resource: Plonk and Plookup Metastate [10.4] Turboplonk [11] Custom gates in plonk [12] Plonk: Thomas Piellard [13] ZKP intro to Plonk - Star Li [14] Multi set checks in Plonk and Plookup: Gabizon [15] Plonk - Kimchi: Mina Protocol [16.1] Kimchi [16.2] Plonk not a monad tutorial [17] ✅ ❌ Redshift - 2019 →📝 Redhsift Summary Spartan - 2019 →📝 Microsoft Halo - 2019 →📝 ✅ ✅ MIRAGE - 2020 →📝 ✅ ❌ Marlin - 2020 →📝 arkworks-rs Doc: Pre lunar and not updated to Aleo/testnet3 [1] Thesis [2] Eurocrypt 2020: Talk video [3] ZK summit - Talk: Pratyush [4] Sin7y tech review: blog [5] Marlin and Me [6] Fractal -2020 →📝 scipr-lab/libiop Fractal - talk [1] Demystifying Fractal 1 -Metastate [2.1] Demystifying Fractal 2 - Metastate [2.2] Lunar - 2020 →📝 ZK study club video SuperSonic - 2020 →📝 Demystifying supersonic 1 -Metastate [1.1] Demystifying supersonic 2- Metastate [1.2] ✅ ✅ Darlin - 2021 →📝 Plonkup -2021 →📝 HorizenOfficial/ginger-lib SnarkPack -2021 →📝 Efficient Aggregation FFlonk -2021 →📝 Brakedown - 2021 →📝 Gemini - 2022 →📝 Elastic SNARKs for diverse environments Hyperplonk - 2022 →📝 EspressoSystems Hyperplonk - benedikt Bunz [1] Delendum [2] Hardware friendliness of MLE-Sumcheck [3] Hardware-optimizations for SumCheck-Binyi Chen [4] Testudo: Groth+Spartan - 2023 →📝 cryptonetlab Jolt - 2023 →📝 Introducing Lasso and Jolt","breadcrumbs":"Zero Knowledge Proofs » Protocols » SNARK Protocols » SNARK Protocols","id":"118","title":"SNARK Protocols"},"119":{"body":"Protocols Paper Implementation Resources Universal Transparent zkSTARK -2018 →📝 Winterfell [1] Ministark [2] Cairo [3] Guide for Ministark ✅ ✅ Aurora - 2019 →📝 Thesis Spooner ✅ ✅ Zilch - 2021 →📝 TrustworthyComputing ✅ ✅ Plonky - 2021 →📝 mir-protocol Plonky: Fast recursive arguments based on Plonk and Halo [1] Plonky: Adding zero Knowledge to Plonk and Halo [2] Plonky2 - 2021 →📝 mir-protocol Orion -2022 →📝 sunblaze-ucb IACR -talk","breadcrumbs":"Zero Knowledge Proofs » Protocols » STARK Protocols » STARK Protocols","id":"119","title":"STARK Protocols"},"12":{"body":"","breadcrumbs":"Glossary » K","id":"12","title":"K"},"120":{"body":"Protocols Paper Implementation Resources Universal Transparent Plookup -2020 →📝 Jellyfish Plookup in action -Talk [1] Plonk and Plookup - Metastate [2] Plonk and Plookup - Khovratovich [3] Mina Protocol[4]](https://o1-labs.github.io/proof-systems/introduction.html)AES with lookup : Daira Hopwood [5] Lookup tables - Ariel Gabizon [6] Caulk - 2022 →📝 caulk-crypto [1] Caulk+ [2] Flookup - 2022 →📝 Baloo - 2022 →📝 CQ - 2022 →📝 Geometry CqLin - 2023 →📝 Lasso - 2023 →📝 Introducing Lasso and Jolt","breadcrumbs":"Zero Knowledge Proofs » Protocols » Lookup Protocols » Lookup Protocols","id":"120","title":"Lookup Protocols"},"121":{"body":"Protocols Paper Implementation Resources Universal Transparent Nova - 2021 →📝 microsoft Srinath Setty - Talk [1] Srinath Setty - Video [2] IACR talk slides [3] IVC:Nova lambdaclass [4] Nova - zkstudy club talk [5] zkstudy club video [6] Supernova - 2022 →📝 jules Champagne supernova: lambdaclass Hypernova - 2023 →📝 CCS: Customizable constraint systems for succinct arguments Sangria - 2023 →📝 Blog Protostar - 2023 →📝 Deep dive into Protostar paper & protocol - Binyi Chen Protogalaxy - 2023 →📝 CycleFold - 2023 →📝","breadcrumbs":"Zero Knowledge Proofs » Protocols » Folding Scheme Protocols » Folding Scheme Protocols","id":"121","title":"Folding Scheme Protocols"},"122":{"body":"Protocols Paper Implementation Resources Universal Transparent vRAM - 2018 →📝 ✅ ❌ Bulletproof - 2018 →📝 Dalek [1] Lovesh [2] ZKP using Bullet proofs - Lovesh Harchandani [1] Notes [2] ✅ ✅ Virgo - 2020 →📝 sunblaze-ucb ✅ ✅ Sigma Protocols →📝 sigmastate Sigma Protocols for the Working Programmer","breadcrumbs":"Zero Knowledge Proofs » Protocols » Other Protocols » Other Protocols","id":"122","title":"Other Protocols"},"123":{"body":"The resources on the mathematics behind ZK proofs delve into the complex theories and mathematical concepts that underpin this innovative technology. These resources are intended for those with a strong background in mathematics, or those looking to deepen their understanding of the mathematical foundations of zero-knowledge proofs and their applications. What will you find here: Atoms and building blocks of a ZKP","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Mathematics","id":"123","title":"Mathematics"},"124":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite Fields","id":"124","title":"Finite Fields"},"125":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Elliptic curves","id":"125","title":"Elliptic curves"},"126":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » FFT","id":"126","title":"FFT"},"127":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » MSM","id":"127","title":"MSM"},"128":{"body":"Number theory explained from first principles An introduction to the theory of finite fields MIT lectures -FInite Field arithmetic Finite field arithmetic Doche Lange Aztec emulated field and group operations","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Finite fields","id":"128","title":"Finite fields"},"129":{"body":"A Fast Large-Integer Extended GCD Algorithm and Hardware Design for Verifiable Delay Functions and Modular Inversion Optimized Binary GCD for Modular Inversion Library of Algorithms Modular Multiplication and Hardware implementations - Review Evaluation of large integer multiplications in hardware - Review Hardware friendly modular mult Montgomery REDC using positive inverse mod r Low latency multipliers and cryptographic puzzles optimizing pairing based cryptography, montgomery arithmetic in rust","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Modular arithmetic","id":"129","title":"Modular arithmetic"},"13":{"body":"Ligero - Ligero is a Zero Knowledge Proof system designed specifically for blockchain applications, offering low computational and storage requirements for verification.","breadcrumbs":"Glossary » L","id":"13","title":"L"},"130":{"body":"The Matrix cookbook Ideal Class Groups","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Related Math","id":"130","title":"Related Math"},"131":{"body":"Finite fields and polynomials Schwarz - Zippel Lemma Curious History of Schwarz-Zippel lemma","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Finite fields » Polynomials","id":"131","title":"Polynomials"},"132":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Cryptographic primitives","id":"132","title":"Cryptographic primitives"},"133":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Elliptic curves","id":"133","title":"Elliptic curves"},"134":{"body":"ECC cryptobook Cures over finite fields - Lectures Elliptic curves Chapter 4 Washington Elliptic Curves: MIT lectures Corbellini - ECC ECC primer Silverman - ECC talk Faster Point Multiplication on Elliptic Curves with Efficient Endomorphisms Solinas - Efficient Arithmetic on Koblitz Curves Koblitz curve cryptosystems Elliptic Curve Cryptosystems (Koblitz Curves) Algorithm to Find Elliptic curves with a subgroup of a given size Elliptic curves number theory and cryptography Elliptic curve Arithmetic Curve addition - Doche-Lange Elliptic Curve Arithmetic Exponentiation -Doche Lange Elliptic curves of characteristic 2 or 3 - John Cook Addition/Doubling formulae Visualize Elliptic curves j invariant of a curve subgroup checks in BLS12 Complete addition formulae : Bernstein - Lange Complete addition formulae for prime order curves FPGA implementation of complete formulae with Montgomery multiplier Survey of Elliptic curves for Proof systems Edwards curves Twisted Edwards curves Subgroup checks for BLS12 Cofactor explained: Elliptic curves dirty little secret Applications of Riemann Roch theorem in cryptography - Borgeaud Quaternion algebras and Isogeny based cryptography","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » General","id":"134","title":"General"},"135":{"body":"Pairings for beginners - Craig Costello Pairings - Vitalik Buterin Pairing friendly curves Pairing implementation revisited Groth_Sahai proofs are not scary Bilinear pairings in cryptography - Dennis Meffert Pairings and poly commitments - David Wong Circom pairing Code Pairings or bilinear maps optimizing emulated pairings Estimating the bit security of pairing friendly curves optimizing pairing based cryptography, montgomery arithmetic in rust","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Pairings","id":"135","title":"Pairings"},"136":{"body":"BLS12-381 For The Rest Of Us BN254 for the rest of us Benchmarking pairing-friendly elliptic curves libraries ecgfp5 - Pornin: Goldilocks ed448 blog John Cook A deep dive into ed25519 Pasta curves -Electric coin Developers guide to constructing application specific curves","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Elliptic curves » Specific curves","id":"136","title":"Specific curves"},"137":{"body":"ZK hashes- General ZKP friendly hash functions: SOK Whats the deal with hashes: zk hack Sponge functions: paper S box properties Hash Functions Monolith for ZK Applicationss STARK friendly hash functions Merkling What is a merkle tree Merkle trees Sparse Merkle trees Merkle Commitment scheme Merkle trees and proof of inclusion why you should not sort your Merkle Leaves Fiat Shamir Merlin: Fiat-Shamir magic generator How to Fiat Shamir Serving up ZKP Frozen Heart vulnerability in Girault proof of knowledge in Bulletproofs in Plonk Hashes Keccak: Sponge and Duplex constructions SHA256 Halo2 16 bit lookup implementation Poseidon POSEIDON: A New Hash Function for Zero-Knowledge Proof Systems some documentation Encryption With Poseidon: Dima Khovratovich SAFE A tool box for Poseidon API SAFE: Faster and simple hashing with ZKP Encoding of long objects in Poseidon - Dmitry Khovratovich Talk Grassi Plonky2: Poseidon gate Penumbra: Poseidon Decaf377 Poseidon Implementations code: filecoin Poseidon in Filecoin - Dmitry Khovratovich code: Ingonyama (python) code: Dusk network code: Dust netowrk - Poseidon merkle code: Triplewz - GO Rescue Rescue-Prime: a Standard Specification (SoK) Observations on Rescue Poseidon vs Rescye MIMC MiMc Mimc7 in Plonk - Custom gates Mimc Roy slides Reinforced concrete Reinforced concrete implementation Plonkup reinforced concrete zkstudyclub Code: Luke Pearson Sinsemilla Sinsemilla: A circuit-efficient, lookup-based collision-resistant hash function ZCash protocol specification BLAKE Blake code Tip5 Tip5 code Hash to Curve Hash to Curve Hash to secp256k1 curve Optimized BLS signatures on EVM Hash Bounties Algebraic Hash bounties","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Hash functions » Hash functions","id":"137","title":"Hash functions"},"138":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Verifiable Delay functions » Verifiable Delay functions","id":"138","title":"Verifiable Delay functions"},"139":{"body":"All about Verifiable Delay Functions (VDF's) - VDFresearch","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Verifiable Delay functions » General","id":"139","title":"General"},"14":{"body":"Marlin - Marlin is a Zero Knowledge Proof system that leverages recursive composition to construct large-scale Zero Knowledge Proofs with low proof sizes and verification times. Merkle Tree - A tree data structure in cryptography that enables efficient verification of the integrity and membership of data elements. Multi-party Computation (MPC) - A cryptographic protocol that enables multiple parties to jointly compute a function over their private inputs while preserving the privacy of those inputs, allowing them to collectively obtain the desired result without revealing individual data to each other.","breadcrumbs":"Glossary » M","id":"14","title":"M"},"140":{"body":"General Arithmetic Circuits: A survey Complexity Zoo Arithmetization schemes for snarks Grobner basis used in circuits Circomscribe - learn circom R1CS constraint system Daira Hopwood - Efficient R1CS circuits: Video Quadratic Arithmetic programs R1CS 0 to H - Vitalik Buterin Aleo - Basics of R1CS Zero Knowledge Proofs: How Cryptographers can prove anything Alex Pinto - Constraint system for snarks Alex Pinto - How to build QAP Alex Pinto - Vanishing polynomial for QAP QAP from zero to hero: Vitalik R1CS workshop - Mir Plonkish arithmetization Refer to Plonk AIR Arithmetization AIR to RAPs - Gabizon AIR-Multivariate Sumcheck - W.Borgeaud AIR assembly Bobbin Threadbare Customizable Constraint system CCS CCS: Customizable constraint systems for succinct arguments A multivariate AIR using Superspartan- Borgeaud","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Arithmetization » Arithmetization","id":"140","title":"Arithmetization"},"141":{"body":"General Overview of commitment schemes: Justin Drakes Comparison of Commitment Schemes review of polynomial commmitments KZG KZG commitments KZG - Suyash Polynomial commitments - Dankrad Feist How to use KZG in proofs Fast KZG proofs Amortized KZG - Feist Khovratovich Multiplying a vector by a Toeplitz matrix PCS multiproofs - Feist New sharding design with tight beacon and shard block integration - Dankrad Feist Protodanksharding - FAQ Vitalik Universal verification equation for data availability sampling KZG friendly curves: El Housseini KZG in practice: Scroll Vector Commitments Verkle Trie - Dankrad Feist Aggregatable vector sub commitments Catalano-Fiore VC Inner product Arguments (IPA) Inner product arguments - Dankrad Feist IPA by hand - arnacube IPA commitment scheme Lambdaclass Lattice based commitment Schemes Vortex SLAP Blog","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Commitment Schemes » Commitment Schemes","id":"141","title":"Commitment Schemes"},"142":{"body":"( needs sorting )","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Secure Multi Party Computation » Secure Multi Party Computation","id":"142","title":"Secure Multi Party Computation"},"143":{"body":"An Introduction to Secret-Sharing-Based Secure Multiparty Computation - Daniel Escudero Yau;s garbled circuits: MPC A gentle introduction to YAU's Garbled circuits Setup ceremonies - Pruden & Matlala Collaborative zk-Snarks a Multi-Prover Zero-Knowledge Proof System Trinocchio: Privacy-Preserving Outsourcing by Distributed Verifiable Computation Zero-Knowledge Proofs on Secret-Shared Data via Fully Linear PCPs Prio: Private, Robust, and Scalable Computation of Aggregate Statistics ATLAS (Goyal, CMU) Efficient and Scalable MPC in the Honest Majority Setting","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Secure Multi Party Computation » General","id":"143","title":"General"},"144":{"body":"( To add papers: Work in progress )","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Proving Methods","id":"144","title":"Proving Methods"},"145":{"body":"Unreasonable power of sumcheck - Thaler Justin Thaler Lecture Intro to Sumcheck protocol -oxsage Inuition behind sumcheck - Wong Sumcheck argument and applications Proving AIR with MultiLinear Sumcheck - Borgeaud","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Sumcheck Protocol","id":"145","title":"Sumcheck Protocol"},"146":{"body":"STARK paper DEEP - FRI Proximity Gaps for Reed-Solomon Codes FRI hackernoon FRI properties FRI erasure code fraud proof Barycentric low deg check - Dankrad Feist Low Degree Testing","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Low degree Testing/FRI","id":"146","title":"Low degree Testing/FRI"},"147":{"body":"A brief history of lookup arguments","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Lookup arguments","id":"147","title":"Lookup arguments"},"148":{"body":"Snarkpack: practical snark aggregation blog talk talk","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Aggregations and recursions","id":"148","title":"Aggregations and recursions"},"149":{"body":"Resource: Awesome Folding How to build a snark that is out of this world - Nat Bunner An incomplete guide to FOlding schemes - Lisa","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » Folding and accumulation schemes","id":"149","title":"Folding and accumulation schemes"},"15":{"body":"Non-interactive Proof - A Zero Knowledge Proof where the prover generates a single proof without any interaction with the verifier. NTT (Number Theoretic Transform) - A mathematical technique used for efficient polynomial multiplication and fast Fourier transforms in various applications such as signal processing, error correction codes, and cryptography.","breadcrumbs":"Glossary » N","id":"15","title":"N"},"150":{"body":"Succinct Proofs and Linear Algebra","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Cryptographic primitives » Proving Methods » General","id":"150","title":"General"},"151":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Computational Primitives","id":"151","title":"Computational Primitives"},"152":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Hardware acceleration","id":"152","title":"Hardware acceleration"},"153":{"body":"Measuring Snark performance frontends-backends and future - Thaler SNark security and peformance - Thaler Decentralized Speed: Advances in Zero Knowledge Proofs Hardware Acceleration for Zero Knowledge Proofs HW acc review - 0xmonia","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Need for hardware acceleration or not?","id":"153","title":"Need for hardware acceleration or not?"},"154":{"body":"Zprize","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Competitions","id":"154","title":"Competitions"},"155":{"body":"PipeZK Algorithms for modern Hardware","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » General HW resources and guides","id":"155","title":"General HW resources and guides"},"156":{"body":"Pantheon of ZKP frameworks - Celer Network ZK Harness ZK Benchmarking -Delendum ZKalc","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » Benchmarks of ZKP primitives","id":"156","title":"Benchmarks of ZKP primitives"},"157":{"body":"TEE for CPU and GPU Nvidia TEE for blockchain applications","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Hardware acceleration » TEE and confidential computing","id":"157","title":"TEE and confidential computing"},"158":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Discrete Fourier Transforms","id":"158","title":"Discrete Fourier Transforms"},"159":{"body":"FFT - Vitalik Reed-Solomon code: Vitalik FFT Notes The Fast Fourier Transform in a Finite Field - Pollard Number Theoretic Transform (NTT): Introduction Gentle intro to NTT 1 (includes rings) Gentle intro to NTT2 (includes rings) Efficient primes for NTT - Goldilocks Goldilocks in nuFHE Goldilocks NTT trick - Solberg Elliptic Curve Fast Fourier Transform (ECFFT) Part I: Fast Polynomial Algorithms over all Finite Fields: Eli Ben-Sasson et.al Talk -zk study club ECFFT algorithm Rust Implementation -Wboregaud Rust ECFFT BN254- Wboregeaud ECFFT-2 Ben-Sasson et.al FFT - Ferror Moreno thesis Zcash FFT FFT for polynomial multiplication A quick barycentric evaluation tutorial - Vitalik Barycentric interpolation - Math Oxford Walsh Hadamard Transform - Borgeaud FFT on finite fields intro","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Algorithms and methods","id":"159","title":"Algorithms and methods"},"16":{"body":"","breadcrumbs":"Glossary » O","id":"16","title":"O"},"160":{"body":"Thesis: BUNTTERFLY: A Flexible Hardware Generator for the Number Theoretic Transform - Jason Vranek CycloneNTT NTL: a library for NTT Zprize 2022","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Discrete Fourier Transforms » Implementations","id":"160","title":"Implementations"},"161":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Multi scalar multiplications","id":"161","title":"Multi scalar multiplications"},"162":{"body":"Fast Multi-scalar Multiplication Methods on Elliptic Curves with Precomputation Strategy Using Montgomery Trick Faster batch forgery identification See section 4 for MSM, bucket method Pippenger's exponentiation algorithm - Bernstein Efficient multi-exponentiation implementation in Python Multi-scalar multiplication: state of the art & new ideas with Gus Gutoski Improved Fast exponentiations - Bodo Moller Fast exponentiation with precomputation - Brickell Gordon et al Matter labs -ALgorithms Ryah Henry - Thesis Efficient Multi exponentiation: Bucket method - Bootle","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Algorithms and methods","id":"162","title":"Algorithms and methods"},"163":{"body":"pipezk MSM with FPGA -Connor Masterson thesis PipeMSM EdMSM CycloneMSM Cuzk Zprize MSM implementations","breadcrumbs":"Zero Knowledge Proofs » Mathematics » Computational Primitives » Multi Scalar Multiplications » Implementations","id":"163","title":"Implementations"},"164":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Fully Homomorphic Encryption","id":"164","title":"Fully Homomorphic Encryption"},"165":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Articles","id":"165","title":"Articles"},"166":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes","id":"166","title":"Schemes"},"167":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Libraries","id":"167","title":"Libraries"},"168":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics","id":"168","title":"Mathematics"},"169":{"body":"What you will find here: Blogs, Articles, PDFs, Videos, Notes","breadcrumbs":"Fully Homomorphic Encryption » Articles » Articles","id":"169","title":"Articles"},"17":{"body":"Pairing-Based Cryptography - A cryptographic approach that leverages mathematical pairings to perform various operations and enable advanced cryptographic protocols. Perfect Zero Knowledge - A level of security provided by a Zero Knowledge proof where the verifier gains no additional knowledge about the secret information being proved, except for the validity of the statement. Plonk - Plonk (Permutation-based SNARK) is a Zero Knowledge Proof system that utilizes permutation arguments to achieve succinctness and efficiency. Privacy - The state of being free from unauthorized intrusion, surveillance, or disclosure of personal or sensitive information. Proof Of Knowledge - A cryptographic concept where a prover demonstrates possession of certain information or knowledge to a verifier without revealing the actual information. Prover - The entity in a Zero Knowledge Proof protocol that possesses knowledge of a secret and aims to prove its knowledge to the verifier. Pseudorandom Function - A pseudorandom function (PRF) is a deterministic function that takes an input and produces an output that appears random, even though it is generated by a deterministic algorithm, making it indistinguishable from a truly random function for practical purposes.","breadcrumbs":"Glossary » P","id":"17","title":"P"},"170":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Articles » UNDER CONSTRUCTION 👷","id":"170","title":"UNDER CONSTRUCTION 👷"},"171":{"body":"Encrypted search using FHE Exploring FHE: Vitalik Sunscreen - intro to fhe for engineers Survey on FHE and applications Computing on encrypted data: Nigel Smart Hands on FHE","breadcrumbs":"Fully Homomorphic Encryption » Articles » Inroductory","id":"171","title":"Inroductory"},"172":{"body":"ML and FHE Solving LLM Privacy with FHE How Snarks fall short for FHE fhevm fhEVM - Morten Dahl","breadcrumbs":"Fully Homomorphic Encryption » Articles » Applications","id":"172","title":"Applications"},"173":{"body":"FPT: a Fixed-Point Accelerator for Torus Fully Homomorphic Encryption cuHE for GPU FHE","breadcrumbs":"Fully Homomorphic Encryption » Articles » Implementations","id":"173","title":"Implementations"},"174":{"body":"Security of FHE Schemes Lattice based attacks On concrete hardness of LWE Security of HE on AN On security of multivariate RLWE","breadcrumbs":"Fully Homomorphic Encryption » Articles » Security","id":"174","title":"Security"},"175":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » Schemes","id":"175","title":"Schemes"},"176":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » UNDER CONSTRUCTION 👷","id":"176","title":"UNDER CONSTRUCTION 👷"},"177":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » BGV","id":"177","title":"BGV"},"178":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » BFV","id":"178","title":"BFV"},"179":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » CKKS","id":"179","title":"CKKS"},"18":{"body":"QAP (Quadratic Arithmetic Programs) - QAP is a method to represent arithmetic circuits as quadratic polynomials, commonly used in Zero Knowledge Proof systems for efficient proof generation and verification.","breadcrumbs":"Glossary » Q","id":"18","title":"Q"},"180":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » FHEW","id":"180","title":"FHEW"},"181":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Schemes » TFHE","id":"181","title":"TFHE"},"182":{"body":"Part 1: Ciphertext types Part 2: Encoding and linear ops part 3: key switching and levelled multiplications Part 4: programmable bootstrapping","breadcrumbs":"Fully Homomorphic Encryption » Schemes » Deep dive: ZAMA AI - Ilaria Chilloti","id":"182","title":"Deep dive: ZAMA AI - Ilaria Chilloti"},"183":{"body":"A curated list of Homomorphic Encryption libraries, and what schemes they use.","breadcrumbs":"Fully Homomorphic Encryption » Libraries » Libraries","id":"183","title":"Libraries"},"184":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Libraries » UNDER CONSTRUCTION 👷","id":"184","title":"UNDER CONSTRUCTION 👷"},"185":{"body":"Libraries Scheme Resources Microsoft SEAL BFV BGV PALISADE BFV FHEW TFHE IBM FHE BGV IBM HElib BGV CKKS Sunscreen - levelled bootstrap BFV Introduction OpenFHE BFV BGV CKKS FHEW TFHE OpenFHE.com TenSEAL - Openmined BFV CKKS Zama AI - Concrete - Python compiler TFHE Zama AI - TFHE-rs - Rust library TFHE Google - FHE TFHE","breadcrumbs":"Fully Homomorphic Encryption » Libraries » Libraries","id":"185","title":"Libraries"},"186":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » Mathematics","id":"186","title":"Mathematics"},"187":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » UNDER CONSTRUCTION 👷","id":"187","title":"UNDER CONSTRUCTION 👷"},"188":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » LWE","id":"188","title":"LWE"},"189":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » FFT","id":"189","title":"FFT"},"19":{"body":"R1CS (Rank-1 Constraint Systems) - R1CS is a mathematical framework used in Zero Knowledge Proof systems to represent computational problems as sets of constraints. Redshift - Redshift is a Zero Knowledge Proof system designed for blockchain applications, offering scalability, efficiency, and post-quantum security. Ring Signature - A cryptographic digital signature scheme that allows a user to sign a message on behalf of a group (or ring) of potential signers, while maintaining the privacy of the actual signer's identity within the group.","breadcrumbs":"Glossary » R","id":"19","title":"R"},"190":{"body":"","breadcrumbs":"Fully Homomorphic Encryption » Mathematics » NTT","id":"190","title":"NTT"},"2":{"body":"ASIC (Application-Specific Integrated Circuit) - A specialized integrated circuit designed for a specific application or function, offering optimized performance and efficiency by implementing dedicated hardware tailored to that specific task. Authentication - The process of verifying the identity of a user, device, or system to ensure that it is genuine and authorized to access certain resources or information. Aurora - Aurora is a Zero Knowledge Proof system that combines zk-SNARKs and Bulletproofs to achieve compact proofs for general-purpose computations. AuroraLight - AuroraLight is an improvement over Aurora that achieves faster prover times and smaller proof sizes while maintaining its generality and security properties.","breadcrumbs":"Glossary » A","id":"2","title":"A"},"20":{"body":"Security - The protection of hardware, software, and data from unauthorized access, theft, damage, or disruption, aiming to maintain confidentiality and integrity. Side-channel Attacks - Attacks that exploit unintended information leakage, such as timing, power consumption, or electromagnetic radiation, to infer secret information. Statistical Zero Knowledge - A level of security offered by a Zero Knowledge proof where the verifier cannot distinguish between a valid proof and a false proof, except with an extremely low probability. Sonic - Sonic (Scalable, Non-Interactive, and Compact) is a Zero Knowledge Proof system that offers scalability and efficiency for verifying large computations. Soundness - The property of a Zero Knowledge Proof protocol that ensures an honest prover cannot convince a verifier of an incorrect statement. Spartan - Spartan is a Zero Knowledge Proof system that achieves transparency, scalability, and post-quantum security without requiring a trusted setup. Supersonic - Supersonic is a Zero Knowledge Proof system that provides high-performance and efficient verification of arithmetic circuits and boolean satisfiability.","breadcrumbs":"Glossary » S","id":"20","title":"S"},"21":{"body":"Trusted Execution - The execution of a program or process in a secure and isolated environment, protecting it from tampering and unauthorized access. Trusted Setup - The process of generating initial parameters for a Zero Knowledge Proof protocol, ensuring that they do not reveal any secret information.","breadcrumbs":"Glossary » T","id":"21","title":"T"},"22":{"body":"","breadcrumbs":"Glossary » U","id":"22","title":"U"},"23":{"body":"Verifier - The entity in a Zero Knowledge Proof protocol that challenges the prover's claim and verifies the validity of the proof without gaining knowledge of the secret.","breadcrumbs":"Glossary » V","id":"23","title":"V"},"24":{"body":"Witness Indistinguishable Proof - A cryptographic proof that guarantees that given two valid proofs for the same statement, it is computationally infeasible for an adversary to distinguish which proof corresponds to the true witness.","breadcrumbs":"Glossary » W","id":"24","title":"W"},"25":{"body":"","breadcrumbs":"Glossary » X","id":"25","title":"X"},"26":{"body":"","breadcrumbs":"Glossary » Y","id":"26","title":"Y"},"27":{"body":"Zero Knowledge Proof - A cryptographic protocol where a prover can demonstrate knowledge of a secret without revealing the secret itself, convincing the verifier of its validity. Zero Knowledge Property - The property of a Zero Knowledge Proof protocol that assures the verifier learns no additional information about the secret beyond its validity. Zk-rollups - zk-rollups, short for Zero-Knowledge Rollups, are Layer 2 scaling solutions for blockchain networks that utilize zero-knowledge proofs to aggregate and validate multiple transactions off-chain, improving scalability and reducing transaction fees while maintaining the security and trustlessness of the underlying blockchain. zk-STARKs - Zero-Knowledge Scalable Transparent Arguments of Knowledge (zk-STARKs) are Zero Knowledge Proofs that achieve transparency and scalability without a trusted setup. zk-SNARKs - Zero-Knowledge Succinct Non-Interactive Arguments of Knowledge (zk-SNARKs) are Zero Knowledge Proofs that provide succinctness and non-interactivity. ZPU - A Zero Knowledge Processing Unit (ZPU) is an application-specific integrated circuit (ASIC) designed to accelerate zero-knowledge proof computations and enhance the efficiency of cryptographic protocols.","breadcrumbs":"Glossary » Z","id":"27","title":"Z"},"28":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Zero Knowledge Proofs","id":"28","title":"Zero Knowledge Proofs"},"29":{"body":"Our curated resources consist of carefully selected, links, linktrees and other almanacs like \"Ingopedia\" . These resources are aimed at helping users access high-quality information in a quick and efficient manner.","breadcrumbs":"Zero Knowledge Proofs » Curated Resources","id":"29","title":"Curated Resources"},"3":{"body":"Bulletproofs - Bulletproofs are a non-interactive Zero Knowledge Proof construction that enables efficient verification of range proofs and arithmetic circuits.","breadcrumbs":"Glossary » B","id":"3","title":"B"},"30":{"body":"Our Video lecture series on ZK proofs offers in-depth and engaging presentations that cover the fundamentals and advanced topics of zero-knowledge proofs. These lectures are designed to educate and inform a wide range of audiences, and will contain series of videos on ZKP's various concepts.","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series","id":"30","title":"Video Lecture Series"},"31":{"body":"ZK Introductory ZKSNARKS STARKS Applications Our articles on ZK proofs are comprehensive and educational pieces that delve into the intricacies of zero-knowledge proofs. They consist of blogs, articles, PDFs, and notes. These articles aim to provide a clear understanding of this cutting-edge technology, its used-case applications, its vulnerabilities and its significance.","breadcrumbs":"Zero Knowledge Proofs » Articles","id":"31","title":"Articles"},"32":{"body":"Our hands-on approach to learning ZK proofs provides interactive and practical training experiences that allow participants to build their skills and knowledge in an engaging way. These hands-on workshops, tutorials, and projects are designed to help learners apply their understanding of ZK proofs in real-world situations, making them an invaluable resource for anyone looking to further their expertise in this field.","breadcrumbs":"Zero Knowledge Proofs » Hands on ZK","id":"32","title":"Hands on ZK"},"33":{"body":"Our collection of mathematical papers, protocols, and code on ZK proofs is a comprehensive resource for researchers, developers, and students in the field of cryptography. These materials provide a deep understanding of the theories, implementations, and practical applications of zero-knowledge proofs, serving as a valuable reference for anyone interested in this cutting-edge technology.","breadcrumbs":"Zero Knowledge Proofs » Protocols","id":"33","title":"Protocols"},"34":{"body":"The resources on the mathematics behind ZK proofs delve into the complex theories and mathematical concepts that underpin this intive technology. These resources are intended for those with a strong background in mathematics, or those looking to deepen their understanding of the mathematical foundations of zero-knowledge proofs and their applications.","breadcrumbs":"Zero Knowledge Proofs » Mathematics","id":"34","title":"Mathematics"},"35":{"body":"Our curated resources consist of carefully selected, links, linktrees and other almanacs like \"Ingopedia\". These resources are aimed at helping users access high-quality information in a quick and efficient manner. What you will find here: Links, Linktrees, Almanacs","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » Curated Resources","id":"35","title":"Curated Resources"},"36":{"body":"A collection of links and Almanacs breaking down ZKPs and related topics. zkProof Standards - Resource ZK Mesh - resource Zero Knowledge Fm Curated list of ZKP implementations Awesome - Matter labs - ZK proofs Awesome - Mikerah - Privacy on Blockchains Awesome - Worldcoin - ZK Machine Learning Resource: Awesome_Plonk Resource: Awesome Folding ZK research 0x ZK canon DAO canon NFT canon Crypto Canon Moonmath manual ZKP knowledge base: Delendum ZKP beginner resources Proofs Arguments and Zero Knowledge - Justin Thaler Discord group Awesome ZKEVM Awesome lattice FPGA's","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » References","id":"36","title":"References"},"37":{"body":"A collection of libraries where you can create a ZKP. Rust Cryptographic libraries Arkworks Lambdaworks by Lambdaclass Gnark: in Golang Circom: creating zk circuits Circom tutorials by 0xparc Halo 2 - library Awesome: Halo2 Halo2 club Latest development in Halo2 Guide to Halo2 source code ZK MOOC halo2 circuit building Building and testing with halo2 workshop slides Anatomy of proof generation by Scroll (KZG) version Halo2 workshop by 0xparc lookup args in Halo2 circuit development in halo2 Icemelon circuit development tutorial Halo2 tutorial: ZK natives Getting started with halo2 Axiom Halo2 app and wasm 1 Halo2 app and wasm 2 Halo2 review Automated analysis of halo2 circuits halo2 circuitry tutorial Zokrates Crrl: Cryptography research library - Thomas Pornin Bellman (not updated) libsnark in C++ Snarky frontend Cairo Cairo resource","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » Libraries","id":"37","title":"Libraries"},"38":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » HW libraries","id":"38","title":"HW libraries"},"39":{"body":"ICICLE Danksharding application SPPARK","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » GPU","id":"39","title":"GPU"},"4":{"body":"Cryptography - The practice and study of secure communication techniques, including encryption, decryption, and various cryptographic protocols. Completeness - The property of a Zero Knowledge Proof protocol that guarantees an honest prover can convince a verifier of a correct statement. Commitment Scheme - A cryptographic protocol that enables a party to commit to a value without revealing it and later prove the committed value's consistency. Computational Zero Knowledge - The lowest level of security among the three types of Zero Knowledge proofs, ensuring that an efficient computational algorithm cannot distinguish between valid and invalid proofs within a reasonable amount of time.","breadcrumbs":"Glossary » C","id":"4","title":"C"},"40":{"body":"BLAZE Blaze developer walkthrough","breadcrumbs":"Zero Knowledge Proofs » Curated Resources » FPGA","id":"40","title":"FPGA"},"41":{"body":"Our Video lecture series on ZK proofs offers in-depth and engaging presentations that cover the fundamentals and advanced topics of zero-knowledge proofs. These lectures are designed to educate and inform a wide range of audiences, and will contain series of videos on ZKP's various concepts. What you will find here: Video playlists of Podcasts, Lectures, and University/Professional Classes","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Lecture Series","id":"41","title":"Lecture Series"},"42":{"body":"University and proffesional level courses on ZK. ZKMOOC - 2023 ZK BIU school - 2019 Cryptography 2018 MIT Modern ZK cryptography 0xparc","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » ZK courses","id":"42","title":"ZK courses"},"43":{"body":"Podcasts and lecture playlists on various ZKP related topics. ZK whiteboard Sessions ZK hack ZK summit Zk study club ZK privacy in cosmos ZK podcast ZK Sessions RISC0 architecture RISC0 Study club Modular arithmetic visually PLONK by David Wong Ingonyama: Moon math club a16z summer seminars ZK Hack: Thaler study group ZKP workshop 2022 ZK Shanghai 2023","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Discussions/Seminars","id":"43","title":"Discussions/Seminars"},"44":{"body":"Advanced University and proffesional level courses on ZK. Meta complexity bootcamp - Simons Institute Foundations of probabilistic proofs - Chiesa Probabilistically checkable and interactive proofs - Chisea Algebraic error correcting codes - Stanford ZKP composition and recursion - Wong Introduction to Elliptic curves BIU winter school Bilinear pairings in cryptography BIU winter school: Advances in MPC Foundations of Block chains - Tim Roughgarden BLockchain and money MIT 2018 DEFI MOOC Fuzzing workshop optimizations for fast algorithms bootcamp","breadcrumbs":"Zero Knowledge Proofs » Video Lecture Series » Advanced Courses/Topics","id":"44","title":"Advanced Courses/Topics"},"45":{"body":"Our articles on ZK proofs are comprehensive and educational pieces that delve into the intricacies of zero-knowledge proofs. They consist of blogs, articles, PDFs, and notes. These articles aim to provide a clear understanding of this cutting-edge technology, its used-case applications, its vulnerabilities and its significance. What you will find here: Blogs, Articles, PDFs, Notes","breadcrumbs":"Zero Knowledge Proofs » Articles » Articles","id":"45","title":"Articles"},"46":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory","id":"46","title":"ZK Introductory"},"47":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » ZKSNARKS","id":"47","title":"ZKSNARKS"},"48":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » STARKS","id":"48","title":"STARKS"},"49":{"body":"","breadcrumbs":"Zero Knowledge Proofs » Articles » Applications","id":"49","title":"Applications"},"5":{"body":"","breadcrumbs":"Glossary » D","id":"5","title":"D"},"50":{"body":"Understanding ZK from beginner to advanced on a surface level.","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » ZK Introductory","id":"50","title":"ZK Introductory"},"51":{"body":"Amit Sahai explaining ZK to people of all ages - video Nico's ZK Jargon Decoder ) KU Lueven: Intro to ZK part 1 Interactive_proofs and Zk The incredible Machine - Aviv Zohar What is a ZKP system - Alin Tomescu A friendly intro to ZKP Life cycle of a ZKP","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Beginner","id":"51","title":"Beginner"},"52":{"body":"An introduction to how zk snarks are possible - Vitalik Zk blog Math survival kit for zk developers - lambdaclass Understanding polynomials Intro to ZK in block chain and economics A journey into ZKP - David Wong","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Intermediate","id":"52","title":"Intermediate"},"53":{"body":"An incomplete guide to zk: why zk matters Why and how Zero knowledge works zk Snarks a gentle introduction The math behind ZkSNARK - video De-mystifying Zk proofs -workshop An evolution of ZKP - Sarah Meiklejohn Zk_primer_1 M.Green Zk_primer_2 M.Green Zero Knowledge: A tutorial by Oded Goldreich Cryptographic Protocls: lectures Using zkSnarks for privacy: Vitalik STARK vs SNARK SNARK vs STARK vs Bulletproofs ZKp from Information theoretic Proof systems 1 - Yuval Ishai ZKP from Information theoretic Proof systems 2 - Yuval Ishai ZKP - Modular approach -Yuval Ishai Misconceptions in ZK-Snarks - Thaler Introduction to range proofs","breadcrumbs":"Zero Knowledge Proofs » Articles » ZK Introductory » Advanced","id":"53","title":"Advanced"},"54":{"body":"Check out blogs, papers, pieces, and videos published by the Ingonyama Team","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Ingonyama Blogs","id":"54","title":"Ingonyama Blogs"},"55":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Fast Danksharding Video & Slides","id":"55","title":"Fast Danksharding Video & Slides"},"56":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Recap: ZK Capture the Flag","id":"56","title":"Recap: ZK Capture the Flag"},"57":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Introducing Blaze: ZK Acceleration for FPGA","id":"57","title":"Introducing Blaze: ZK Acceleration for FPGA"},"58":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Hardware Review: GPUs , FPGAs and Zero Knowledge Proofs","id":"58","title":"Hardware Review: GPUs , FPGAs and Zero Knowledge Proofs"},"59":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » RISC Zero Prover Protocol & Analysis","id":"59","title":"RISC Zero Prover Protocol & Analysis"},"6":{"body":"","breadcrumbs":"Glossary » E","id":"6","title":"E"},"60":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » ZK Hardware Table Stakes part 1 -MSM","id":"60","title":"ZK Hardware Table Stakes part 1 -MSM"},"61":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Unleashing Secure AI","id":"61","title":"Unleashing Secure AI"},"62":{"body":"Medium Link Fast-Danksharding Implementation","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Fast Danksharding using ICICLE","id":"62","title":"Fast Danksharding using ICICLE"},"63":{"body":"Medium Link ICICLE - GPU Library","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Introducing ICICLE: An Open-Source GPU Library for Zero Knowledge Acceleration","id":"63","title":"Introducing ICICLE: An Open-Source GPU Library for Zero Knowledge Acceleration"},"64":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » A Brief History of Lookup Arguments","id":"64","title":"A Brief History of Lookup Arguments"},"65":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » How Zero-Knowledge Proofs Will Change Gaming Forever","id":"65","title":"How Zero-Knowledge Proofs Will Change Gaming Forever"},"66":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Intro to ECNTT from Starkware Sessions 2023","id":"66","title":"Intro to ECNTT from Starkware Sessions 2023"},"67":{"body":"YouTube Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Deep Dive into the Sumcheck Protocol with Justin Thaler","id":"67","title":"Deep Dive into the Sumcheck Protocol with Justin Thaler"},"68":{"body":"Medium Link Paper","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Multi-Precision Fast Modular Multiplication","id":"68","title":"Multi-Precision Fast Modular Multiplication"},"69":{"body":"Medium Link","breadcrumbs":"Zero Knowledge Proofs » Articles » Ingonyama Blogs » Hardware-friendliness of HyperPlonk","id":"69","title":"Hardware-friendliness of HyperPlonk"},"7":{"body":"Fiat-Shamir Heuristic - 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FPGA (Field-Programmable Gate Array) - A reconfigurable integrated circuit that can be programmed and reprogrammed to perform a wide range of tasks, offering flexibility and customization for various applications without requiring a fixed design. 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