• ElGamal
• Installation
• Usage
  • Quick start
    • Encryption
    • Decryption
  • Methods
    • ElGamal([p], [g], [y], [x])
    • setSecurityLevel(level)
    • checkSecurity()
    • initialize([lengthOfOrder])
    • initializeRemotely([lengthOfOrder])
    • fillIn()
    • encrypt(message)
    • decrypt(cypherPair)
    • randomGroupMember()
    • export(deep)
    • import(engine)
    • power(exponent)
    • add(a, b)
    • multiply(a, b)
  • Properties
• Example
• Contributing
• Support
• License

ElGamal

This module is an implementation of ElGamal Encryption System in Javascript which is secured regarding the last security suggestions.

As the name of the package suggests, we are trying to keep this module simple and basic! Hence we are trying to develop this module according to original ElGamal:

• The engine works over Cyclic Groups of Integers
• In safest mode, The underlying Cyclic Group is a Multiplicative Group of a large prime number order
• Security of engine depends on security of Discrete Logarithms problem.

NOTE: The Module is developed for educational goals, although we developed it securely but the risk of using it in production environment is on you!

Installation

Either you are using Node.js or a browser, you can use it locally by downloading it from npm:

npm install basic_simple_elgamal

Usage

To include this module in your code simply:

const ElGamal = require('basic_simple_elgamal');

If you are using it in a browser, you may need to use a tool such as browserify to compile your code.

Quick start

After including the module into your code:

1. Get an instance of ElGamal:

   const elgamal = new ElGamal();
   

2. Initialize your instance:

   //2048 is the key length.
   await elgamal.initializeRemotely(2048);
   

3. Make sure your engine is secure:

   elgamal.checkSecurity();
   

   Now your engine is ready to use.

Encryption

Since engine works over Cyclics Groups, at first you should map your messages into group members!

This mapping doesn't have any confidentially value and you can publish it publicly. Hence to keep the flexibility of engine, we don't offer any strict way for mapping the messages but you can use any algorithm on your choice.

To get the group members, you can call randomGroupMember() method!

Assume you have a message m and you want to encrypt it:

1. Map this message to a group member:

       const mappedM = elgamal.randomGroupMember();
   

2. Encrypt the message:

    let ciphertext = elgamal.encrypt(mappedM);
   

   And you're done.

Decryption

Having the resulted cyphertext, you can decrypt it as below:

    let decryptedMessage = elgamal.decrypt(cipherText);

The decryptedMessage is the original group member which you encrypted, so to get the original message, you should apply your mapping to it!

Methods

All methods which you may need are documented here. If a method is not documented, it means it is an internal method and you shouldn't call it directly.

While introducing the methods, we use specific Terms which are listed below:

• Throws Error: Indicates the methods throw an error, the type or reason of possible errors is explained in the method's explanation.
• Async: Indicates this method is an asynchronous method which means you should wait for it to complete its execution
• Secure: Before calling these methods you need to call the checkSecurity() and get true as return value.

ElGamal([p], [g], [y], [x])

• p: The modulus of multiplicative group.
• g: The generator of cyclic group.
• y: The encryption key.
• x: The decryption key.
• Return: An instance of engine.
• Throws Error

These parameters are large integers.
All four parameters should be of type string or big-integer otherwise it will be initialized with undefined or will throw an error.

The modulus p can be prime or not considering engine's security level.

The modulus p and generator g are required for defining the cyclic group, the encryption key y and decryption key x are required for ElGama Encryption. So providing x and y without p and g is meaningless.
Hence you can provide p and g, then call fillIn() method to let engine pick the values y and x automatically.

Although the engine gives you this option to initialize it manually but we strongly recommend to use initialize() or initializeRemotely() instead of using constructor!

setSecurityLevel(level)

• level: Is level of security.
• Returns: void
• Throws Error

level is one of the following strings: 'HIGH', 'LOW', 'MEDIUM'. if you pass another value except this three values, you will encounter an error.

By default the security level is 'HIGH' and it is strongly recommended to don't change it.

More Info:

At 'HIGH' security level: The underlying Cyclic Group is made using Safe and Sophie Germain primes.

At 'MEDIUM' security level: The modulus of group is a prime number. We don't recomend this level because initializing engine at this level requires high cpu usage.

At 'LOW' security level: There is no limitation over engine but also there is no guarantee that engine will works correctly.

checkSecurity()

• Returns: boolean

This method checks the ElGamal engine against the security level and if it satisfies the conditions then it will returns true and activates the engine otherwise it will returns false and don't let you to use secure methods.

initialize([lengthOfOrder])

• lengthOfOrder: The length of underlying group order in bits.
• Returns: void
• Async

This method requires high cpu usage because it tries to initialize the engine locally. Also it uses multithreading to do its job.

As mentioned above, this method requires high cpu usage and because of that we recommend to use initializeRemotely() instead. This method just developed to enable engine to work independently in case of no network connection.

lengthOfOrder parameter is an arbitrary integer but we recommend to pass a value larger than 2048. Also by default its value is 2048.

initializeRemotely([lengthOfOrder])

• lengthOfOrder: The length of underlying group order in bits.
• Returns: void
• Async

Initialize the engine by connecting to a remote databas hence it requires a network connection to do its job.

The information received from remote Database are public and you don't need to worry about its security. Also we verify the received information to make sure there is no midway manipulation.

lengthOfOrder parameter indicates length of group order and can be one of the following values: 2048, 3072, 4096 and 8192.

More Info: After initializing the engine either by using constructor, initialize() or initializeRemotely(), the encryption key is equal to your public key! You can set the correct encryption key by setting the publicKey as mentioned in Properties section.

fillIn()

• Returns: void

If you just have the group information(which are modulus p and group order g) and you want to use this group in ElGamal encryption, you can call this method to set the private key and its corresponding public key.

NOTE: You don't need to call this method if you use initialize() or initializeRemotely() methods. This is useful only if you use constructor without private/public key to initialize the engine.

encrypt(message)

• message: A group member which represents your message.
• Returns: An object containing a pair of cyphertexts.
• Async
• Throws Error
• Secure

Encrypts your passed message and returns the corresponding cyphertext.

message parameter should be a member of underlying Cyclic Group. We don't check for its membership but yourself should care about it.

Throws an error if you didn't call checkSecurity() method or it returns false which means the engine doesn't satisfy the considered security level. Also it throws an error if provided information is not complete(in case of initializing engine manually by calling constructor).

More Info: The resulting cyphertext is an object containing two below properties:

1. c1: Shared secret.
2. c2: Encrypted message.

decrypt(cypherPair)

• cypherPair: same resulted cyphertext from encrypt() method
• Returns: The decrypted message which is an integer and a member of Cyclic Group
• Async
• Secure
• Throws Error

Decrypts the given cyphertext and returns corresponding plaintext.

Throws an error if you didn't call checkSecurity() method or it returns false which means the engine doesn't satisfy the considered security level. Also it throws an error if provided information is not complete (in case of initializing engine manually by calling constructor).

randomGroupMember()

• Returns: big-integer
• Async

Returns a group member randomly.
You can use this function to make your customized mapping between messages and group members.

This method is cryptographically secure so don't hesitate to use it.

export(deep)

• deep: boolean
• Returns: The exported engine.

Exports engine as an object then you can import it again using import()

deep parameters inidicates whether you want the whole engine to be experted or just public info of it.
Set deep as true result in exporting your random keys as well as other info. (You can read more about random key at ElGamal).

Note: Your private key will be exported if and only if your security level is at 'LOW'.
So if you need your private key, which is not recommended but you may need for your need, you should first use setSecurityLevel() to decrease the security level.

By using this method you are enable to export and transfer your engine.

import(engine)

• engine: The resulted object from calling [export()] method.
• Returns: void

Imports ElGamal engine so that you can use it again.

NOTE: You may need to call checkSecurity() to activate secure methods.

power(exponent)

• exponent: Is exponenet of power operation.
• Returns: big-integer

Computes modular exponentiation with generator g as base of exponentiation.

All parameters are of string type or big-integer type.

This method is not part of elgamal but it is a part of Cyclic group calculations, its provided just to fullfill your other common needs.

add(a, b)

• a: The first operand.
• b: The second operand.
• Returns: big-integer

Calculates (a + b) mod p and returns the result.

All parameters are of string type or big-integer type.

This method is not part of elgamal but it is a part of Modular calculations. Its provided just to fullfill your other common needs.

multiply(a, b)

• a: The first operand.
• b: The second operand.
• Returns: big-integer

Calculates (a.b) mod p and returns the result.

All parameters are of string type or big-integer type.

This method is not part of elgamal but it is a part of Modular calculations. Its provided just to fullfill your other common needs.

Properties

You can get or set these properties as you wish:

1. generator
2. groupOrder
3. modulus
4. publicKey
5. PrivateKey *

* Using these properties is not secure and is not recommended as well. Also setting these properties will work if and only if the security level is at 'LOW'

Example

A simple example is provided at ./tests/encryption-decryption.js file which is available at GitHub page too.

Contributing

Since this module is developed at Software Security Lab, you can pull requests but merging it depends on Software Security Lab decision.
Also you can open issues first then we can discuss about it.

Support

If you need help you can either open an issue in GitHub page or contact the developers by mailing to [email protected]

License

This work is published under ISC license.