Pollard's kangaroo for SECPK1

A simple Pollard's kangaroo ECDLP solver for SECPK1.

Usage:

Kangaroo [-v] [-t nbThread] [-d dpBit] [gpu] [-check]
         [-gpuId gpuId1[,gpuId2,...]] [-g g1x,g1y[,g2x,g2y,...]]
         inFile
 -v: Print version
 -gpu: Enable gpu calculation
 -gpu gpuId1,gpuId2,...: List of GPU(s) to use, default is 0
 -g g1x,g1y,g2x,g2y,...: Specify GPU(s) kernel gridsize, default is 2*(MP),2*(Core/MP)
 -d: Specify number of leading zeros for the DP method (default is auto)
 -t nbThread: Secify number of thread
 -l: List cuda enabled devices
 -check: Check GPU kernel vs CPU
 inFile: intput configuration file

Structure of the input file:

• All values are in hex format
• Public keys can be given either in compressed or uncompressed format

Start range
End range
Key #1
Key #2
...

ex

49dccfd96dc5df56487436f5a1b18c4f5d34f65ddb48cb5e0000000000000000
49dccfd96dc5df56487436f5a1b18c4f5d34f65ddb48cb5effffffffffffffff
0459A3BFDAD718C9D3FAC7C187F1139F0815AC5D923910D516E186AFDA28B221DC994327554CED887AAE5D211A2407CDD025CFC3779ECB9C9D7F2F1A1DDF3E9FF8
0335BB25364370D4DD14A9FC2B406D398C4B53C85BE58FCC7297BD34004602EBEC

Note on Time/Memory tradeoff of the DP method

The distinguished point (DP) method is an efficent method for storing random walks and detect collision between them. Instead of storing all points of all kanagroo's random walks, we store only points that have an x value starting with dp zero bits. When 2 kangaroos collide, they will then follow the same path because their jumps are a function of their x values. The collsion will be then detected until the 2 kangaroos reach a distinguished point.
This has a drawback when you have a lot of kangaroos and looking for collision in a small range as the overhead is in the order of nbKangaroo.2^dp until a collision is detected. If dp is too small a large number of point will enter in the central table, will decrease performance and quicly fill the RAM. Powerfull GPUs with large number of cores won't be very efficient on small range, you can try to decrease the grid size in order to have less kangaroos but the GPU performance may not be optimal. Yau can change manualy the dp size using the -d option, take in considration that it will require about nbKangaroo.2^dp more operations to complete.

How it works

The program uses 2 herds of kangaroos, a tame herd and a wild herd. When 2 kangoroos (a wild one and a tame one) collide, the key can be solved. Due to the birthday paradox, a collision happens (in average) after 2.sqrt(k2-k1) group operations, the 2 herds have the same size. To detect collision, the distinguished points method is used with a hashtable.

Here is a brief description of the algorithm:

We have to solve P = k.G, P is the public key, we know that k lies in the range [k1,k2], G is the SecpK1 generator point.
Group operations are additions on the elliptic curve, scalar operations are done modulo the order of the curve.

n = floor(log2(sqrt(k2-k1)))+1

• Create a jump point table jP = [G,2G,4G,8G,...,2^n-1.G]
• Create a jump distance table jD = [1,2,4,8,....,2^n-1]

for all i in herdSize
  tame_i = rand(0..(k2-k1)) # Scalar operation
  tamePos_i = (k1+tame_i).G # Group operation
  wild_i = rand(0..(k2-k1)) - (k2-k1)/2 # Scalar operation
  wildPos_i = P + wild_i.G # Group operation

found = false

while not found
  for all i in herdSize
     tamePos_i = tamePos_i + jP[tamePos_i.x % n] # Group operation
     tame_i += jD[tamePos_i.x % n] # Scalar operation
     wildPos_i = wildPos_i + jP[wildPos_i.x % n] # Group operation
     wild_i += jD[wildPos_i.x % n] # Scalar operation
     if tamePos_i is distinguished
       add (TAME,tamePos_i,tame_i) to hashTable
     if wildPos_i is distinguished
       add (WILD,wildPos_i,wild_i) to hashTable
  found = is there a collision in hashTable between a tame and a wild kangaroo ?

(Tame,Wild) = Collision
k = k1 + Tame.dist - Wild.dist

Compilation

Windows

Install CUDA SDK and open Kangaroo.sln in Visual C++ 2017.
You may need to reset your Windows SDK version in project properties.
In Build->Configuration Manager, select the Release configuration.
Build and enjoy.

Note: The current release has been compiled with CUDA SDK 10.0, if you have a different release of the CUDA SDK, you may need to update CUDA SDK paths in Kangaroo.vcxproj using a text editor. The current nvcc option are set up to architecture starting at 3.0 capability, for older hardware, add the desired compute capabilities to the list in GPUEngine.cu properties, CUDA C/C++, Device, Code Generation.

Linux

Install CUDA SDK.
Depending on the CUDA SDK version and on your Linux distribution you may need to install an older g++ (just for the CUDA SDK).
Edit the makefile and set up the good CUDA SDK path and appropriate compiler for nvcc.

CUDA       = /usr/local/cuda-8.0
CXXCUDA    = /usr/bin/g++-4.8

You can enter a list of architecture (refer to nvcc documentation) if you have several GPU with different architecture. Compute capability 2.0 (Fermi) is deprecated for recent CUDA SDK. Kangaroo need to be compiled and linked with a recent gcc (>=7). The current release has been compiled with gcc 7.3.0.
Go to the Kangaroo directory. ccap is the desired compute capability.

$ g++ -v
gcc version 7.3.0 (Ubuntu 7.3.0-27ubuntu1~18.04)
$ make all (for build without CUDA support)
or
$ make gpu=1 ccap=20 all

Runnig Kangaroo (Intel(R) Xeon(R) CPU, 8 cores, @ 2.93GHz, Quadro 600 (x2))

$pons@linpons:~/Kangaroo$cat in.txt 
0
FFFFFFFFFFFFFF
02E9F43F810784FF1E91D8BC7C4FF06BFEE935DA71D7350734C3472FE305FEF82A
pons@linpons:~/Kangaroo$export LD_LIBRARY_PATH=/usr/local/cuda-8.0/lib64
pons@linpons:~/Kangaroo$./kangaroo -t 4 -gpu -gpuId 0,1 in.txt 
Kangaroo v1.2
Start:0
Stop :FFFFFFFFFFFFFF
Keys :1
Number of CPU thread: 4
Range width: 2^56
Number of random walk: 2^16.64 (Max DP=9)
DP size: 9 [0xff80000000000000]
SolveKeyCPU Thread 0: 1024 kangaroos
SolveKeyCPU Thread 2: 1024 kangaroos
SolveKeyCPU Thread 1: 1024 kangaroos
SolveKeyCPU Thread 3: 1024 kangaroos
GPU: GPU #0 Quadro 600 (2x48 cores) Grid(4x96) (13.5 MB used)
SolveKeyGPU Thread GPU#0: creating kangaroos...
GPU: GPU #1 Quadro 600 (2x48 cores) Grid(4x96) (13.5 MB used)
SolveKeyGPU Thread GPU#1: creating kangaroos...
SolveKeyGPU Thread GPU#0: 2^15.58 kangaroos in 334.8ms
SolveKeyGPU Thread GPU#1: 2^15.58 kangaroos in 364.7ms
[22.67 MKey/s][GPU 13.04 MKey/s][Count 2^29.06][Dead 0][28s][89.1MB]  
Key# 0 Pub:  0x02E9F43F810784FF1E91D8BC7C4FF06BFEE935DA71D7350734C3472FE305FEF82A 
       Priv: 0x378ABDEC51BC5D 

Done: Total time 29s 

Example of usage

Input file: in.txt

49dccfd96dc5df56487436f5a1b18c4f5d34f65ddb48cb5e0000000000000000
49dccfd96dc5df56487436f5a1b18c4f5d34f65ddb48cb5effffffffffffffff
0459A3BFDAD718C9D3FAC7C187F1139F0815AC5D923910D516E186AFDA28B221DC994327554CED887AAE5D211A2407CDD025CFC3779ECB9C9D7F2F1A1DDF3E9FF8
04A50FBBB20757CC0E9C41C49DD9DF261646EE7936272F3F68C740C9DA50D42BCD3E48440249D6BC78BC928AA52B1921E9690EBA823CBC7F3AF54B3707E6A73F34
0404A49211C0FE07C9F7C94695996F8826E09545375A3CF9677F2D780A3EB70DE3BD05357CAF8340CB041B1D46C5BB6B88CD9859A083B0804EF63D498B29D31DD1
040B39E3F26AF294502A5BE708BB87AEDD9F895868011E60C1D2ABFCA202CD7A4D1D18283AF49556CF33E1EA71A16B2D0E31EE7179D88BE7F6AA0A7C5498E5D97F
04837A31977A73A630C436E680915934A58B8C76EB9B57A42C3C717689BE8C0493E46726DE04352832790FD1C99D9DDC2EE8A96E50CAD4DCC3AF1BFB82D51F2494
040ECDB6359D41D2FD37628C718DDA9BE30E65801A88A00C3C5BDF36E7EE6ADBBAD71A2A535FCB54D56913E7F37D8103BA33ED6441D019D0922AC363FCC792C29A
0422DD52FCFA3A4384F0AFF199D019E481D335923D8C00BADAD42FFFC80AF8FCF038F139D652842243FC841E7C5B3E477D901F88C5AB0B88EE13D80080E413F2ED
04DB4F1B249406B8BD662F78CBA46F5E90E20FE27FC69D0FBAA2F06E6E50E536695DF83B68FD0F396BB9BFCF6D4FE312F32A43CF3FA1FE0F81DF70C877593B64E0
043BD0330D7381917F8860F1949ACBCCFDC7863422EEE2B6DB7EDD551850196687528B6D2BC0AA7A5855D168B26C6BAF9DDCD04B585D42C7B9913F60421716D37A
04332A02CA42C481EAADB7ADB97DF89033B23EA291FDA809BEA3CE5C3B73B20C49C410D1AD42A9247EB8FF217935C9E28411A08B325FBF28CC2AF8182CE2B5CE38
04513981849DE1A1327DEF34B51F5011C5070603CA22E6D868263CB7C908525F0C19EBA6BD2A8DCF651E4342512EDEACB6EA22DA323A194E25C6A1614ABD259BC0
04D4E6FA664BD75A508C0FF0ED6F2C52DA2ADD7C3F954D9C346D24318DBD2ECFC6805511F46262E10A25F252FD525AF1CBCC46016B6CD0A7705037364309198DA1
0456B468963752924DBF56112633DC57F07C512E3671A16CD7375C58469164599D1E04011D3E9004466C814B144A9BCB7E47D5BACA1B90DA0C4752603781BF5873
04D5BE7C653773CEE06A238020E953CFCD0F22BE2D045C6E5B4388A3F11B4586CBB4B177DFFD111F6A15A453009B568E95798B0227B60D8BEAC98AF671F31B0E2B
04B1985389D8AB680DEDD67BBA7CA781D1A9E6E5974AAD2E70518125BAD5783EB5355F46E927A030DB14CF8D3940C1BED7FB80624B32B349AB5A05226AF15A2228
0455B95BEF84A6045A505D015EF15E136E0A31CC2AA00FA4BCA62E5DF215EE981B3B4D6BCE33718DC6CF59F28B550648D7E8B2796AC36F25FF0C01F8BC42A16FD9

Result: On a Xeon X5647 2.93GHz with 12GB of RAM (Ubuntu 18.04) CPU Only

pons@linpons:~/Kangaroo$ ./kangaroo in.txt 
Kangaroo v1.0
Start:49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E0000000000000000
Stop :49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EFFFFFFFFFFFFFFFF
Keys :16
Number of CPU thread: 8
Range width: 2^64
Number of random walk: 2^13.00 (Max DP=17)
DP size: 17 [0xffff800000000000]
Solvekey Thread 0: 1024 TAME kangaroos
Solvekey Thread 1: 1024 TAME kangaroos
Solvekey Thread 2: 1024 TAME kangaroos
Solvekey Thread 3: 1024 TAME kangaroos
Solvekey Thread 4: 1024 WILD kangaroos
Solvekey Thread 5: 1024 WILD kangaroos
Solvekey Thread 6: 1024 WILD kangaroos
Solvekey Thread 7: 1024 WILD kangaroos
[18.00 MKey/s][Count 2^34.40][20:47][Dead 10][20.2MB]  
Key# 0 Pub:  0x0259A3BFDAD718C9D3FAC7C187F1139F0815AC5D923910D516E186AFDA28B221DC 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EBB3EF3883C1866D4 
[18.18 MKey/s][Count 2^33.80][13:44][Dead 3][15.4MB]  
Key# 1 Pub:  0x02A50FBBB20757CC0E9C41C49DD9DF261646EE7936272F3F68C740C9DA50D42BCD 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EB5ABC43BEBAD3207 
[18.07 MKey/s][Count 2^30.28][01:12][Dead 1][2.8MB]  
Key# 2 Pub:  0x0304A49211C0FE07C9F7C94695996F8826E09545375A3CF9677F2D780A3EB70DE3 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E5698AAAB6CAC52B3 
[18.18 MKey/s][Count 2^32.78][06:44][Dead 2][9.4MB]  
Key# 3 Pub:  0x030B39E3F26AF294502A5BE708BB87AEDD9F895868011E60C1D2ABFCA202CD7A4D 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E59C839258C2AD7A0 
[18.18 MKey/s][Count 2^33.82][13:54][Dead 3][15.6MB]  
Key# 4 Pub:  0x02837A31977A73A630C436E680915934A58B8C76EB9B57A42C3C717689BE8C0493 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E765FB411E63B92B9 
[18.18 MKey/s][Count 2^33.07][08:16][Dead 1][10.9MB]  
Key# 5 Pub:  0x020ECDB6359D41D2FD37628C718DDA9BE30E65801A88A00C3C5BDF36E7EE6ADBBA 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E7D0E6081C7E0E865 
[18.18 MKey/s][Count 2^34.45][21:27][Dead 4][20.7MB]  
Key# 6 Pub:  0x0322DD52FCFA3A4384F0AFF199D019E481D335923D8C00BADAD42FFFC80AF8FCF0 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EC737344CA673CE28 
[18.18 MKey/s][Count 2^33.50][11:06][Dead 0][13.4MB]  
Key# 7 Pub:  0x02DB4F1B249406B8BD662F78CBA46F5E90E20FE27FC69D0FBAA2F06E6E50E53669 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E38160DA9EBEAECD7 
[18.17 MKey/s][Count 2^33.20][09:02][Dead 1][11.6MB]  
Key# 8 Pub:  0x023BD0330D7381917F8860F1949ACBCCFDC7863422EEE2B6DB7EDD551850196687 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E79D808CAB1DECF8D 
[18.18 MKey/s][Count 2^32.25][04:40][Dead 0][7.2MB]  
Key# 9 Pub:  0x02332A02CA42C481EAADB7ADB97DF89033B23EA291FDA809BEA3CE5C3B73B20C49 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E54CAD3CFBC2A9C2B 
[18.18 MKey/s][Count 2^32.75][06:38][Dead 1][9.3MB]  
Key#10 Pub:  0x02513981849DE1A1327DEF34B51F5011C5070603CA22E6D868263CB7C908525F0C 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E0D5ECCC38D0230E6 
[18.18 MKey/s][Count 2^33.63][12:12][Dead 1][14.3MB]  
Key#11 Pub:  0x03D4E6FA664BD75A508C0FF0ED6F2C52DA2ADD7C3F954D9C346D24318DBD2ECFC6 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EE3579364DE939B0C 
[18.18 MKey/s][Count 2^33.51][11:12][Dead 0][13.5MB]  
Key#12 Pub:  0x0356B468963752924DBF56112633DC57F07C512E3671A16CD7375C58469164599D 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E7C43B8E079AE7278 
[18.16 MKey/s][Count 2^33.89][14:33][Dead 3][16.1MB]  
Key#13 Pub:  0x03D5BE7C653773CEE06A238020E953CFCD0F22BE2D045C6E5B4388A3F11B4586CB 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E8D63EF128EF66B42 
[18.18 MKey/s][Count 2^34.10][16:51][Dead 5][17.7MB]  
Key#14 Pub:  0x02B1985389D8AB680DEDD67BBA7CA781D1A9E6E5974AAD2E70518125BAD5783EB5 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E2452DD26BC983CD5 
[18.18 MKey/s][Count 2^33.92][14:55][Dead 3][16.3MB]  
Key#15 Pub:  0x0355B95BEF84A6045A505D015EF15E136E0A31CC2AA00FA4BCA62E5DF215EE981B 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E7AD38337C7F173C7 

Done: Total time 03:07:38 

On an i7-4770 with a GTX 1050 Ti (GPU only):

C:\C++\Kangaroo\VC_CUDA10\x64\Release>Kangaroo.exe -t 0 -gpu ..\..\in.txt
Kangaroo v1.0
Start:49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E0000000000000000
Stop :49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EFFFFFFFFFFFFFFFF
Keys :16
Number of CPU thread: 0
Range width: 2^64
Number of random walk: 2^18.58 (Max DP=11)
DP size: 11 [0xFFE0000000000000]
GPU: GPU #0 GeForce GTX 1050 Ti (6x128 cores) Grid(12x256) (45.0 MB used)
SolveKeyGPU Thread GPU#0: creating kangaroos...
SolveKeyGPU Thread GPU#0: 2^18.58 kangaroos
[115.23 MKey/s][GPU 115.23 MKey/s][Count 2^33.52][Dead 5][02:02][463.9MB]
Key# 0 Pub:  0x0259A3BFDAD718C9D3FAC7C187F1139F0815AC5D923910D516E186AFDA28B221DC
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EBB3EF3883C1866D4
[115.22 MKey/s][GPU 115.22 MKey/s][Count 2^32.41][Dead 1][01:01][218.3MB]
Key# 1 Pub:  0x02A50FBBB20757CC0E9C41C49DD9DF261646EE7936272F3F68C740C9DA50D42BCD
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EB5ABC43BEBAD3207
[115.13 MKey/s][GPU 115.13 MKey/s][Count 2^32.99][Dead 0][01:29][323.5MB]
Key# 2 Pub:  0x0304A49211C0FE07C9F7C94695996F8826E09545375A3CF9677F2D780A3EB70DE3
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E5698AAAB6CAC52B3
[115.21 MKey/s][GPU 115.21 MKey/s][Count 2^32.66][Dead 0][01:12][258.7MB]
Key# 3 Pub:  0x030B39E3F26AF294502A5BE708BB87AEDD9F895868011E60C1D2ABFCA202CD7A4D
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E59C839258C2AD7A0
[115.22 MKey/s][GPU 115.22 MKey/s][Count 2^33.26][Dead 1][01:47][389.7MB]
Key# 4 Pub:  0x02837A31977A73A630C436E680915934A58B8C76EB9B57A42C3C717689BE8C0493
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E765FB411E63B92B9
[114.51 MKey/s][GPU 114.51 MKey/s][Count 2^34.70][Dead 8][04:42][1044.9MB]
Key# 5 Pub:  0x020ECDB6359D41D2FD37628C718DDA9BE30E65801A88A00C3C5BDF36E7EE6ADBBA
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E7D0E6081C7E0E865
[115.21 MKey/s][GPU 115.21 MKey/s][Count 2^32.00][Dead 1][47s][164.7MB]
Key# 6 Pub:  0x0322DD52FCFA3A4384F0AFF199D019E481D335923D8C00BADAD42FFFC80AF8FCF0
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EC737344CA673CE28
[115.21 MKey/s][GPU 115.21 MKey/s][Count 2^32.12][Dead 0][51s][179.6MB]
Key# 7 Pub:  0x02DB4F1B249406B8BD662F78CBA46F5E90E20FE27FC69D0FBAA2F06E6E50E53669
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E38160DA9EBEAECD7
[115.06 MKey/s][GPU 115.06 MKey/s][Count 2^33.88][Dead 5][02:42][595.5MB]
Key# 8 Pub:  0x023BD0330D7381917F8860F1949ACBCCFDC7863422EEE2B6DB7EDD551850196687
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E79D808CAB1DECF8D
[115.23 MKey/s][GPU 115.23 MKey/s][Count 2^31.71][Dead 0][39s][136.2MB]
Key# 9 Pub:  0x02332A02CA42C481EAADB7ADB97DF89033B23EA291FDA809BEA3CE5C3B73B20C49
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E54CAD3CFBC2A9C2B
[83.23 MKey/s][GPU 83.23 MKey/s][Count 2^30.23][Dead 0][17s][51.3MB]
Key#10 Pub:  0x02513981849DE1A1327DEF34B51F5011C5070603CA22E6D868263CB7C908525F0C
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E0D5ECCC38D0230E6
[114.85 MKey/s][GPU 114.85 MKey/s][Count 2^34.98][Dead 20][05:41][1269.3MB]
Key#11 Pub:  0x03D4E6FA664BD75A508C0FF0ED6F2C52DA2ADD7C3F954D9C346D24318DBD2ECFC6
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EE3579364DE939B0C
[115.22 MKey/s][GPU 115.22 MKey/s][Count 2^33.99][Dead 2][02:54][642.5MB]
Key#12 Pub:  0x0356B468963752924DBF56112633DC57F07C512E3671A16CD7375C58469164599D
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E7C43B8E079AE7278
[115.11 MKey/s][GPU 115.11 MKey/s][Count 2^33.12][Dead 0][01:37][351.9MB]
Key#13 Pub:  0x03D5BE7C653773CEE06A238020E953CFCD0F22BE2D045C6E5B4388A3F11B4586CB
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E8D63EF128EF66B42
[115.22 MKey/s][GPU 115.22 MKey/s][Count 2^31.36][Dead 0][32s][108.8MB]
Key#14 Pub:  0x02B1985389D8AB680DEDD67BBA7CA781D1A9E6E5974AAD2E70518125BAD5783EB5
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E2452DD26BC983CD5
[115.22 MKey/s][GPU 115.22 MKey/s][Count 2^31.49][Dead 0][34s][118.0MB]
Key#15 Pub:  0x0355B95BEF84A6045A505D015EF15E136E0A31CC2AA00FA4BCA62E5DF215EE981B
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E7AD38337C7F173C7

Done: Total time 29:44

Articles

• [1] Using Equivalence Classes to Accelerate Solvingthe Discrete Logarithm Problem in a Short Interval https://www.iacr.org/archive/pkc2010/60560372/60560372.pdf