Mark1 is a high-performance, parallelized Pollard's Kangaroo algorithm implementation for solving ECDLP (Elliptic Curve Discrete Logarithm Problem) on the secp256k1 curve. It features wrap-aware kangaroos, configurable jump sizes, live statistics, loop detection, and restart counters.
Based on the original Pollard's Kangaroo algorithm Uses SECP256K1 implementation from JeanLucPons/VanitySearch Inspired by various cryptographic research papers
- Optimized AVX2 Implementation: Leverages modern CPU instructions for maximum performance
- Parallel Processing: Utilizes OpenMP for multi-threaded execution
- Smart Kangaroo Management:
- Configurable jump table size (
--kparameter) - Wrap-around detection for out-of-range kangaroos
- Brent's loop detection algorithm
- Restart counters for stuck kangaroos
- Configurable jump table size (
- Efficient DP Storage:
- Compact representation of distinguished points
- SIMD-accelerated Bloom filter for quick lookups
- Configurable DP bits (
--dp_bits)
- Live Statistics: Real-time monitoring of hops, speed, and restarts
- Range Support: Solves for arbitrary ranges (
--rangeparameter) - Result Verification: Automatically verifies found private keys
--range START:END: Range to search (decimal or hex with 0x prefix)
--pubkey PUBKEY: Target public key (compressed or uncompressed)
--dp_point N: Number of distinguished points to generate (auto-calculated if omitted)
--dp_bits N: Distinguished point mask bits (default: 12)
--k N: Jump table size (default: range_bits/2)
--ram N: RAM limit in GB (default: 16)
--save-dp: Save distinguished points to DP.bin
--load-dp: Load distinguished points from DP.bin. You can skip Phase1
Example performance on modern CPUs:
| CPU Model | Threads | Speed (Hops/s) |
|---|---|---|
| Ryzen 9 7945HX | 32 | ~160 MH/s |
| Ryzen 7 5800H | 16 | ~65 MH/s |
Below is an example of Mark1 in action, solving a Satoshi puzzle:
55 bits
./Mark1 --range 18014398509481983:36028797018963967 --pubkey 0385a30d8413af4f8f9e6312400f2d194fe14f02e719b24c3f83bf1fd233a8f963 --dp_point 500000 --dp_bits 10 --ram 32
=========== Phase-0: RAM summary ===========
DP table : 26.1Mb ( 500000 / 666667 slots, load 75.00% )
Bloom : 977Kb
--------------------------------------------
Total : 27.0Mb
========== Phase-1: Building traps =========
Unique traps: 500000/500000 (done)
=========== Phase-2: Kangaroos =============
Speed: 35.91 MH/s | Hops: 179568640 | Restart wild: 0 | Time: 0:0:5
============= Phase-3: Result ==============
Private key : 0x000000000000000000000000000000000000000000000000006ABE1F9B67E114
Found by thr: 17
Wild wraps : 0 [no wrap]
Wild restart: 0
Total time : 00:00:01.190
Private key : saved to FOUND.txt60 bits
./Mark1 --range 576460752303423487:1152921504606846975 --pubkey 0348e843dc5b1bd246e6309b4924b81543d02b16c8083df973a89ce2c7eb89a10d --dp_point 600000 --dp_bits 8 --ram 32
=========== Phase-0: RAM summary ===========
DP table : 31.3Mb ( 600000 / 800000 slots, load 75.00% )
Bloom : 1.14Mb
--------------------------------------------
Total : 32.4Mb
========== Phase-1: Building traps =========
Unique traps: 600000/600000 (done)
=========== Phase-2: Kangaroos =============
Speed: 126.51 MH/s | Hops: 632553472 | Restart wild: 0 | Time: 0:0:5
============= Phase-3: Result ==============
Private key : 0x0000000000000000000000000000000000000000000000000FC07A1825367BBE
Found by thr: 3
Wild wraps : 0 [no wrap]
Wild restart: 0
Total time : 00:00:04.096
Private key : saved to FOUND.txt75 bits
./Mark1 --range 18889465931478580854783:37778931862957161709567 --pubkey 03726b574f193e374686d8e12bc6e4142adeb06770e0a2856f5e4ad89f66044755 --dp_point 200000000 --dp_bits 8 --ram 32
=========== Phase-0: RAM summary ===========
DP table : 10.2Gb ( 200000000 / 268435456 slots, load 74.51% )
Bloom : 381Mb
--------------------------------------------
Total : 10.6Gb
========== Phase-1: Building traps =========
Unique traps: 200000000/200000000 (done)
=========== Phase-2: Kangaroos =============
Speed: 109.95 MH/s | Hops: 133433945344 | Restart wild: 0 | Time: 0:14:05
============= Phase-3: Result ==============
Private key : 0x0000000000000000000000000000000000000000000004C5CE114686A1336E07
Found by thread: 12
Wild wraps : 0 [no wrap]
Wild restart: 0
Total time : 00:14:06.325
Private key saved to FOUND.txt80 bits
./Mark1 --range 604462909807314587353087:1208925819614629174706175 --pubkey 037e1238f7b1ce757df94faa9a2eb261bf0aeb9f84dbf81212104e78931c2a19dc --dp_point 500000000 --dp_bits 12 --ram 32
=========== Phase-0: RAM summary ===========
DP table : 25.5Gb ( 500000000 / 666666667 slots, load 75.00% )
Bloom : 954Mb
--------------------------------------------
Total : 26.4Gb
========== Phase-1: Building traps =========
Unique traps: 500000000/500000000 (done)
=========== Phase-2: Kangaroos =============
Speed: 103.94 MH/s | Hops: 364681496320 | Restart wild: 0 | Time: 0:38:10
============= Phase-3: Result ==============
Private key : 0x00000000000000000000000000000000000000000000EA1A5C66DCC11B5AD180
Found by thread: 6
Wild wraps : 0 [no wrap]
Wild restart: 0
Private key saved to FOUND.txtThe example is given for a range of 55 bits, 32 processor threads and 500000 traps.
Added a little utility for analyzing DP traps. Example:
./DP-analyzer --segments 32 --range 18014398509481983:36028797018963967 --dp-file DP.binOutput below
root@ubuntu:/home/ubuntu/Mark1# ./DP-analyzer --segments 32 --range 18014398509481983:36028797018963967 --dp-file DP.bin
DP traps distribution over 32 segments:
Seg | Count | %tot | bits | minGap | p10Gap | medGap | p90Gap | avgGap | maxGap | density | k_rec | skew
-------------------------------------------------------------------------------------------------------------------------------------------------
0 | 155318 | 3.11% | 50 | 2 | 286335376 |2041413870 |8085569486 |3623099368 |3552218984021 | 0.000000 | 15 |979.436534
1 | 156796 | 3.14% | 50 | 2 | 266774533 |1931183793 |7883611228 |3590341941 |4399117378806 | 0.000000 | 15 |1224.264182
2 | 155609 | 3.11% | 50 | 2 | 283131936 |1990537296 |7906291154 |3617709244 |4000365272898 | 0.000000 | 15 |1104.773019
3 | 156448 | 3.13% | 50 | 2 | 280172024 |1999201034 |7955045112 |3598274225 |5401529215151 | 0.000000 | 15 |1500.144404
4 | 157073 | 3.14% | 50 | 2 | 281980083 |2005302274 |7973237048 |3583946403 |3804280200361 | 0.000000 | 15 |1060.477984
5 | 156256 | 3.13% | 50 | 2 | 277359734 |1988458088 |7903342526 |3600276614 |3258375964972 | 0.000000 | 15 |904.034895
6 | 155787 | 3.12% | 50 | 2 | 278801873 |2005488092 |7952784062 |3601435538 |4232977379595 | 0.000000 | 15 |1174.358364
7 | 156567 | 3.13% | 50 | 2 | 270949436 |1949770794 |7802611769 |3595552606 |4947136280444 | 0.000000 | 15 |1374.904297
8 | 156281 | 3.13% | 50 | 2 | 278083606 |2003415064 |7998123974 |3602078945 |4628010601319 | 0.000000 | 15 |1283.816539
9 | 155915 | 3.12% | 50 | 2 | 274125618 |1945121589 |7852976100 |3610616291 |4159899322423 | 0.000000 | 15 |1151.129994
10 | 155883 | 3.12% | 50 | 2 | 279524569 |1987651282 |7871576928 |3611356782 |4693611330708 | 0.000000 | 15 |1298.680872
11 | 156528 | 3.13% | 50 | 2 | 271361466 |1968998187 |7883254958 |3596483266 |4696727578309 | 0.000000 | 15 |1304.922267
12 | 156481 | 3.13% | 50 | 2 | 273464370 |1965471699 |7780065510 |3597563569 |4284650639922 | 0.000000 | 15 |1189.986777
13 | 156187 | 3.12% | 50 | 2 | 276673633 |2005537281 |7925947878 |3604354303 |4901598490295 | 0.000000 | 15 |1358.910286
14 | 156310 | 3.13% | 50 | 2 | 277530934 |1998481292 |7900271938 |3601452747 |4683570121239 | 0.000000 | 15 |1299.466909
15 | 156350 | 3.13% | 50 | 2 | 285419591 |2009611626 |7897409630 |3600520356 |3215995680395 | 0.000000 | 15 |892.203027
16 | 155975 | 3.12% | 50 | 2 | 281152998 |2015756288 |8052479864 |3609225694 |2890969052050 | 0.000000 | 15 |799.994257
17 | 156031 | 3.12% | 50 | 2 | 277374484 |1995540443 |7886524837 |3607952486 |4777993680880 | 0.000000 | 15 |1323.295068
18 | 156521 | 3.13% | 50 | 2 | 283481766 |1996747242 |7916935052 |3596639316 |7571021838220 | 0.000000 | 15 |2104.026714
19 | 156573 | 3.13% | 50 | 2 | 275178276 |1965786740 |7804236786 |3595406356 |4832049039431 | 0.000000 | 15 |1342.950742
20 | 155969 | 3.12% | 50 | 2 | 288375244 |2013886639 |8073247333 |3609002012 |4266529273273 | 0.000000 | 15 |1181.190883
21 | 156329 | 3.13% | 50 | 2 | 274246703 |1975993583 |7995808487 |3601043691 |2667023143930 | 0.000000 | 15 |739.625045
22 | 156004 | 3.12% | 50 | 2 | 286017612 |2012492985 |8098438698 |3608512336 |4574693881646 | 0.000000 | 15 |1266.750657
23 | 156320 | 3.13% | 50 | 2 | 293534665 |2077601990 |8104920033 |3601236410 |5457974825091 | 0.000000 | 15 |1514.583596
24 | 155814 | 3.12% | 50 | 2 | 266874628 |1928124778 |7843863288 |3612965012 |4798497317200 | 0.000000 | 15 |1327.132795
25 | 156340 | 3.13% | 50 | 2 | 279685957 |1986149024 |7864819970 |3600785268 |3723418006343 | 0.000000 | 15 |1033.057221
26 | 156431 | 3.13% | 50 | 2 | 271927490 |1948407910 |7804697457 |3598703513 |4434011671808 | 0.000000 | 15 |1231.113637
27 | 156475 | 3.13% | 50 | 2 | 275642613 |1963488087 |7936075680 |3597702173 |4435852977078 | 0.000000 | 15 |1231.968369
28 | 155783 | 3.12% | 50 | 2 | 272438208 |1973809063 |7964625118 |3613679903 |3462464465466 | 0.000000 | 15 |957.154723
29 | 156833 | 3.14% | 50 | 2 | 286945505 |2026290252 |8056189891 |3589481788 |4220043502566 | 0.000000 | 15 |1174.669290
30 | 155943 | 3.12% | 50 | 2 | 272663138 |1958078456 |7778688670 |3609979876 |5436255377986 | 0.000000 | 15 |1504.896312
31 | 156716 | 3.13% | 50 | 2 | 274699741 |1972006372 |7855666186 |3592149293 |6174146753199 | 0.000000 | 15 |1717.789018
Empty segments: 0 Min/Max/Mean/Var count: 155318/157073/156245.19/143979.21
Requirements:
- Ubuntu Linux or WSL2 for Windows
- GCC 9+ or Clang 10+
- OpenMP support
- AVX2 capable CPU
git clone https://github.com/yourusername/Mark1.git
cd Mark1
**Mark1 compiling**
g++ Mark1.cpp Int.cpp SECP256K1.cpp Point.cpp Random.cpp IntMod.cpp IntGroup.cpp Timer.cpp -O3 -march=native -funroll-loops -ftree-vectorize -fstrict-aliasing -fno-semantic-interposition -fvect-cost-model=unlimited -fno-trapping-math -fipa-ra -fipa-modref -flto -fassociative-math -fopenmp -mavx2 -mbmi2 -madx -std=c++17 -fopenmp -pthread -o Mark1
**DP-analyzer compiling**
g++ DP-analyzer.cpp Int.cpp -O3 -march=native -funroll-loops -ftree-vectorize -fstrict-aliasing -fno-semantic-interposition -fvect-cost-model=unlimited -fno-trapping-math -fipa-ra -fipa-modref -flto -fassociative-math -fopenmp -mavx2 -mbmi2 -madx -std=c++17 -fopenmp -pthread -o DP-analyzer
V1.4: Added DP analyzer.
V1.3: Full SSD rework: double hashing, MAX_LOAD=0.5, bloom filter size increasing (10 bit), batched inserting/checking, MADV_SEQUENTIAL. Thanks OpenAI for ChatGPT helping to solve these problems. This is amazing!
V1.2: SSD rework. Dp table storing on SSD, instead of RAM. A few security updates and speed increasing.
V1.1: Added save and load distinguished points (DP) from file (DP.bin). This feature was coded by NoMachine.
V1.0: Release
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