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Baby Step Giant Step for SECPK1

A simple Baby Step Giant Step program for SecpK1.

Structure of the input file:

  • All values are in hex format
  • Public keys can be given either in compressed or uncompressed format
Babystep size
Start range
End range
Key #1
Key #2
...

ex

40000000
49dccfd96dc5df56487436f5a1b18c4f5d34f65ddb48cb5e0000000000000000
49dccfd96dc5df56487436f5a1b18c4f5d34f65ddb48cb5effffffffffffffff
0459A3BFDAD718C9D3FAC7C187F1139F0815AC5D923910D516E186AFDA28B221DC994327554CED887AAE5D211A2407CDD025CFC3779ECB9C9D7F2F1A1DDF3E9FF8
0335BB25364370D4DD14A9FC2B406D398C4B53C85BE58FCC7297BD34004602EBEC

How it works

It uses a hash table (25bit hash) to store the baby steps. 2^30 baby steps is about 9GB (we do not store full point, only a part of it, false collisions are handled later). Here is a brief description of the algoritm:

We have to solve P = k.G, we know that k lies in the range ]k1,k2], G is the SecpK1 generator point.

 # Baby Step number
 # With enough memory, the best choice is m = floor(sqrt(k2-k1)) for a single key
 m = Baby Step number
 Compute a table of [G,2.G,3.G,..,b.G,...,m.G]
 S = P - k1.G
 found = false
 step = 0
 while not found and step<(k2-k1) {
   if S is in the table {
     b = Index of S in the table
     found = true
   }
   if not found {
     # Giant step
     S = S - m.G
     step = step + m
   }
 }
 k = k1 + step + b

Example of usage

On a Xeon X5647 2.93GHz with 12GB of RAM (Ubuntu 18.04)

Input file: in.txt

40000000
49dccfd96dc5df56487436f5a1b18c4f5d34f65ddb48cb5e0000000000000000
49dccfd96dc5df56487436f5a1b18c4f5d34f65ddb48cb5effffffffffffffff
0459A3BFDAD718C9D3FAC7C187F1139F0815AC5D923910D516E186AFDA28B221DC994327554CED887AAE5D211A2407CDD025CFC3779ECB9C9D7F2F1A1DDF3E9FF8
04A50FBBB20757CC0E9C41C49DD9DF261646EE7936272F3F68C740C9DA50D42BCD3E48440249D6BC78BC928AA52B1921E9690EBA823CBC7F3AF54B3707E6A73F34
0404A49211C0FE07C9F7C94695996F8826E09545375A3CF9677F2D780A3EB70DE3BD05357CAF8340CB041B1D46C5BB6B88CD9859A083B0804EF63D498B29D31DD1
040B39E3F26AF294502A5BE708BB87AEDD9F895868011E60C1D2ABFCA202CD7A4D1D18283AF49556CF33E1EA71A16B2D0E31EE7179D88BE7F6AA0A7C5498E5D97F
04837A31977A73A630C436E680915934A58B8C76EB9B57A42C3C717689BE8C0493E46726DE04352832790FD1C99D9DDC2EE8A96E50CAD4DCC3AF1BFB82D51F2494
040ECDB6359D41D2FD37628C718DDA9BE30E65801A88A00C3C5BDF36E7EE6ADBBAD71A2A535FCB54D56913E7F37D8103BA33ED6441D019D0922AC363FCC792C29A
0422DD52FCFA3A4384F0AFF199D019E481D335923D8C00BADAD42FFFC80AF8FCF038F139D652842243FC841E7C5B3E477D901F88C5AB0B88EE13D80080E413F2ED
04DB4F1B249406B8BD662F78CBA46F5E90E20FE27FC69D0FBAA2F06E6E50E536695DF83B68FD0F396BB9BFCF6D4FE312F32A43CF3FA1FE0F81DF70C877593B64E0
043BD0330D7381917F8860F1949ACBCCFDC7863422EEE2B6DB7EDD551850196687528B6D2BC0AA7A5855D168B26C6BAF9DDCD04B585D42C7B9913F60421716D37A
04332A02CA42C481EAADB7ADB97DF89033B23EA291FDA809BEA3CE5C3B73B20C49C410D1AD42A9247EB8FF217935C9E28411A08B325FBF28CC2AF8182CE2B5CE38
04513981849DE1A1327DEF34B51F5011C5070603CA22E6D868263CB7C908525F0C19EBA6BD2A8DCF651E4342512EDEACB6EA22DA323A194E25C6A1614ABD259BC0
04D4E6FA664BD75A508C0FF0ED6F2C52DA2ADD7C3F954D9C346D24318DBD2ECFC6805511F46262E10A25F252FD525AF1CBCC46016B6CD0A7705037364309198DA1
0456B468963752924DBF56112633DC57F07C512E3671A16CD7375C58469164599D1E04011D3E9004466C814B144A9BCB7E47D5BACA1B90DA0C4752603781BF5873
04D5BE7C653773CEE06A238020E953CFCD0F22BE2D045C6E5B4388A3F11B4586CBB4B177DFFD111F6A15A453009B568E95798B0227B60D8BEAC98AF671F31B0E2B
04B1985389D8AB680DEDD67BBA7CA781D1A9E6E5974AAD2E70518125BAD5783EB5355F46E927A030DB14CF8D3940C1BED7FB80624B32B349AB5A05226AF15A2228
0455B95BEF84A6045A505D015EF15E136E0A31CC2AA00FA4BCA62E5DF215EE981B3B4D6BCE33718DC6CF59F28B550648D7E8B2796AC36F25FF0C01F8BC42A16FD9

Result:

pons@linpons:~/BSGS$ ./bsgs in.txt 
BSGS v1.0
BabyStep:0x40000000 (2^30.00)
Start:49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E0000000000000000
Stop :49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EFFFFFFFFFFFFFFFF
Keys :16
Number of CPU thread: 8
BabyStep Thread 0: 0x1 -> 0x8000000
BabyStep Thread 3: 0x18000001 -> 0x20000000
BabyStep Thread 1: 0x8000001 -> 0x10000000
BabyStep Thread 2: 0x10000001 -> 0x18000000
BabyStep Thread 4: 0x20000001 -> 0x28000000
BabyStep Thread 5: 0x28000001 -> 0x30000000
BabyStep Thread 6: 0x30000001 -> 0x38000000
BabyStep Thread 7: 0x38000001 -> 0x40000000
[2.05 MKey/s][Cnt 2^30.00][08:38][8959.9MB]  
Sort Thread 0: 00000000 -> 00400000
Sort Thread 1: 00400000 -> 00800000
Sort Thread 2: 00800000 -> 00C00000
Sort Thread 3: 00C00000 -> 01000000
Sort Thread 7: 01C00000 -> 02000000
Sort Thread 6: 01800000 -> 01C00000
Sort Thread 4: 01000000 -> 01400000
Sort Thread 5: 01400000 -> 01800000
[2.51 MSort/s][Cnt 2^25.00][13s][8959.9MB]  
GiantStep Thread 1: 49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E2000000000000000
GiantStep Thread 0: 49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E0000000000000000
GiantStep Thread 2: 49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E4000000000000000
GiantStep Thread 3: 49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E6000000000000000
GiantStep Thread 4: 49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E8000000000000000
GiantStep Thread 5: 49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EA000000000000000
GiantStep Thread 6: 49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EC000000000000000
GiantStep Thread 7: 49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EE000000000000000
[13.67 MKey/s][Cnt 2^33.76][17:46][8959.9MB]  
Key# 0 Pub:  0x0259A3BFDAD718C9D3FAC7C187F1139F0815AC5D923910D516E186AFDA28B221DC 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EBB3EF3883C1866D4 
[13.68 MKey/s][Cnt 2^33.43][14:07][8959.9MB]  
Key# 1 Pub:  0x02A50FBBB20757CC0E9C41C49DD9DF261646EE7936272F3F68C740C9DA50D42BCD 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EB5ABC43BEBAD3207 
[13.68 MKey/s][Cnt 2^33.49][14:44][8959.9MB]  
Key# 2 Pub:  0x0304A49211C0FE07C9F7C94695996F8826E09545375A3CF9677F2D780A3EB70DE3 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E5698AAAB6CAC52B3 
[13.68 MKey/s][Cnt 2^33.68][16:49][8959.9MB]  
Key# 3 Pub:  0x030B39E3F26AF294502A5BE708BB87AEDD9F895868011E60C1D2ABFCA202CD7A4D 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E59C839258C2AD7A0 
[13.64 MKey/s][Cnt 2^33.48][14:36][8959.9MB]  
Key# 4 Pub:  0x02837A31977A73A630C436E680915934A58B8C76EB9B57A42C3C717689BE8C0493 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E765FB411E63B92B9 
[13.66 MKey/s][Cnt 2^33.86][19:00][8959.9MB]  
Key# 5 Pub:  0x020ECDB6359D41D2FD37628C718DDA9BE30E65801A88A00C3C5BDF36E7EE6ADBBA 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E7D0E6081C7E0E865 
[13.65 MKey/s][Cnt 2^31.84][04:41][8959.9MB]  
Key# 6 Pub:  0x0322DD52FCFA3A4384F0AFF199D019E481D335923D8C00BADAD42FFFC80AF8FCF0 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EC737344CA673CE28 
[13.68 MKey/s][Cnt 2^33.59][15:41][8959.9MB]  
Key# 7 Pub:  0x02DB4F1B249406B8BD662F78CBA46F5E90E20FE27FC69D0FBAA2F06E6E50E53669 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E38160DA9EBEAECD7 
[13.65 MKey/s][Cnt 2^33.69][16:53][8959.9MB]  
Key# 8 Pub:  0x023BD0330D7381917F8860F1949ACBCCFDC7863422EEE2B6DB7EDD551850196687 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E79D808CAB1DECF8D 
[13.65 MKey/s][Cnt 2^33.37][13:35][8959.9MB]  
Key# 9 Pub:  0x02332A02CA42C481EAADB7ADB97DF89033B23EA291FDA809BEA3CE5C3B73B20C49 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E54CAD3CFBC2A9C2B 
[13.68 MKey/s][Cnt 2^32.74][08:42][8959.9MB]  
Key#10 Pub:  0x02513981849DE1A1327DEF34B51F5011C5070603CA22E6D868263CB7C908525F0C 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E0D5ECCC38D0230E6 
[13.68 MKey/s][Cnt 2^30.73][02:10][8959.9MB]  
Key#11 Pub:  0x03D4E6FA664BD75A508C0FF0ED6F2C52DA2ADD7C3F954D9C346D24318DBD2ECFC6 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5EE3579364DE939B0C 
[13.67 MKey/s][Cnt 2^33.82][18:27][8959.9MB]  
Key#12 Pub:  0x0356B468963752924DBF56112633DC57F07C512E3671A16CD7375C58469164599D 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E7C43B8E079AE7278 
[13.66 MKey/s][Cnt 2^32.76][08:51][8959.9MB]  
Key#13 Pub:  0x03D5BE7C653773CEE06A238020E953CFCD0F22BE2D045C6E5B4388A3F11B4586CB 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E8D63EF128EF66B42 
[13.66 MKey/s][Cnt 2^31.11][02:49][8959.9MB]  
Key#14 Pub:  0x02B1985389D8AB680DEDD67BBA7CA781D1A9E6E5974AAD2E70518125BAD5783EB5 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E2452DD26BC983CD5 
[13.67 MKey/s][Cnt 2^33.76][17:42][8959.9MB]  
Key#15 Pub:  0x0355B95BEF84A6045A505D015EF15E136E0A31CC2AA00FA4BCA62E5DF215EE981B 
       Priv: 0x49DCCFD96DC5DF56487436F5A1B18C4F5D34F65DDB48CB5E7AD38337C7F173C7 

Done: Total time 03:35:53