Pollard's kangaroo ECDLP solver

[j2002ba2]

Jumps (the points) are the same, only their private keys are different;

instead of using, for example, 2543*G as jump, you use (2543*32)*G', where G' = inv(32)*G

It sounds quite useless to me.

To get the benefits of kangaroo algorithm, you need to use a specific mean step.

G' makes all the steps multiple of 32, visiting only 1/32 of the points. This is instant sqrt(32) times slowdown.

Why you are visiting only 1/32 of the points? You are working in a wider interval, then it is normal to use larger jumps.

The optimal would be increase the length of the jumps by sqrt(32) instead of 32, but you have to increase it.

If you change the jumps old DPs are useless.

[arulbero]

If you change the jumps old DPs are useless.

I didn't change the jumps, I changed only the interval. In this interval the points are more by a factor of 32. And I moved the point P in this new interval.

[j2002ba2]

If you change the jumps old DPs are useless.

And I moved the point P in this new interval.

How?

[arulbero]

If you change the jumps old DPs are useless.

And I moved the point P in this new interval.

How?

I moved P in the interval C in this way: P -> P' = inv(32)*P

To be more precise: the wide of the interval is the same (2^119*G' = 2^114*G) as the old interval, and we use the same jumps (that look like they were x32 bigger, but they are not) and we perform the same number of steps for each path (2^25), then we shouldn't go out of the interval.

The points in this interval are closer (the distance between 2 consecutive points is (1/32)*G instead of G)

But you are right on a point: if we use the old jumps, from the point of view of G' they are all multiples of 32, each single path could visit only 1/32 of the points; in this case even if we used many kangaroos in parallel we would have to do more steps!      

[Jean_Luc]

It is necessary to use same jumps otherwise path are incompatible.
And the mean has also to be controlled.
Implementing changing of G is rather an heavy task so I would like to have at least an estimation of the loss due to the fact that all paths of new DP will have all points multiple of 32.
We will probably also use DP28 or DP27 for #120

[arulbero]

It is necessary to use same jumps otherwise path are incompatible.
And the mean has also to be controlled.
Implementing changing of G is rather an heavy task so I would like to have at least an estimation of the loss due to the fact that all paths of new DP will have all points multiple of 32.

I will do some tests tomorrow, but I fear that it is not worth it. For now don't work on it.

The mean is correct, the jumps are the same but the main point is:

each path must have the possibility to reach any point in the interval to maximize the probability, but in this case each path could reach only 1/32 of the points.

For example, only the paths starting from a multiple of 32 has the chance to collide with a old DPs, all the others haven't.

[brainless]

It is necessary to use same jumps otherwise path are incompatible.
And the mean has also to be controlled.
Implementing changing of G is rather an heavy task so I would like to have at least an estimation of the loss due to the fact that all paths of new DP will have all points multiple of 32.
We will probably also use DP28 or DP27 for #120

finally you agree, to go back at normal work for 120 as worked for 115, no implements, no changes, no new developments,

[j2002ba2]

If you change the jumps old DPs are useless.

And I moved the point P in this new interval.

How?

I moved P in the interval C in this way: P -> P' = inv(32)*P

This would work properly only when the private key of P is zero mod 32. P=k*G, k=0 (mod 32).

Otherwise the point is guaranteed to not be in the interval.

The probability of being in the new interval is 1/32, which is about 3%. In all other 97% the algorithm would fail to find a point in any reasonable time.

If you somehow can deterministically move points from bigger interval to smaller, then no kangaroos are needed, ECDLP is solved. In the 1/32 case - in just 8 steps (!!!).

[Etar]

What i have done using proposed arulbero method.. I solve pazzle 59 bit and save work. Then  i tame all wild DPs with previous private key in file.
And multiply distance of each DP by 32
After that i compile kangaroo.exe where G*inv(32)= (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
I can`t say if new wild DP collide old tame from workfile or it is collsion with both new DPs but here is some test with pazzle 64bit

Code:

DPs JUST MOVED TO NEW INTERVAL WITHOUT SHIFTING PUB
P=P/32
Start:10000000000000000
Stop :1FFFFFFFFFFFFFFFF
Range width: 2^64
Expected operations: 2^33.08
DP size: 15 [0xFFFE000000000000]
[15.25 MK/s][GPU 0.00 MK/s][Count 2^32.37][Dead 0][06:56 (Avg 09:53)][9.2/30.2MB]
Key# 0 [1S]Pub:  0x0299A240D5FD67F0F9DBC558AF072E26B285B5DF1FACD1E9509A168A9523F53958
       Priv: 0x1A838B13505B26867
Done: Total time 06:56

REPEAT FOR MORE TEST
DPs JUST MOVED TO NEW INTERVAL WITHOUT SHIFTING PUB
P=P/32
Start:10000000000000000
Stop :1FFFFFFFFFFFFFFFF
Keys :1
Range width: 2^64
DP size: 15 [0xFFFE000000000000]
[15.27 MK/s][GPU 0.00 MK/s][Count 2^32.43][Dead 1][07:18 (Avg 09:52)][9.5/30.9MB]
Key# 0 [1S]Pub:  0x0299A240D5FD67F0F9DBC558AF072E26B285B5DF1FACD1E9509A168A9523F53958
       Priv: 0x1A838B13505B26867
Done: Total time 07:20

PUB SHIFTED AND DPs MOVED TO NEW INTERVAL
P=(P-0x10000000000000000*G)/32
Start:0
Stop :FFFFFFFFFFFFFFFF
Range width: 2^64
Expected operations: 2^33.08
DP size: 15 [0xFFFE000000000000]
[15.13 MK/s][GPU 0.00 MK/s][Count 2^33.46][Dead 1][14:35 (Avg 09:58)][15.1/42.9MB]
Key# 0 [1S]Pub:  0x02B0090246C76FA061A11AF1165F652344FDF191FBC74B4295E7DF2FEDB388B5C7
       Priv: 0xA838B13505B26867+0x10000000000000000=0x1A838B13505B26867
Done: Total time 14:37

REPEAT FOR MORE TEST
PUB SHIFTED AND DPs MOVED TO NEW INTERVAL
P=(P-0x10000000000000000*G)/32
Start:0
Stop :FFFFFFFFFFFFFFFF
Range width: 2^64
DP size: 15 [0xFFFE000000000000]
[15.21 MK/s][GPU 0.00 MK/s][Count 2^32.29][Dead 0][06:32 (Avg 09:55)][9.0/29.6MB]
Key# 0 [1S]Pub:  0x02B0090246C76FA061A11AF1165F652344FDF191FBC74B4295E7DF2FEDB388B5C7
       Priv: 0xA838B13505B26867+0x10000000000000000=0x1A838B13505B26867
Done: Total time 06:32

REPEAT FOR MORE TEST
PUB SHIFTED AND DPs MOVED TO NEW INTERVAL
P=(P-0x10000000000000000*G)/32
Start:0
Stop :FFFFFFFFFFFFFFFF
Range width: 2^64
Expected operations: 2^33.08
DP size: 15 [0xFFFE000000000000]
[15.16 MK/s][GPU 0.00 MK/s][Count 2^32.61][Dead 0][08:01 (Avg 09:57)][10.2/32.6MB]
Key# 0 [1S]Pub:  0x02B0090246C76FA061A11AF1165F652344FDF191FBC74B4295E7DF2FEDB388B5C7
       Priv: 0xA838B13505B26867+0x10000000000000000=0x1A838B13505B26867
Done: Total time 08:02

REPEAT FOR MORE TEST
PUB SHIFTED AND DPs MOVED TO NEW INTERVAL
P=(P-0x10000000000000000*G)/32
Start:0
Stop :FFFFFFFFFFFFFFFF
Range width: 2^64
Expected operations: 2^33.08
DP size: 15 [0xFFFE000000000000]
[14.86 MK/s][GPU 0.00 MK/s][Count 2^33.54][Dead 1][15:45 (Avg 10:09)][15.7/43.9MB]
Key# 0 [1S]Pub:  0x02B0090246C76FA061A11AF1165F652344FDF191FBC74B4295E7DF2FEDB388B5C7
       Priv: 0xA838B13505B26867+0x10000000000000000=0x1A838B13505B26867
Done: Total time 15:46


NORAML SOLVING WITH RIGHT G
Start:10000000000000000
Stop :1FFFFFFFFFFFFFFFF
Range width: 2^64
DP size: 15 [0xFFFE000000000000]
[20.33 MK/s][GPU 0.00 MK/s][Count 2^33.38][Dead 1][10:02 (Avg 07:25)][12.4/37.8MB]
Key# 0 [1S]Pub:  0x0230210C23B1A047BC9BDBB13448E67DEDDC108946DE6DE639BCC75D47C0216B1B
       Priv: 0x1A838B13505B26867
Done: Total time 10:02

[arulbero]

This would work properly only when the private key of P is zero mod 32. P=k*G, k=0 (mod 32).

Otherwise the point is guaranteed to not be in the interval.

The probability of being in the new interval is 1/32, which is about 3%. In all other 97% the algorithm would fail to find a point in any reasonable time.

If you somehow can deterministically move points from bigger interval to smaller, then no kangaroos are needed, ECDLP is solved. In the 1/32 case - in just 8 steps (!!!).

No, it is not like you say:

if you know that P lies in [1G,100G]

then you know that 2P lies in [2G,4G...,400G]

and that kP lies in [kG, k2G, k3G, ..., k100G]

that remains true even if k is inv(2), inv(3) and so on.

[arulbero]

What i have done using proposed arulbero method.. I solve pazzle 59 bit and save work. Then  i tame all wild DPs with previous private key in file.
And multiply distance of each DP by 32
After that i compile kangaroo.exe where G*inv(32)= (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
I can`t say if new wild DP collide old tame from workfile or it is collsion with both new DPs but here is some test with pazzle 64bit

....

Thanks, but we need a test with at least 1000 public keys, to measure the difference.

[arulbero]

Implementing changing of G is rather an heavy task so I would like to have at least an estimation of the loss due to the fact that all paths of new DP will have all points multiple of 32.
We will probably also use DP28 or DP27 for #120

If you are going to change the DP size too, it can't work, because with more steps for each path you have to lower the jumps mean.

[j2002ba2]

This would work properly only when the private key of P is zero mod 32. P=k*G, k=0 (mod 32).

Otherwise the point is guaranteed to not be in the interval.

The probability of being in the new interval is 1/32, which is about 3%. In all other 97% the algorithm would fail to find a point in any reasonable time.

If you somehow can deterministically move points from bigger interval to smaller, then no kangaroos are needed, ECDLP is solved. In the 1/32 case - in just 8 steps (!!!).

No, it is not like you say:

if you know that P lies in [1G,100G]

then you know that 2P lies in [2G,4G...,400G]

and that kP lies in [kG, k2G, k3G, ..., k100G]

that remains true even if k is inv(2), inv(3) and so on.

You are right, my mistake. The point would lay properly in the G' interval.

[Etar]

-snip-
Thanks, but we need a test with at least 1000 public keys, to measure the difference.

if JeanLuc can compile GPU version where can change G or at least version with fixed G = a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb
it will be much faster make tests.

[COBRAS]

Help me someone please:

Code:

C:\dna>gend -t 16 -d 18 -w save -ws -wi 3600  -o result.txt dataDNA2.txt
Kangaroo v1.11alpha
Start:20000000000000000
Stop :1000000000000000000
Keys :1
Number of CPU thread: 16
Range width: 2^72
Jump Avg distance: 2^36.04
Number of kangaroos: 2^14.00
Suggested DP: 18
Expected operations: 2^37.10
Expected RAM: 33.4MB
DP size: 18 [0xFFFFC00000000000]
SolveKeyCPU Thread 1: 1024 kangaroos
SolveKeyCPU Thread 4: 1024 kangaroos
SolveKeyCPU Thread 3: 1024 kangaroos
SolveKeyCPU Thread 13: 1024 kangaroos
SolveKeyCPU Thread 7: 1024 kangaroos
SolveKeyCPU Thread 11: 1024 kangaroos
SolveKeyCPU Thread 6: 1024 kangaroos
SolveKeyCPU Thread 14: 1024 kangaroos
SolveKeyCPU Thread 9: 1024 kangaroos
SolveKeyCPU Thread 8: 1024 kangaroos
SolveKeyCPU Thread 5: 1024 kangaroos
SolveKeyCPU Thread 2: 1024 kangaroos
SolveKeyCPU Thread 15: 1024 kangaroos
SolveKeyCPU Thread 12: 1024 kangaroos
SolveKeyCPU Thread 10: 1024 kangaroos
SolveKeyCPU Thread 0: 1024 kangaroos
[23.11 MK/s][GPU 0.00 MK/s][Count 2^36.09][Dead 2][01:00:08 (Avg 01:46:01)][10.5/33.5MB]
SaveWork: save..............................done [12.0 MB] [00s] Wed Jun 17 13:50:05 2020
[23.09 MK/s][GPU 0.00 MK/s][Count 2^37.09][Dead 3][02:00:20 (Avg 01:46:06)][19.0/49.2MB]
SaveWork: save..............................done [20.5 MB] [00s] Wed Jun 17 14:50:18 2020
[23.09 MK/s][GPU 0.00 MK/s][Count 2^37.67][Dead 5][03:00:23 (Avg 01:46:07)][27.5/60.1MB]
SaveWork: save..............................done [29.0 MB] [00s] Wed Jun 17 15:50:21 2020
[23.02 MK/s][GPU 0.00 MK/s][Count 2^38.08][Dead 7][04:00:26 (Avg 01:46:24)][35.9/69.4MB]
SaveWork: save..............................done [37.4 MB] [00s] Wed Jun 17 16:50:24 2020
[23.01 MK/s][GPU 0.00 MK/s][Count 2^38.40][Dead 10][04:59:21 (Avg 01:46:28)][44.2/78.0MB]

There is my mistake ?

p.s. who help me fined privkey I will gift GPU farm in BTC !

[WanderingPhilospher]

Help me someone please:

Code:

C:\dna>gend -t 16 -d 18 -w save -ws -wi 3600  -o result.txt dataDNA2.txt
Kangaroo v1.11alpha
Start:20000000000000000
Stop :1000000000000000000
Keys :1
Number of CPU thread: 16
Range width: 2^72
Jump Avg distance: 2^36.04
Number of kangaroos: 2^14.00
Suggested DP: 18
Expected operations: 2^37.10
Expected RAM: 33.4MB
DP size: 18 [0xFFFFC00000000000]
SolveKeyCPU Thread 1: 1024 kangaroos
SolveKeyCPU Thread 4: 1024 kangaroos
SolveKeyCPU Thread 3: 1024 kangaroos
SolveKeyCPU Thread 13: 1024 kangaroos
SolveKeyCPU Thread 7: 1024 kangaroos
SolveKeyCPU Thread 11: 1024 kangaroos
SolveKeyCPU Thread 6: 1024 kangaroos
SolveKeyCPU Thread 14: 1024 kangaroos
SolveKeyCPU Thread 9: 1024 kangaroos
SolveKeyCPU Thread 8: 1024 kangaroos
SolveKeyCPU Thread 5: 1024 kangaroos
SolveKeyCPU Thread 2: 1024 kangaroos
SolveKeyCPU Thread 15: 1024 kangaroos
SolveKeyCPU Thread 12: 1024 kangaroos
SolveKeyCPU Thread 10: 1024 kangaroos
SolveKeyCPU Thread 0: 1024 kangaroos
[23.11 MK/s][GPU 0.00 MK/s][Count 2^36.09][Dead 2][01:00:08 (Avg 01:46:01)][10.5/33.5MB]
SaveWork: save..............................done [12.0 MB] [00s] Wed Jun 17 13:50:05 2020
[23.09 MK/s][GPU 0.00 MK/s][Count 2^37.09][Dead 3][02:00:20 (Avg 01:46:06)][19.0/49.2MB]
SaveWork: save..............................done [20.5 MB] [00s] Wed Jun 17 14:50:18 2020
[23.09 MK/s][GPU 0.00 MK/s][Count 2^37.67][Dead 5][03:00:23 (Avg 01:46:07)][27.5/60.1MB]
SaveWork: save..............................done [29.0 MB] [00s] Wed Jun 17 15:50:21 2020
[23.02 MK/s][GPU 0.00 MK/s][Count 2^38.08][Dead 7][04:00:26 (Avg 01:46:24)][35.9/69.4MB]
SaveWork: save..............................done [37.4 MB] [00s] Wed Jun 17 16:50:24 2020
[23.01 MK/s][GPU 0.00 MK/s][Count 2^38.40][Dead 10][04:59:21 (Avg 01:46:28)][44.2/78.0MB]

There is my mistake ?

p.s. who help me fined privkey I will gift GPU farm in BTC !

Are you sure pub key lies in that range?

[Etar]

@arulbero here is 10 test with random generated pubkeys in range 2^64
With trick 7 pub was solved much faster then expected op 2^33.09

Code:

Key 143e9176030d0b8bf
RandomPUB-> (cab7241bcdfec03c635b21091e59a3a420ed777f155c4c029f7b2d946d008fbb7c7e36c1e5048b29ec03c82f3cbf302694338793f97e3f3711d10f845e673952)
Compressed RandomPUB->  02cab7241bcdfec03c635b21091e59a3a420ed777f155c4c029f7b2d946d008fbb
Range +2^ 5
NewG-> (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
NewPUB-> (812b19ef5f1ce43327dfe7cb460a4d2b5b38596e29841690fb9f4ec4fcea6657bf878cc2f8cefb3f4a6659ab438fb33dd57c0c6c9a04044ccf0abd0ed8916199)
Compressed NewPUB->  03812b19ef5f1ce43327dfe7cb460a4d2b5b38596e29841690fb9f4ec4fcea6657
[20.33 MK/s][GPU 0.00 MK/s][Count 2^32.23][Dead 0][04:49 (Avg 07:30)][8.8/29.0MB]
Key# 0 [1S]Pub:  0x03812B19EF5F1CE43327DFE7CB460A4D2B5B38596E29841690FB9F4EC4FCEA6657
       Priv: 0x143E9176030D0B8BF
       
Key 1d7cc7042b0e6c8aa
RandomPUB-> (77e7d49ea9bdbfccd9cc8c88b2fc5808f4d12e6d292af6ab8083fada9b7594188d9e048f77083465cf3f159a6526443a5e366a831d6a8affc56e011409fe4540)
Compressed RandomPUB->  0277e7d49ea9bdbfccd9cc8c88b2fc5808f4d12e6d292af6ab8083fada9b759418
Range +2^ 5
NewG-> (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
NewPUB-> (a4061ecdb7080196bc629b5004da2363ad299d01d95d8c198b0b94fe119107a1ac2ce9e962ed090994647325db45e4637fba255f057826cbe4761c17251b079c)
Compressed NewPUB->  02a4061ecdb7080196bc629b5004da2363ad299d01d95d8c198b0b94fe119107a1
[20.26 MK/s][GPU 0.00 MK/s][Count 2^34.02][Dead 1][16:30 (Avg 07:31)][20.2/51.0MB]
Key# 0 [1S]Pub:  0x02A4061ECDB7080196BC629B5004DA2363AD299D01D95D8C198B0B94FE119107A1
       Priv: 0x1D7CC7042B0E6C8AA
       
Key 14433db2637b6ec72
RandomPUB-> (1718f8425fd183eb37e01be7b84a7b06f1415b0aec470e135a92f240a0f3189ad490fbf36ef547822769f3a4e9c443a535c81fde74dbd4a325aaebf9ad4a4c3f)
Compressed RandomPUB->  031718f8425fd183eb37e01be7b84a7b06f1415b0aec470e135a92f240a0f3189a
Range +2^ 5
NewG-> (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
NewPUB-> (7dccbb29945ea96eb03ef1785c726840400fb085898f774e11bc7783201b10ac20949b00b2823c039060e5aa29342e67c8001d5437ae092d4cb5f5e235ea07b1)
Compressed NewPUB->  037dccbb29945ea96eb03ef1785c726840400fb085898f774e11bc7783201b10ac
[20.31 MK/s][GPU 0.00 MK/s][Count 2^31.59][Dead 0][03:02 (Avg 07:30)][7.1/24.1MB]
Key# 0 [1S]Pub:  0x037DCCBB29945EA96EB03EF1785C726840400FB085898F774E11BC7783201B10AC
       Priv: 0x14433DB2637B6EC72       
  
Key 186c6d302861aa5d4
RandomPUB-> (bd3fc59260f5a4bfb23ceb68f45c0df8738e6a5e2c14ae73c12c2ccd49efc2cf18a119a8eb3b312634915e76663d3e8abc7fa92b3369c9fe18df9202aed8f43a)
Compressed RandomPUB->  02bd3fc59260f5a4bfb23ceb68f45c0df8738e6a5e2c14ae73c12c2ccd49efc2cf
Range +2^ 5
NewG-> (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
NewPUB-> (a43d497e079bd0e0b4b01696f9fd440d80bea697c4d16944aad70fd1c3e1c69b4cc38b9a3e46947f88846b1ff635dcfa8f9ead5e40a929ccbdfb195dfa833837)
Compressed NewPUB->  03a43d497e079bd0e0b4b01696f9fd440d80bea697c4d16944aad70fd1c3e1c69b
[19.64 MK/s][GPU 0.00 MK/s][Count 2^32.25][Dead 1][05:01 (Avg 07:46)][8.8/29.2MB]
Key# 0 [1S]Pub:  0x03A43D497E079BD0E0B4B01696F9FD440D80BEA697C4D16944AAD70FD1C3E1C69B
       Priv: 0x186C6D302861AA5D4
       
Key 115ae794f1b157387
RandomPUB-> (bc79deb0aa33e401b6516aa12e1453be54219d49a90ad1a2da6c719735bb97484b1d66bf0ec1179da6f7237a978217f23b316bb6c6eb24354285b907d5f5c798)
Compressed RandomPUB->  02bc79deb0aa33e401b6516aa12e1453be54219d49a90ad1a2da6c719735bb9748
Range +2^ 5
NewG-> (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
NewPUB-> (0acef8d439064a79442be1617962bb4a6652c416f7efc44abca87f7540896fc9d89e67ed3ce3c3f1d1c508f306dd43763a813fb8f70607dd62d88979237f5173)
Compressed NewPUB->  030acef8d439064a79442be1617962bb4a6652c416f7efc44abca87f7540896fc9
[20.31 MK/s][GPU 0.00 MK/s][Count 2^30.69][Dead 0][01:38 (Avg 07:30)][5.7/19.4MB]
Key# 0 [1S]Pub:  0x030ACEF8D439064A79442BE1617962BB4A6652C416F7EFC44ABCA87F7540896FC9
       Priv: 0x115AE794F1B157387

Key 12b44e75c6538812e
RandomPUB-> (2c83c61b3a928e6fe442d4daefceaefe8c0e196801b4a8ced75187efce583e14003240025a4f2a108c1cc140b16b1b508a0ea00c9004402b9fd0140d0d960b06)
Compressed RandomPUB->  022c83c61b3a928e6fe442d4daefceaefe8c0e196801b4a8ced75187efce583e14
Range +2^ 5
NewG-> (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
NewPUB-> (b8cfa6e97786c3bc6c83f358c493e99df89394e6dfc1b2584f7f51ce8f663d77f13aeb4be38cfef304919b5f340a25a099ab575dbe296b5385402006dbccb82f)
Compressed NewPUB->  03b8cfa6e97786c3bc6c83f358c493e99df89394e6dfc1b2584f7f51ce8f663d77
[20.30 MK/s][GPU 0.00 MK/s][Count 2^29.68][Dead 0][49s (Avg 07:30)][4.9/16.5MB]
Key# 0 [1S]Pub:  0x03B8CFA6E97786C3BC6C83F358C493E99DF89394E6DFC1B2584F7F51CE8F663D77
       Priv: 0x12B44E75C6538812E

Key 1cce23dd0b4634576
RandomPUB-> (5447c4299276d72d8d1e7bb66252547983a8d92ad2d2d833305aed3a4f1e0a6b68d4692e2fda1698b52769032538c4381a892629ccc013c505d73ab23ef29499)
Compressed RandomPUB->  035447c4299276d72d8d1e7bb66252547983a8d92ad2d2d833305aed3a4f1e0a6b
Range +2^ 5
NewG-> (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
NewPUB-> (cbeb76c10701217ed60bc264b2456e52cfdbe2d5e0e2816b322d641565196b85092ad3e5bf4d59605ba79ddfb451995a3d7e03e033dc17e98f60a13a6b944246)
Compressed NewPUB->  02cbeb76c10701217ed60bc264b2456e52cfdbe2d5e0e2816b322d641565196b85
[19.41 MK/s][GPU 0.00 MK/s][Count 2^33.75][Dead 4][13:40 (Avg 07:51)][17.4/46.8MB]
Key# 0 [1S]Pub:  0x02CBEB76C10701217ED60BC264B2456E52CFDBE2D5E0E2816B322D641565196B85
       Priv: 0x1CCE23DD0B4634576

Key 1a4a0fa7d600bf8ad
RandomPUB-> (6da8a0aa2ff57c6d0cab60a9b8f57fb513925a3ad9516004d922540e9cc63b77e30878cf48ea3c1bce88cda4704246cc06c0a0e69cf71e00d774f25b29d382f0)
Compressed RandomPUB->  026da8a0aa2ff57c6d0cab60a9b8f57fb513925a3ad9516004d922540e9cc63b77
Range +2^ 5
NewG-> (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
NewPUB-> (5a63e4e33c8f8a4ebda575aed3cb86610ce245b068a6bdf7e54cce3ab0a784e35ef6dd1ef9e92dcb1660bf0aeaa4f913b73b04c107de89b4c27e135e02d76534)
Compressed NewPUB->  025a63e4e33c8f8a4ebda575aed3cb86610ce245b068a6bdf7e54cce3ab0a784e3
[19.82 MK/s][GPU 0.00 MK/s][Count 2^30.96][Dead 0][02:00 (Avg 07:41)][6.0/20.6MB]
Key# 0 [1S]Pub:  0x025A63E4E33C8F8A4EBDA575AED3CB86610CE245B068A6BDF7E54CCE3AB0A784E3
       Priv: 0x1A4A0FA7D600BF8AD

Key 1e2e59c8fe307a32b
RandomPUB-> (c91b934ed57a546e4478d3100cc2094469380093c9f0cb8c81370c4363c7b8277cbcbd6ca337e853c734eee3bf0fba215b22d1a6b4ba7faad29073648669a530)
Compressed RandomPUB->  02c91b934ed57a546e4478d3100cc2094469380093c9f0cb8c81370c4363c7b827
Range +2^ 5
NewG-> (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
NewPUB-> (5c6ee892e22560f823fe6c4169427a3f2c5a2cb8fabfbb57d5290254e3bc5ed6e31b2acdc92ae029de597448e0ef1139bf02240e7e71df02675c82069abd483b)
Compressed NewPUB->  035c6ee892e22560f823fe6c4169427a3f2c5a2cb8fabfbb57d5290254e3bc5ed6
[20.05 MK/s][GPU 0.00 MK/s][Count 2^33.83][Dead 3][14:42 (Avg 07:36)][18.3/48.1MB]
Key# 0 [1S]Pub:  0x035C6EE892E22560F823FE6C4169427A3F2C5A2CB8FABFBB57D5290254E3BC5ED6
       Priv: 0x1E2E59C8FE307A32B

Key 133b730227ed508f3
RandomPUB-> (50a8653f615f6136ad6a6139f010957c5a2d69ea4b656edd81302a7da97f88a98d5d63f66596df306dbc6c6cf9bc1c00ed434586a0e9784b9ef6dba68885d0e3)
Compressed RandomPUB->  0350a8653f615f6136ad6a6139f010957c5a2d69ea4b656edd81302a7da97f88a9
Range +2^ 5
NewG-> (a3c9d9de2ba89d61c63af260be9759d752b8bfef56ee41b2dab2b99871af38a8,b639cb2d3e0f1940d5e5333061d489159d1783ba821eaef15f78802d002f63fb)
NewPUB-> (d6818a457f8d8089c87e2ac76d265a12a2eed541cc3b19a1daec7d50053dc4ee5986d1f7b43efd34a7a703919e9ca868b925091101f8414b0971b9962a62d505)
Compressed NewPUB->  03d6818a457f8d8089c87e2ac76d265a12a2eed541cc3b19a1daec7d50053dc4ee
[20.17 MK/s][GPU 0.00 MK/s][Count 2^32.48][Dead 1][05:40 (Avg 07:33)][9.6/31.3MB]
Key# 0 [1S]Pub:  0x03D6818A457F8D8089C87E2AC76D265A12A2EED541CC3B19A1DAEC7D50053DC4EE
       Priv: 0x133B730227ED508F3

Tomorrow i will publish result with the same pubs but without trick.

[arulbero]

@arulbero here is 10 test with random generated pubkeys in range 2^64
With trick 7 pub was solved much faster then expected op 2^33.09
---
Tomorrow i will publish result with the same pubs but without trick.

Thanks, but a test must have:

a) 1000 pub_keys
b) the average steps after 1000 pub_keys

I think it is better to use a lower range to get the results quickly.

[aliashraf]

What's the point of this thread after all? Bragging with number theory algorithms

Fifty pages, one thousand posts, so many merits, ... what does it have to do with bitcoin?

Seriously, I don't get it. I understand bitcoin has roots in cryptography it is called cryptocurrency after all and cryptography is mostly, if not all, about number theory,  but is it really a bitcoin "development and technical discussion"? I don't think so.

[WanderingPhilospher]

What's the point of this thread after all? Bragging with number theory algorithms

Fifty pages, one thousand posts, so many merits, ... what does it have to do with bitcoin?

Seriously, I don't get it. I understand bitcoin has roots in cryptography it is called cryptocurrency after all and cryptography is mostly, if not all, about number theory,  but is it really a bitcoin "development and technical discussion"? I don't think so.

Some posts are off topic but the "number theories" over the last few pages are trying to determine if you can reuse previous kangaroo work. Therefore, it is for the development of this Pollard's kangaroo ECDLP solver.

But thank you for adding a post that shall fall under the off-topic category. See, even you contributed.