Pollard's kangaroo ECDLP solver

[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.

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.

And what is relevant to bitcoin development here? Nothing! The whole thread belongs to the off-topic subforum, IMO.

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[Jean_Luc]

50 pages and 2.25BTC unlocked in less than 2 months ! Rather a good score, no ?

[keychainX]

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.

And what is relevant to bitcoin development here? Nothing! The whole thread belongs to the off-topic subforum, IMO.

The whole point is to find a backdoor to break bitcoin private keys.

The Pollard algo can be used in many ways to decrease the search space so in my opinion it has a lot to do with Bitcoin.

/KX

[COBRAS]

50 pages and 2.25BTC unlocked in less than 2 months ! Rather a good score, no ?

yes this is good score.

Not listen all not health critics.

[RXUser]

Yes just ignore the off-topic spams. thanks for this thread, it is very relevant and not only to Bitcoin development.

[aliashraf]

50 pages and 2.25BTC unlocked in less than 2 months ! Rather a good score, no ?

No!

[COBRAS]

50 pages and 2.25BTC unlocked in less than 2 months ! Rather a good score, no ?

No!

Go away from there, ok ?

[Etar]

@arulbero test with 1000 pub keys fulfilled.
Workfile taken from puzzle 49 bit and prepared to work in the range 54 bit.
Each wild DPs tamed. All DPs multipled by 32 and checked (x-coordinate was correct when distance*G' )
-xbit was 5 so G'=G*inv(32) = (bb2228d3ea32cb3c1eb160cc824a4ba8115f9a7f415d18ddcaac8193defc2c47,71f8c9c7cc35f99b8b2abcdcab86d12cb7539b3fbb45bc433b3bd9421b35be53)
1000 keys was generated in range 40000000000000:7fffffffffffff
Each pubkeys was multipled by inv(32) and solved with G'and Kangaroo v1.4
Expected operations 2^28.06
Total op was 261530636052 = 2^37.93
In average 2^27.98

[COBRAS]

@arulbero test with 1000 pub keys fulfilled.
Workfile taken from puzzle 49 bit and prepared to work in the range 54 bit.
Each wild DPs tamed. All DPs multipled by 32 and checked (x-coordinate was correct when distance*G' )
-xbit was 5 so G'=G*inv(32) = (bb2228d3ea32cb3c1eb160cc824a4ba8115f9a7f415d18ddcaac8193defc2c47,71f8c9c7cc35f99b8b2abcdcab86d12cb7539b3fbb45bc433b3bd9421b35be53)
1000 keys was generated in range 40000000000000:7fffffffffffff
Each pubkeys was multipled by inv(32) and solved with G'and Kangaroo v1.4
Expected operations 2^28.06
Total op was 261530636052 = 2^37.93
In average 2^27.98

Hello

"Total op was 261530636052 = 2^37.93" this for 1000 pubkey or only one ?

[arulbero]

@arulbero test with 1000 pub keys fulfilled.
Workfile taken from puzzle 49 bit and prepared to work in the range 54 bit.
Each wild DPs tamed. All DPs multipled by 32 and checked (x-coordinate was correct when distance*G' )
-xbit was 5 so G'=G*inv(32) = (bb2228d3ea32cb3c1eb160cc824a4ba8115f9a7f415d18ddcaac8193defc2c47,
71f8c9c7cc35f99b8b2abcdcab86d12cb7539b3fbb45bc433b3bd9421b35be53)
1000 keys was generated in range 40000000000000:7fffffffffffff
Each pubkeys was multipled by inv(32) and solved with G'and Kangaroo v1.4
Expected operations 2^28.06
Total op was 261530636052 = 2^37.93
In average 2^27.98

Many thanks.

The gain (- 5,4%) is little, how many DPs have you generated for the key in 49 bit?

If you have generated 2^25.08 points, then:

(2^x  +  2^25.08) tame * (2^x) wild = 2^54 couples

2^(2x) + 2^(25.08)*2^x - 2^54 = 0

--> x = 2^26.81

Then you should have computed on average 2^26.81 tame-steps + 2^26.81 wild-steps = 2^27.81 steps

[COBRAS]

@arulbero test with 1000 pub keys fulfilled.
Workfile taken from puzzle 49 bit and prepared to work in the range 54 bit.
Each wild DPs tamed. All DPs multipled by 32 and checked (x-coordinate was correct when distance*G' )
-xbit was 5 so G'=G*inv(32) = (bb2228d3ea32cb3c1eb160cc824a4ba8115f9a7f415d18ddcaac8193defc2c47,71f8c9c7cc35f99b8b2abcdcab86d12cb7539b3fbb45bc433b3bd9421b35be53)
1000 keys was generated in range 40000000000000:7fffffffffffff
Each pubkeys was multipled by inv(32) and solved with G'and Kangaroo v1.4
Expected operations 2^28.06
Total op was 261530636052 = 2^37.93
In average 2^27.98

Many thanks.

The gain (- 5,7%) is little, how many DPs did you have generate for the key in 49 bit?

Etar, this is a CPU or GPU version ?

[Etar]

-snip-
The gain (- 5,4%) is little, how many DPs have you generated for the key in 49 bit?
-snip-

DP Count  : 240568 2^17.876 in 49bit workfile. i have source file and converted file. I can share if you want to verify DPs. But each DP after multiplication was verifed with G' and x-coordinate correct.

Code:

DP bits   : 8
Start     : 40000000000000
Stop      : 7FFFFFFFFFFFFF
Key       : 025C396BA4347253BBAAFFAC6D4F9BA092847B27F2599EB2EB225DDA54F9964190
Count     : 0 2^-inf
Time      : 00s
DP Size   : 9.3/30.6MB
DP Count  : 240568 2^17.876
HT Max    : 8 [@ 01D30E]
HT Min    : 0 [@ 000001]
HT Avg    : 0.92
HT SDev   : 0.95

-snip-
"Total op was 261530636052 = 2^37.93" this for 1000 pubkey or only one ?

For 1000 pubkeys

-snip-

Etar, this is a CPU or GPU version ?

Test done on CPU

[COBRAS]

"For 1000 pubkeys"

Think I not understand something but, for 1000 pubkeys 2^37.93 is very fast.

[Etar]

"For 1000 pubkeys"

Think I not understand something but, for 1000 pubkeys 2^37.93 is very fast.

expected op for 1 pub = 2^28.06
1000 pubkeys ~2^ 9.965
2^28.06*2^9.965=(28.06+9.965)=2^38.025
So 2^37.93 is little-little bit faster then expected

[arulbero]

-snip-
The gain (- 5,4%) is little, how many DPs have you generated for the key in 49 bit?
-snip-

DP Count  : 240568 2^17.876 in 49bit workfile

Then you have computed 2^17.876 * 2^8 = 2^25.876 points,


(2^x  +  2^25.876) tame * (2^x) wild = 2^54 couples

--> x = 26.67  

In theory it would be enough 2^27.67 steps instead of 2^27.98.

To get 2^27.98, it is like 2^25.876 was worth about 2^21.8, the effect of reuse of old DPs is reduced by a factor of 16.

[Etar]

-snip-

To get 2^27.98, it is like 2^25.876 was worth about 2^21.8, the effect of reuse of old DPs is reduced by a factor of 16.

I think that for birthday paradox is a big difference between have 16Tame DP and 2 wild DP or 9tame and 9wild.
Maybe if Kangaroo app first launch wild (as you say somewhere above) gain the same amount as tame DPs maybe in this case we will have faster result.

[arulbero]

-snip-

To get 2^27.98, it is like 2^25.876 was worth about 2^21.8, the effect of reuse of old DPs is reduced by a factor of 16.

I think that for birthday paradox is a big difference between have 16Tame DP and 2 wild DP or 9tame and 9wild.
Maybe if Kangaroo app first launch wild (as you say somewhere above) gain the same amount as tame DPs maybe in this case we will have faster result.

Yes, but in that case there is no big difference:

(2^x  +  2^25.876) tame * (2^x + 2^25.876) wild = 2^54 couples

2^x + 2^25.876 = 2^27

x = log2(2^27-2^25.876) = 26.1

--> only 2^26.1 tame + 2^26.1 wild  + 2^25.876 wild steps are needed -> 2^27.61

[Jean_Luc]

The best time complexity with the birthday paradox and kangaroo having a starting position uniformly distributed in [0..N] is obtained when drawing alternatively one tame and one wild. When using DP0, you get ~2.sqrt(N). When using DPx, it is like drawing alternatively 2^x TAME and then 2^x WILD, you have then a DP overhead.
I managed to get the formula for parallel version which is: ~2.CubicRoot( N (k.theta + sqrt(N)) ) where theta=2^dpbit and k the number of kangaroo-2 running in parallel.
For theta=1 (DP0) and k=0 (or when k.theta << sqrt(N)) we well get ~2.sqrt(N), when k.theta >> sqrt(N), the time complexity tend to ~2.CubicRoot(k.N.theta).
So it is important to choose a DP such as k.theta << sqrt(N).

[Etar]

The best time complexity with the birthday paradox and kangaroo having a starting position uniformly distributed in [0..N] is obtained when drawing alternatively one tame and one wild. When using DP0, you get ~2.sqrt(N). When using DPx, it is like drawing alternatively 2^x TAME and then 2^x WILD, you have then a DP overhead.
I managed to get the formula for parallel version which is: ~2.CubicRoot( N (k.theta + sqrt(N)) ) where theta=2^dpbit and k the number of kangaroo-2 running in parallel.
For theta=1 (DP0) and k=0 (or when k.theta << sqrt(N)) we well get ~2.sqrt(N), when k.theta >> sqrt(N), the time complexity tend to ~2.CubicRoot(k.N.theta).
So it is important to choose a DP such as k.theta << sqrt(N).

In that case best choice for solving keys is using CPU  
i7 7 thread 20Mop/s and 7168 kangaroos
2080ti 1.4Gop/s and 4464292 kangaroos
1.4Gop/s / 20Mop/s = 70 CPU the same speed but also only 501760 Kangaroos, 8.9 times less DP overhead.

[brainless]

-snip-
The gain (- 5,4%) is little, how many DPs have you generated for the key in 49 bit?
-snip-

DP Count  : 240568 2^17.876 in 49bit workfile. i have source file and converted file. I can share if you want to verify DPs. But each DP after multiplication was verifed with G' and x-coordinate correct.

Code:

DP bits   : 8
Start     : 40000000000000
Stop      : 7FFFFFFFFFFFFF
Key       : 025C396BA4347253BBAAFFAC6D4F9BA092847B27F2599EB2EB225DDA54F9964190
Count     : 0 2^-inf
Time      : 00s
DP Size   : 9.3/30.6MB
DP Count  : 240568 2^17.876
HT Max    : 8 [@ 01D30E]
HT Min    : 0 [@ 000001]
HT Avg    : 0.92
HT SDev   : 0.95

-snip-
"Total op was 261530636052 = 2^37.93" this for 1000 pubkey or only one ?

For 1000 pubkeys

-snip-

Etar, this is a CPU or GPU version ?

Test done on CPU

Etar
if i am not wrong
you have 49 bit 1000 pubkeys
you shift dp file to 54 bit
and you have this info
" Expected operations 2^28.06, Total op was 261530636052 = 2^37.93 "
if i am not wrong you total op 2^38 work = to search 1 pubkey in 2^76 bitrange
76 bit = 75557863725914323419135
54 bit = 18014398509481983
distance = 4194303 for 1000 pub key
and for 1 pubkey = 419.4303
and for 32*g = 134217.72
in short you used tooo much time as compare to equal 76 bit work
hope u understand