Pollard's kangaroo ECDLP solver

[WanderingPhilospher]

-snip-
PS. Actually instead of solving pk110 within the range [2^109 ... 2^110-1] the program solves the key pk110s within the range [0 ... 2^109-1]

Thanks for the detailed answer. This is very clear now.

Can you help make it clear to me

So the tames work from range 0...meaning 0x0 to 0x3FFFFFFFFFFFFFFFFFFFFFFFFFFFF  (for pubkey 110)?

The range is shifted, not expanded. Shift means the move of start and end values both by the SAME value.
Instead of range [2000000000000000000000000000 ... 3fffffffffffffffffffffffffff] the program works with range [0 ... 1fffffffffffffffffffffffffff]

PS. Do you really like these hex values posted here? They are difficult to understand by a human (as difficult to count "f" and "0" signs). So i represented them earlier by the powers of 2 (2^109 and 2^110) which is much easier to understand.

I'll have to digest this the SAME value is throwing me off a little. It makes sense by what you said; you subtracted the 20000....from both values to get 0 and the 1ffff...
What is the advantage or purpose of shifting?

As far as ranges, I'm good with either, hex or powers, just wanted to keep it simple (for me, maybe for others) since we input a range start and range end on the input file versus a -bits flag.

[Etar]

Here is my merged workfile for pazzle#110(109bit)
https://drive.google.com/file/d/1eZNnWJnNdRhWp-ZnaxYhwfRVKZHiadEg
DP=28. there is not so many DPs because i start with DP=31(collected half of expected Dps) than drop to 28.
Maybe somebody it can help to solve key.

Code:

DP bits   : 28
Start     : 2000000000000000000000000000
Stop      : 3FFFFFFFFFFFFFFFFFFFFFFFFFFF
Key       : 0309976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Count     : 0 2^-inf
Time      : 00s
DP Size   : 801.1/1216.5MB
DP Count  : 26183698 2^24.642
HT Max    : 152 [@ 02F8EB]
HT Min    : 57 [@ 029D90]
HT Avg    : 99.88
HT SDev   : 9.99

[WanderingPhilospher]

Here is my merged workfile for pazzle#110(109bit)
https://drive.google.com/file/d/1eZNnWJnNdRhWp-ZnaxYhwfRVKZHiadEg
DP=28. there is not so many DPs because i start with DP=31(collected half of expected Dps) than drop to 28.
Maybe somebody it can help to solve key.

Code:

DP bits   : 28
Start     : 2000000000000000000000000000
Stop      : 3FFFFFFFFFFFFFFFFFFFFFFFFFFF
Key       : 0309976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Count     : 0 2^-inf
Time      : 00s
DP Size   : 801.1/1216.5MB
DP Count  : 26183698 2^24.642
HT Max    : 152 [@ 02F8EB]
HT Min    : 57 [@ 029D90]
HT Avg    : 99.88
HT SDev   : 9.99

Did you lose all the DPs @ 31, when you dropped to 28?

[Etar]

-snip-
Did you lose all the DPs @ 31, when you dropped to 28?

I did not lose any DPs, they are only reduced to 28bit. Somewere i have file with dp=31, if you need i can share

Code:

DP bits   : 31
Start     : 2000000000000000000000000000
Stop      : 3FFFFFFFFFFFFFFFFFFFFFFFFFFF
Key       : 0309976BA5570966BF889196B7FDF5A0F9A1E9AB340556EC29F8BB60599616167D
Count     : 0 2^-inf
Time      : 00s
DP Size   : 383.0/485.2MB
DP Count  : 12483809 2^23.574
HT Max    : 85 [@ 03430F]
HT Min    : 19 [@ 00B5CE]
HT Avg    : 47.62
HT SDev   : 6.90

There is link to DP=31 file https://drive.google.com/file/d/1zmrmcQJ3NSbwnF2AJ4RH-vbab0VOgJSt

P.S. If somebody can share  work it will be good. Maybe one of us can solve key in this way.

[MrFreeDragon]

-snip-
There is link to DP=31 file https://drive.google.com/file/d/1zmrmcQJ3NSbwnF2AJ4RH-vbab0VOgJSt

P.S. If somebody can share  work it will be good. Maybe one of us can solve key in this way.

I also shared some files earlier.
Can you please upload your files to here: https://gofile.io
You can do it without registration, and you can delete them with your admin link at any time. Unfortunately google does not allow do download your file without google account.

[Etar]

-snip-
I also shared some files earlier.
Can you please upload your files to here: https://gofile.io
You can do it without registration, and you can delete them with your admin link at any time. Unfortunately google does not allow do download your file without google account.

i was try several times but got this

Code:

Error
The upload has failed
Please try again later, Gofile could be in maintenance.

try now dp=31 https://drive.google.com/file/d/1zmrmcQJ3NSbwnF2AJ4RH-vbab0VOgJSt
dp=28 https://drive.google.com/file/d/1eZNnWJnNdRhWp-ZnaxYhwfRVKZHiadEg

[patatasfritas]

I was testing "directory merge" function and RAM memory is quickly exhausted. I was thinking that I forgot to free temp HashTable in each reading iteration; but I changed the code and the problem remains
The merged saveFile is 5GB, and in merge process takes up about 14GB of RAM.

I think the more obvious solution is to sort files from bigger to smallest when are merged; or use only small saveFiles.


On the other hand, the -ws flag I think is problematic when using -wsplit, generating larger files than necessary. Do you think it is interesting to separate the DP and the kangaroos into different save files?


As next improvements, I will work on improving the export of the DPs and the possibility of modifying the DP bits in a save file to reduce its size if we have chosen a too low DP value. It can also be interesting to remove from a save file the distances to share it without gifting the prize.

[dextronomous]

If someone wants to run a solver with small DPs, but the server’s resources don’t allow it, then you can use the -wsplit option,
which appears in version 1.7 of the solver.
But in any case, you must have a PC that can merge files. I just had such a problem.
Now I can safely merge files on my home PC. In order not to do it all manually, you need a grabber and a merger.
File grabber is launched on the server, merger is launched on the home PC.
Merger communicates with the grabber and requests files from him. The graber sends, if any, and then removes them from the server.
The merger, in turn, after receiving the file from the grabber, starts the merge process, during which it is possible to find the key, after merge temp file deleted.
Grabber gives files only to an authorized merger.
If it helps someone, archive with source codes, compiled programs and example .bat files: https://drive.google.com/file/d/1wQWLCRsYY2s4DH2OZHmyTMMxIPn8kdsz
Edit: fixed little memory leak at grabber side.

As before, the sources under Purebasic.
mergeServer(grabber):

Code:

-pass >password for merger authorization
-port >listening port, where merger will be connect
-ext  >by this extension, the grabber will search for files in the folder,
       for ex. using -ext part, than you should start server with -w xxxx.part

mergeClient(merger):

Code:

-jobtime 60000>request a file from the grabber every 60s
-name >it is name of your merger, useless, just for stats
-pass >password for authorization(should be the same as in grabber)
-server >host:port grabber
-workfile >name of your masterfile
-merger >Kangaroo.exe by default

been seeing this one.
1:30:21  [GETWORK] INVALID CRC32 FILE > NEED:ffffffffd52c4232, GOT:79ffe57 is this still ok. thanks man, great piece.

[Etar]

-snip-
been seeing this one.
1:30:21  [GETWORK] INVALID CRC32 FILE > NEED:ffffffffd52c4232, GOT:79ffe57 is this still ok. thanks man, great piece.

It is not a problem, if CRC32 invalid, that file will be send in next time.

[brainless]

Anybody can explain why tame DP shifted to zero?
For test i use pubkey 04e6dabff2705a80acc23ae121956873c4ff9fd31cb0faca522c33624e23657e04125c04d29ea83 874332ea8aef3b3467f22665a4970df415be756bcdf5675e569
range ffff...fffffffffffff  -dp 4
when i look to hashtable i see this
x: 5311104a8554e94684e07e9d8c0d112f
d: 0000000000000000000589fd3365a64e
Before i was think that programm add begin range to tame DP, but i see now that there no addiding.
becouse when 0000000000000000000589fd3365a64e * G get 6b4599cecd305b927a266d311d800005311104a8554e94684e07e9d8c0d112f and this is our x
In this case i have a question for what distance for ex.2AA need if range start from ffff
ok, when we will start range from for ex. 2^109 in that case all distance before will be useless?
becouse they are will produce x-coordinates that is before range 2^109.
I do not understand this moment..

Because the Tame Kangaroos are dependent only on the interval size, while the Wild Kangaroos are dependent on the interval size and the public key. We want to keep the algorithm as generic as possible, and also the ability to reuse the Tame Kangaroos for multiple key searches.

As relating to the Wild Kangaroos, [working_public_key] = [(original_public_key) - (beginning_range)*(secp256k1_generator_point)].
[distinguished_point] = [(+-traveled_distance)*(secp256k1_generator_point)] + [working_public key]

You will need to add back the (beginning_range) when there’s a collision to solve for the (original_public_key).

" and also the ability to reuse the Tame Kangaroos for multiple key searches. "

can we aspect multi pubkeys support coming, maybe yes or maybe no, its all depand dev thinking, maybe he prefer to work a lot more calc for client/server, or maybe he he think add this func and then optimize all thing togather

[WanderingPhilospher]

I was testing "directory merge" function and RAM memory is quickly exhausted. I was thinking that I forgot to free temp HashTable in each reading iteration; but I changed the code and the problem remains
The merged saveFile is 5GB, and in merge process takes up about 14GB of RAM.

I think the more obvious solution is to sort files from bigger to smallest when are merged; or use only small saveFiles.


On the other hand, the -ws flag I think is problematic when using -wsplit, generating larger files than necessary. Do you think it is interesting to separate the DP and the kangaroos into different save files?


As next improvements, I will work on improving the export of the DPs and the possibility of modifying the DP bits in a save file to reduce its size if we have chosen a too low DP value. It can also be interesting to remove from a save file the distances to share it without gifting the prize.

I tested dir merge on PC with 24GB RAM and 10 dir files that were probably 500MB a piece but I didn't check the RAM usage.

Alek76's version is similar to what you are talking about as far as separating files. He has (in current version) 8 text files that are generated, 4 tames and 4 wild. I modified it a little bit and used 2 tames and 4 wilds. Then, he has a python comparator that compares all the files to check for a solved key. I tried/trying to figure out how to merge that with JP's (this) version, but can't figure out how to read the files well enough to understand how to build the python comparator.

[WanderingPhilospher]

Jean Luc...your Kangaroo is now a fast solver...especially for the lower bits, 90 on down. I know the higher the bits the longer it takes to solve. But what can you do from this point forward to make solving the higher bits, optimized/faster?

In all the articles and research papers I have read, well most of them, they talk about subgroups. Can this not be done?

Example, if we are trying to solve a key for the range 10000:1FFFF, currently we can only use the exact range started with for the same key. Can we not setup hash and jump table for 10000:1FFFF (precomp of sorts) and then attack the range with different starting points?

Example:
1 - 10000:1FFFF
2 - 11000:1FFFF
3-  12000:1FFFF
....
10- 1A000-1FFFF

or attack in smaller bits such as

100FF-1100
101FF-1200
etc?

My PC alone can solve 64 bit in 1 minute...what if we randomly generate 64 bit (or whatever bit number desired) inside the larger bit range and use the
-m option to stop the search in this section and move to the next randomly generated 64 bit piece. or better yet, make it a sequential 64 bit search inside of a 110 bit range. With numerous GPUs, you could assign each one a different range so the sequential piece is sped up.
Example:
gpu 1- attacking 10000-11000 in smaller sequential bits
gpu 2- attacking 11001-12000 in smaller sequential bits
etc

Anyone, thoughts?

[COBRAS]

Jean Luc...your Kangaroo is now a fast solver...especially for the lower bits, 90 on down. I know the higher the bits the longer it takes to solve. But what can you do from this point forward to make solving the higher bits, optimized/faster?

In all the articles and research papers I have read, well most of them, they talk about subgroups. Can this not be done?

Example, if we are trying to solve a key for the range 10000:1FFFF, currently we can only use the exact range started with for the same key. Can we not setup hash and jump table for 10000:1FFFF (precomp of sorts) and then attack the range with different starting points?

Example:
1 - 10000:1FFFF
2 - 11000:1FFFF
3-  12000:1FFFF
....
10- 1A000-1FFFF

or attack in smaller bits such as

100FF-1100
101FF-1200
etc?

My PC alone can solve 64 bit in 1 minute...what if we randomly generate 64 bit (or whatever bit number desired) inside the larger bit range and use the
-m option to stop the search in this section and move to the next randomly generated 64 bit piece. or better yet, make it a sequential 64 bit search inside of a 110 bit range. With numerous GPUs, you could assign each one a different range so the sequential piece is sped up.
Example:
gpu 1- attacking 10000-11000 in smaller sequential bits
gpu 2- attacking 11001-12000 in smaller sequential bits
etc

Anyone, thoughts?

I think if you fined key in 64 bit, you not need next 64 bit, but if you fined only on 3*64 bits false and after only 1  BINGO 64 bit, this is I  think not = 256 bytes key and fourth 64 bits with private key will be not 256 bytes key too.........

[WanderingPhilospher]

Jean Luc...your Kangaroo is now a fast solver...especially for the lower bits, 90 on down. I know the higher the bits the longer it takes to solve. But what can you do from this point forward to make solving the higher bits, optimized/faster?

In all the articles and research papers I have read, well most of them, they talk about subgroups. Can this not be done?

Example, if we are trying to solve a key for the range 10000:1FFFF, currently we can only use the exact range started with for the same key. Can we not setup hash and jump table for 10000:1FFFF (precomp of sorts) and then attack the range with different starting points?

Example:
1 - 10000:1FFFF
2 - 11000:1FFFF
3-  12000:1FFFF
....
10- 1A000-1FFFF

or attack in smaller bits such as

100FF-1100
101FF-1200
etc?

My PC alone can solve 64 bit in 1 minute...what if we randomly generate 64 bit (or whatever bit number desired) inside the larger bit range and use the
-m option to stop the search in this section and move to the next randomly generated 64 bit piece. or better yet, make it a sequential 64 bit search inside of a 110 bit range. With numerous GPUs, you could assign each one a different range so the sequential piece is sped up.
Example:
gpu 1- attacking 10000-11000 in smaller sequential bits
gpu 2- attacking 11001-12000 in smaller sequential bits
etc

Anyone, thoughts?

I think if you fined key in 64 bit, you not need next 64 bit, but if you fined only on 3*64 bits false and after only 1  BINGO 64 bit, this is I  think not = 256 bytes key and fourth 64 bits with private key will be not 256 bytes key too.........

the 64 bit doesn't need to equal anything...
it could be a sequential 40, 41, 42, 50, 56, 72, 80, etc bit range. The object is to check the smaller ranges (subgroups?) inside a larger range for the same key.

[WanderingPhilospher]

I really like this race
HardwareCollector or Zielar ?

There is a high probability that if we combine HardwareCollector's and Zielar's working files there will be the required collision.

There is also a way to check it right now without sharing the whole files - only the information with X-coordinates and kangaroo type should be shared (excluding distances), and if we have the same X-coordinate with different types (wild and tame) so we can confirm that the key is found.

HWCollector and Zielar, do you want me to perform such check for you? 

Thanks for the offer, but I’ve not started yet as I am giving time for Zielar to solve the challenge first. He has poured a lot of resources to it already, and out of common courtesy, I will begin late Sunday night assuming that he’s hasn’t solved it yet. But I am working on precomputation for the 115-bit private key challenge. 

Hardware, how long are you running your precomp for? You have a set # of DPs or a percentage? 2/3 ops?

[Jean_Luc]

@MrFreeDragon
Thanks for the link, was funny

@patatasfritas
About the merger, yes, I know, I currently working on a low RAM usage version and the integration of your features.
concerning sug group, I didn't have a look yet but splitting range is not a good way of parallelization, you have only a gain of sqrt(n) where n is the number of subgroup.

[Etar]

As relating to the Wild Kangaroos, [working_public_key] = [(original_public_key) - (beginning_range)*(secp256k1_generator_point)].
[distinguished_point] = [(+-traveled_distance)*(secp256k1_generator_point)] + [working_public key]

You will need to add back the (beginning_range) when there’s a collision to solve for the (original_public_key).

Can you explain me this, please.
Searching key 0xa123fe3456
Searching pub key 0xe6dabff2705a80acc23ae121956873c4ff9fd31cb0faca522c33624e23657e04125c04d29ea83 874332ea8aef3b3467f22665a4970df415be756bcdf5675e569
range 0..fffffffffffff  (so there no shifting and working pubkey=original pubkey)
Look to hashtable..
x=0x7760a4827fcb4d02210c4fb962f48c49
d=0x40000000000000000006a6bdf014bd68
that mean that type wild and sign +
ok let`s verify (0x0a123fe3456+0x6a6bdf014bd68)*G = 0xd4814ad2a48ec5f0f1fdce8832800007760a4827fcb4d02210c4fb962f48c49 result corrrect
let`se other DP
x=0x3c628f41e76f5bce8566c3dfa2c3fff0
d=0xc000000000000000000617445c562205
that mean that type wild and sign -
But 0x617445c562205>0x0a123fe3456.. And here is question how it can be that key - distance is out of range???
Ok. it is addidng point not addiding key + distance
(0xe6dabff2705a80acc23ae121956873c4ff9fd31cb0faca522c33624e23657e04,0x125c04d29ea83874332ea8aef3b3467f22665a4970df415be756bcdf5675e569)
+ (fb12e2e7eba822db7582b91da81c0f1d991a6fec79d170733a1eceb039b3e1f9,ee2e79d5326d178c91ed36ca52f9be4f04c42e3cf7cabb3299e070bc1231bb05)
=(dcbae520622e89bd4c0062bb82400003c628f41e76f5bce8566c3dfa2c3fff0,b6fdc18b5be9048e837759b86efa422511b717ed9e7bc2d7b1936c06a0620cfe)
and x coordinate is correct,, but any way tame will never get this point becouse it is out of range 0..fffffffffffff
So not all wild can be tame. We can tame all wild with sign + but each wild with sign - should be verifid with range.
In that case we can add tamed wild to experience.

[WanderingPhilospher]

If anyone is interested...

Looking for some people to partner up to attack the rest of the puzzles.

We take a range, divide it up (for #115, if there were 4 people, person 1 = 400...4FF..., person 2 = 500...5FF..., etc.) and split BTC when solved.

I have 2^28.5 kangaroos ready for the hunt. Hopefully other people have about the same or we divide ranges up based on kangaroo power?

Etar had a good idea, but I would have no clue how to set it up though.

[Etar]

If anyone is interested...

Looking for some people to partner up to attack the rest of the puzzles.

We take a range, divide it up (for #115, if there were 4 people, person 1 = 400...4FF..., person 2 = 500...5FF..., etc.) and split BTC when solved.

I have 2^28.5 kangaroos ready for the hunt. Hopefully other people have about the same or we divide ranges up based on kangaroo power?

Etar had a good idea, but I would have no clue how to set it up though.

Split range it is bad idea. kangaroo never say that there no key, you can check this range even with 4sqrt(n) and break opereation after a lot of operations
but this does not guarantee that there is no key. And in that case you will lose chance to get prize forever.

[WanderingPhilospher]

If anyone is interested...

Looking for some people to partner up to attack the rest of the puzzles.

We take a range, divide it up (for #115, if there were 4 people, person 1 = 400...4FF..., person 2 = 500...5FF..., etc.) and split BTC when solved.

I have 2^28.5 kangaroos ready for the hunt. Hopefully other people have about the same or we divide ranges up based on kangaroo power?

Etar had a good idea, but I would have no clue how to set it up though.

Split range it is bad idea. kangaroo never say that there no key, you can check this range even with 4sqrt(n) and break opereation after a lot of operations
but this does not guarantee that there is no key. And in that case you will ose chance to get prize forever.

So attack it like you had mentioned? Central server collects all DPs, and people paid out based on percentage of DPs their machines sent to central server? I said you had a good idea, I just don't know how to set that up where it's a. efficient, b. reliable