Topic: Pollard's kangaroo ECDLP solver - page 120. (Read 60624 times)

-snip-
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..

zielar, how are you?

You used to perform 4sqrt(N) group operations, so your probability to find the #110 should be approx 90%. But why the funds still have not been transferred? from #110?

@JeanLuc tell me please about shifting.
Indeed, in order to use the DP from the previous work, we still need to shift the range and subtract the range of the public key?

Question from newbie, please redirect me if it was already explained:
let's say I have public key (uncompressed, 04....). Is there a way to find the expected start/stop range?

Question from newbie, please redirect me if it was already explained:
let's say I have public key (uncompressed, 04....). Is there a way to find the expected start/stop range?

Yes you're right. I will fix this.
Thanks for the useful work, I will take your mods (work on windows ?) and apd it to the official release.

In "wsplit" mode, the time and count should be reset after every save? When I merged all split files the total time are incorrect.

In "wsplit" mode, the time and count should be reset after every save? When I merged all split files the total time are incorrect.


What is the best way to combine all the save files?

I added a "Directory Merge" option to merge more than two files at once (https://github.com/PatatasFritas/FriedKangaroo/commit/f36c560135710f9956677eb3dcda78ffd1ccb0a4)

Example with 40bits key

pubkey: 03a2efa402fd5268400c77c20e574ba86409ededee7c4020e4b9f0edbee53de0d4
priv: 0xe9ae4933d6

We get a wild DP from savefile, x-coord and distance

Distance: 0x100d3439c4
Starting point (offset): 2^39 = 0x8000000000


The tame distance 0x79bb7d6d9a returns X-coord 0000157f1985299f1bda6646dd76bff14d4321506319af572ab7604e22f2d172.

-snip-
I was "crack" my brain but cant understand how get this coordinates

(374deeae22c93f955cb83ad2071f7e2256f6e109cad7bca6d71dc7b24414bb36,171165b64fcd4f9916032c06f806f7293828d66300e543217875bea98daf734a)

for this starting point  - 40000000000000
-snip-

@JeanLuc and other folks who has knowledge in this area..
From what I realized that DP is just the x coordinate with a certain number of leading zeros .. like a brilliant among stones.
Kangaroo algorithm, creates a tribe of tame and a tribe of wild kangaroos.
Tame kangaroos are tied to a range, and wild to the desired public key.
Now the idea itself .. Why can not we use the experience of previous work?
What I mean. For example, we’ll start accumulating experience with a 54-bit key
The range where this private key located is
40000000000000
7fffffffffffff
and seek public key 0385a30d8413af4f8f9e6312400f2d194fe14f02e719b24c3f83bf1fd233a8f963
we can shift the range to 0
and subtract the beginning of the range from the public key
(0x85a30d8413af4f8f9e6312400f2d194fe14f02e719b24c3f83bf1fd233a8f963,0x0eb400323654cec63999b56f4ba44e8b21ab92d9d697fabe4666df3678585669)
-
(374deeae22c93f955cb83ad2071f7e2256f6e109cad7bca6d71dc7b24414bb36,171165b64fcd4f9916032c06f806f7293828d66300e543217875bea98daf734a)
=
(b1f8ba606a61026d1ecaa93d9e9ceb12260c33e92809ed1ecb0850a2856accc1,ac46d892583d7fdd24a25a229b6ea8d17add77b1f410a9d30441e0acbec19c74)
and range
0
3fffffffffffff
as result we will have key 0x2ABE1F9B67E114
if we add range we can regenerate real key
0x2ABE1F9B67E114+0x40000000000000=0x6ABE1F9B67E114
So we have a saved working file, where there are DP both tame and wild kangaroos in range 0-3fffffffffffff
DP of wild kangaroos we do not need more  so they are tied to the public key.
We can cut only tame kangaroos points from the work file and save to a new file.
And this tame will be correct for next puzzle because they are in the same range as next pazzle(after shifting ofcourse)
So we can use this file like initial to next pazzle
Next 59bit Puzzle..
range
800000000000000
fffffffffffffff
and seek public key 0348e843dc5b1bd246e6309b4924b81543d02b16c8083df973a89ce2c7eb89a10d
do the same thing, shift the range to 0 and subtract the beginning of the range from the public key
(0x48e843dc5b1bd246e6309b4924b81543d02b16c8083df973a89ce2c7eb89a10d,0xd094fcabf8995e2a25c73298a9f7419720db622daff89c67fd5535f6ac29720f)
-
(8991225911b9132d28f5c6bc763ceab7d18c37060e8bd1d7ed44db7560788c1e,da8b4d987cc9ac9b27b8763559b136fa36969c84fdef9e11635c42228e8f0ef1)
=
(2b90a8680d08cf81e15e209acadbb16b7bdff19787d6d13ca6a7852fee8d1013,447a29425ea9773471ad9810d21a976cf5bd4bdb46d0c8ae537591dce43252f2)
and range
0
7ffffffffffffff
Don`t forget that we already have some tame DPs on this range(0-3fffffffffffff), so we should find collision faster!
result key is 0x7C07A1825367BBE
add range and real key
0x7C07A1825367BBE+0x800000000000000=0xFC07A1825367BBE
than do the same, cut from work file only tame kangaroos, save and solve next pazzle...
In this case, after each puzzle, we will already have more and more DP points from tame kangaroos.
What you think?

40000000000000
7fffffffffffff
and seek public key 0385a30d8413af4f8f9e6312400f2d194fe14f02e719b24c3f83bf1fd233a8f963
we can shift the range to 0
and subtract the beginning of the range from the public key
(0x85a30d8413af4f8f9e6312400f2d194fe14f02e719b24c3f83bf1fd233a8f963,0x0eb400323654cec63999b56f4ba44e8b21ab92d9d697fabe4666df3678585669)
-
(374deeae22c93f955cb83ad2071f7e2256f6e109cad7bca6d71dc7b24414bb36,171165b64fcd4f9916032c06f806f7293828d66300e543217875bea98daf734a)
=
(b1f8ba606a61026d1ecaa93d9e9ceb12260c33e92809ed1ecb0850a2856accc1,ac46d892583d7fdd24a25a229b6ea8d17add77b1f410a9d30441e0acbec19c74)
and range
0
3fffffffffffff

if you still haven't managed to export the workfile, here are the changes I made to the code to export the DPs to txt.

The X-coord is 128+18 bits and distance 126bits. The X-coordinate could be re-generated from the distance if necessary.

https://github.com/PatatasFritas/FriedKangaroo/commit/1669df5f91ef2cc8a7619b21f66883fa164ab602