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Topic
Board Development & Technical Discussion
Topic OP
LLL & Babai's Plane Algorithm to find Private key
by
krashfire
on 13/09/2024, 18:19:56 UTC
I was testing on 2 signatures. both created with different K nonce.

as we all know, it will not lead to the correct private key unless the same nonce is reuse. However, i extended the code to include Babai's Nearest plane algorithm to readjust the wrong private key and to get it closer to the correct private key by "guiding it to the correct pubkey coordinates and it manage to give me the partial private key. I think this is interesting and will be exploring further to recover full private key.

result from my test.

Code:

root@MSI:/home/krash/test# python3 test.py
INFO:__main__:Using 2 signatures to build the lattice...
INFO:__main__:Short vectors after LLL reduction:
INFO:__main__:Short vector: (166728803922956164814674931204777127007, 0, -269917836034390020152096309044001076683, 0)
INFO:__main__:Short vector: (284880382552528911560114733869411675383, 0, 233299777452147397360970206987837337582, 0)
INFO:__main__:Short vector: (0, 115792089237316195423570985008687907853269984665640564039457584007908834671663, 0, 0)
INFO:__main__:Short vector: (191322878670180847261800180723017804593, 0, -63475476205101254537288001668546129622, 115792089237316195423570985008687907853269984665640564039457584007913129639936)
INFO:__main__:Completed LLL reduction.
INFO:__main__:partial private key from Babai: 000000000000000000000000000000007d6eccb306788626b5f389b33f092c5f