jakecraige/keyrecovery

Private Key Recovery Tool

A command line tool and Golang library to recover private keys from insecurely generated elliptic curve signatures if they were generated with flaws which allow it. It also provides a tool to generate insecure signatures for testing the tool and analyzing them.

See the Trail of Bits post on ECDSA to learn more about the type of attacks implemented.

Supported Curves & Signatures

Curve	Signature
secp256k1	ECDSA-SHA256, ECDSA-KECCAK256
P256	ECDSA-SHA256, ECDSA-KECCAK256
P384	ECDSA-SHA256, ECDSA-KECCAK256
P521	ECDSA-SHA512

Attacks

Nonce Reuse

$ bin/keyrecovery generate --curve=P256 --sig-type=ECDSA-SHA256 --mode=nonce-reuse | tee sigs.txt
c7c88a612961672296961826db7860482016c2788e83c4b54905fce744564746a82c70e1e60ec1ed8c93e327288bdbb75d5d5625c66d758b9301bf14c776286d8e2aa0ffa3b57ef13860f138ed535e46c89799a448d7e3becd3974e0d05261ec398943a917b9c7f504db89e31e2b24319aa96c353d275f2588347cbefa79810d6578616d706c65206e6f6e63652d726575736520736967202331
c7c88a612961672296961826db7860482016c2788e83c4b54905fce744564746a82c70e1e60ec1ed8c93e327288bdbb75d5d5625c66d758b9301bf14c776286d8e2aa0ffa3b57ef13860f138ed535e46c89799a448d7e3becd3974e0d05261ec392bcc70cd3aba11d325240c742b75f6ab0e44096ee04aae14dc8b90d100533f6578616d706c65206e6f6e63652d726575736520736967202332

$ cat sigs.txt | bin/keyrecovery recover --curve=P256 --sig-type=ECDSA-SHA256 --mode=nonce-reuse
Recovered private key:
   pub: c7c88a612961672296961826db7860482016c2788e83c4b54905fce744564746a82c70e1e60ec1ed8c93e327288bdbb75d5d5625c66d758b9301bf14c776286d
  priv: 548f9ae92d49e3855aa81abaca8581e1df35d4a377a3b776226865b4f7095ff7

Nonce Bias

TODO: Implement fixed bit bias recovery with LLL