An exploit is a method or piece of code that takes advantage of a vulnerability to produce an unintended effect. In ECDSA, reusing a nonce across signatures exposes enough information to recover that nonce and then the private key. section 9.5.2
The reused-nonce attack proceeds in a short chain:
- Compare two signatures made with the same nonce; their identical r values reveal the implementation failure. section 9.5.2
A failing ECDSA implementation
A test signs “Hello World!” and a time-derived message with a fixed nonce. Both signatures produce the same r value; the exploit recovers the nonce, derives the private key, and verifies a new signature against the original public key.
The defensive rule is direct: generate a unique, random nonce for every ECDSA signature. Even partial nonce leakage can enable more advanced attacks, so randomness remains a critical security boundary. section 9.5.2
