1. Biased Nonce Sense: Lattice Attacks against Weak ECDSA Signatures in Cryptocurrencies 2019 Bitcoin FinancialCryptography Signatures
    Joachim Breitner and Nadia Heninger
    [View PDF on eprint.iacr.org]
    [Show BibTex Citation]

    @misc{cryptoeprint:2019:023,
    author = {Joachim Breitner and Nadia Heninger},
    title = {Biased Nonce Sense: Lattice Attacks against Weak ECDSA Signatures in Cryptocurrencies},
    howpublished = {Cryptology ePrint Archive, Report 2019/023},
    year = {2019},
    note = {\url{https://eprint.iacr.org/2019/023}},
    }

In this paper, we compute hundreds of Bitcoin private keys and dozens of Ethereum, Ripple, SSH, and HTTPS private keys by carrying out cryptanalytic attacks against digital signatures contained in public blockchains and Internet-wide scans. The ECDSA signature algorithm requires the generation of a per-message secret nonce. If this nonce is not generated uniformly at random, an attacker can potentially exploit this bias to compute the long-term signing key. We use a lattice-based algorithm for solving the hidden number problem to efficiently compute private ECDSA keys that were used with biased signature nonces due to multiple apparent implementation vulnerabilities.

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