Macchetti, M. 2023. A novel related nonce attack for ecdsa. [Cryptology ePrint Archive, Paper 2023/305].
Added by: Jack (2023-03-06 22:25) Last edited by: Jack (2023-03-06 22:35)
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Abstract
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We describe a new related nonce attack able to extract the original signing key from a small collection of ECDSA signatures gener- ated with weak PRNGs. Under suitable conditions on the modulo order of the PRNG, we are able to attack linear, quadratic, cubic as well as arbitrary degree recurrence relations (with unknown coefficients) with few signatures and in negligible time. We also show that for any collec- tion of randomly generated ECDSA nonces, there is one more nonce that can be added following the implicit recurrence relation, and that would allow retrieval of the private key; we exploit this fact to present a novel rogue nonce attack against ECDSA. Up to our knowledge, this is the first known attack exploiting generic and unknown high-degree algebraic relations between nonces that do not require assumptions on the value of single bits or bit sequences (e.g. prefixes and suffixes).
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Blog:
https://research.kudelskisecurity.com/2023/03/06/polynonce-a-tale-of-a-novel-ecdsa-attack-and-bitcoin-tears/
Added by: Jack Last edited by: Jack
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