Paper 2019/023
Biased Nonce Sense: Lattice Attacks against Weak ECDSA Signatures in Cryptocurrencies
Joachim Breitner and Nadia Heninger
Abstract
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.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Financial Cryptography and Data Security 2019
- Keywords
- Hidden number problemECDSALatticesBitcoinCrypto
- Contact author(s)
- nadiah @ cs ucsd edu
- History
- 2019-04-30: revised
- 2019-01-09: received
- See all versions
- Short URL
- https://ia.cr/2019/023
- License
-
CC BY
BibTeX
@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, Paper 2019/023},
year = {2019},
url = {https://eprint.iacr.org/2019/023}
}
