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Title: Biased Nonce Sense: Lattice Attacks Against Weak ECDSA Signatures in Cryptocurrencies
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.
Authors:
;
Award ID(s):
1651344
Publication Date:
NSF-PAR ID:
10174436
Journal Name:
FC 2019: Financial Cryptography and Data Security
Page Range or eLocation-ID:
3-20
Sponsoring Org:
National Science Foundation
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