ECDSA Cracking Methods
William J. Buchanan, Jamie Gilchrist, Keir Finlow-Bates
TL;DR
The paper analyzes nonce-related vulnerabilities in ECDSA and their implications for blockchain security, particularly in Bitcoin and Ethereum. It catalogs five attack families—revealed nonces, weak nonces via the LLL algorithm, nonce reuse, two-key/shared-nonce scenarios, and fault attacks—and provides the mathematical relations enabling private-key recovery under each weakness. It highlights that robust nonce generation and usage are essential to preserve ECDSA security in practice. The work serves as a practical guide for developers and security practitioners to recognize and mitigate nonce-related risks in real-world deployments.
Abstract
The ECDSA (Elliptic Curve Digital Signature Algorithm) is used in many blockchain networks for digital signatures. This includes the Bitcoin and the Ethereum blockchains. While it has good performance levels and as strong current security, it should be handled with care. This care typically relates to the usage of the nonce value which is used to create the signature. This paper outlines the methods that can be used to break ECDSA signatures, including revealed nonces, weak nonce choice, nonce reuse, two keys and shared nonces, and fault attack.