ECDSA

Full Title

Elliptic Curves with DSA

Context

One of the weaknesses of ECDSA is a fault attack. In the fault attack in ECDSA we only require two signatures. One is produced without a fault (r,s), and the other has a fault (rf,sf). From these, we can generate the private key [1,2].

• Here is the Sage code for this

[1] Sullivan, G. A., Sippe, J., Heninger, N., & Wustrow, E. (2022). Open to a fault: On the passive compromise of {TLS} keys via transient errors. In 31st USENIX Security Symposium (USENIX Security 22) (pp. 233-250). [2] Poddebniak, D., Somorovsky, J., Schinzel, S., Lochter, M., & Rösler, P. (2018, April). Attacking deterministic signature schemes using fault attacks. In 2018 IEEE European Symposium on Security and Privacy (EuroS&P) (pp. 338-352). IEEE.