Fault Attack on Schnorr Based Identification and Signature Schemes

In this paper, we study the security of Schnorr based identification and signature schemes. Like the carry attack of Fouque et al. at CHES last year, we exploit the carry knowledge from fault attack on other public-key schemes like DSA and other ECDSA signature scheme, Schnorr and GPS authentication and signature schemes. These attacks can be used to recover very efficiently the secret key and it is worth noticing that the complexity of the attack depends on the equation involving the secret key. We also present different techniques to learn the carry leakage using fault analysis.