Fault Resistant RSA Signatures: Chinese Remaindering in Both Directions

Fault attacks are one of the most severe attacks against secure embedded cryptographic implementations. Block ciphers such as AES, DES or public key algorithms such as RSA can be broken with as few as a single or a handful of erroneous computation results. Many countermeasures have been proposed both at the algorithmic level and using ad-hoc methods. In this paper, we address the problem of finding efficient countermeasures for RSA signature computations based on the Chinese Remainder Theorem for which one uses the inverse operation (verification) in order to secure the algorithm against fault attacks. We propose new efficient methods with associated security proofs in two different models; our methods protect against run-time errors, computation errors, and most permanent errors in the key parameters as well. We also extend our methods with infective computation strategies to secure the algorithm against doublefaults.