CRT RSA Algorithm Protected Against Fault Attacks

Embedded devices performing RSA signatures are subject to Fault Attacks, particularly when the Chinese Remainder Theorem is used. In most cases, the modular exponentiation and the Garner recombination algorithms are targeted. To thwart Fault Attacks, we propose a new generic method of computing modular exponentiation and we prove its security in a realistic fault model. By construction, our proposal is also protected against Simple Power Analysis. Based on our new resistant exponentiation algorithm, we present two different ways of computing CRT RSA signatures in a secure way. We show that those methods do not increase execution time and can be easily implemented on low-resource devices.