A secure exponentiation algorithm resistant to a combined attack on RSA implementation

Because two types of side-channel attacks, namely passive information leakages and active fault injections, are considered separate implementation threats to cryptographic modules, most countermeasures against these attacks have been independently developed. However, Amiel et al. demonstrated that a fault injection combined with a simple power analysis (SPA) can break such a classical Rivest, Shamir, and Adelman (RSA) system implementation. In this paper, we show that this combined attack (CA) can be applied to the Boscher, Naciri, and Prouff algorithm, which is an SPA/fault attack (FA)-resistant exponentiation method for RSA implementation. Furthermore, this paper proposes a novel exponentiation algorithm resistant to power analysis and an FA as well as to the CA. The proposed exponentiation algorithm can be employed for secure Chinese remainder theorem-RSA implementation. In addition, the paper presents some experimental results of an SPA under the assumption of a successful fault injection.