Secure RSA implementation against horizontal correlation power analysis attack

Abstract

Since passive leakage information analysis and active fault injection attacks on naive implementation of the Rivest, Shamir, and Adelman (RSA) cryptosystem can be used to retrieve a secret key, several countermeasures against these attacks have been developed. In this paper, we point out that the horizontal correlation power analysis (HCPA) attack can be applied to the square-multiply ladder exponentiation algorithm and its variants, which are used for secure RSA implementation. Furthermore, we propose a novel exponentiation algorithm to defeat previous implementation attacks, as well as the HCPA attack, in particular. This algorithm is designed to overcome weakness against the HCPA attack by adopting an intermediate message update technique based on an extended modulus. We can employ the proposed exponentiation algorithm to implement a secure Chinese remainder theorem-based RSA (CRT-RSA) cryptosystem by thwarting the Bellcore attack.