Some Ways to Secure Elliptic Curve Cryptosystems

Abstract

Side Channel Attacks have become a serious threat for cryptographic applications on devices with small resources. Indeed, it turns out that the usual randomization techniques cannot prevent the recent DPA attacks (RPA and ZPA). The implementation of elliptic curve cryptosystems (ECC) on such devices must combine an optimized use of space memory with a high level of security and efficiency. In this paper we present an efficient SCA-resistant algorithm based on the fixed-base comb method. We propose to modify the binary representation of the secret scalar in order to obtain a new sequence of non-zero bit-strings. This, combined with the use of Randomized Linearly-transformed coordinates (RLC), will prevent the SCA attacks on the comb method, including RPA and ZPA. Furthermore, our algorithm optimizes the size of the precomputed table; we only store 2w-1 points instead of 2w −1 for the fixed-base comb method, without affecting in any way the computation time. We also present a parallel architecture implementation of the proposed algorithm including the countermeasures for preventing the recent attacks RPA and ZPA.