Some ways to secure elliptic curve cryptosystems

Side Channel Attacks have become a serious threat for cryptographic applications oil 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 all optimized use of space memory with a high level of security and efficiency. In this paper we present all 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 precornputed table; we only store 2(w-1) points instead of 2(w-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.