Security Analysis of wrNAF and SPA Resistant Scalar Multiplication

Signed digit radix-r representation (such as omegarNAF) is used for the efficient implementation of the pairing based cryptosystems. The side channel attack, which uses the leaked information such as power consumption and timing information from a cryptographic device, is a serious threat to the implementations of a cryptosystem. In this paper, we utilize the simple power analysis technique to analyze the security of the scalar multiplication using omegarNAF representation and we can see that the omegarNAF is not a SPA resistant receding. In order to resist against SPA, we present two integer recodings (right-to-left and left-to-right) using two special digit sets respectively. The two recodings can be used to perform the scalar multiplication with a fixed sequence of operations without inserting dummy operations. Compared to Han´s fixed pattern scheme, the proposed schemes can reduce about 16.7% to 37.5% table sizes (the number of precomputed and needed to be stored points) for r = 3, 5 and w = 2, 3,4, 5.