Signed MSB-Set Comb Method for Elliptic Curve Point Multiplication

Comb method is an efficient method to calculate point multiplication in elliptic curve cryptography, but vulnerable to power-analysis attacks. Various algorithms have been proposed recently to make the comb method secure to power-analysis attacks. In this paper, we present an efficient comb method and its Simple Power Analysis (SPA)-resistant counterpart. We first present a novel comb recoding algorithm which converts an integer to a sequence of signed, MSB-set comb bit-columns. Using this recoding algorithm, the signed MSB-set comb method and a modified, SPA-resistant version are then presented. Measures and precautions to make the proposed SPA-resistant comb method resist all power-analysis attacks are also discussed, along with performance comparison with other comb methods. We conclude that our comb methods are among the most efficient comb methods in terms of number of precomputed points and computational complexity.