Efficient Modular Exponentiation Resistant to Simple Power Analysis in DSA-Like Systems

In this paper, based on the concept of asynchronous strategy, we propose a new novel method to compute modular exponentiations against simple power analysis (SPA) in DSA-like schemes. Since the probabilities of digits in different detected computations are equivalent, the proposed methods are resistant to simple power analysis. Based on the SU₁ method of asynchronous strategy, an efficient SPA-resistant method is proposed and has expected time complexity nS + 0.667nM (⇋1.467nM), where n, S, and M are the number of digits, squaring and multiplication, respectively. Although the performance can be further improved by using signed-digit representations, the security is reduced because of the non-equivalent probabilities of digits.