Horizontal SCA Attacks on Binary kP Algorithms using Chevallier-Mames Atomic Blocks

Abstract

Scalar multiplication kP is the operation most frequently targeted in Elliptic Curve (EC) cryptosystems. To protect against single-trace Side-Channel Analysis (SCA) attacks, the atomicity principle and various atomic block patterns have been proposed in the past. In this work we use our software and hardware implementations to demonstrate that binary right-to left and left-to-right kP algorithms, when implemented with Chevallier-Mames atomic block patterns, are still vulnerable to single-trace SCA attacks. The vulnerability remains true for the left-to-right kP algorithm with projective coordinate randomization.