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

TL;DR

This paper demonstrates that binary scalar multiplication algorithms in elliptic curve cryptography, even when using atomic block patterns for protection, remain vulnerable to single-trace side-channel attacks.

Contribution

It shows that Chevallier-Mames atomic block patterns do not fully prevent single-trace SCA vulnerabilities in binary kP algorithms.

Findings

Binary right-to-left and left-to-right kP algorithms are vulnerable to SCA.

Atomic block patterns do not eliminate vulnerabilities in these implementations.

Vulnerability persists even with projective coordinate randomization.

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.