Atomicity Improvement for Elliptic Curve Scalar Multiplication

TL;DR

This paper enhances the atomicity-based protection of elliptic curve scalar multiplication against side-channel attacks, proposing an improved pattern that yields up to 10.6% efficiency gains, especially relevant for embedded devices.

Contribution

It introduces a novel atomic pattern improvement method that outperforms previous techniques in efficiency for elliptic curve scalar multiplication.

Findings

Up to 10.6% efficiency improvement over previous methods

Reevaluation of classical assumptions for embedded device security

Enhanced atomic scalar multiplication pattern

Abstract

In this paper we address the problem of protecting elliptic curve scalar multiplication implementations against side-channel analysis by using the atomicity principle. First of all we reexamine classical assumptions made by scalar multiplication designers and we point out that some of them are not relevant in the context of embedded devices. We then describe the state-of-the-art of atomic scalar multiplication and propose an atomic pattern improvement method. Compared to the most efficient atomic scalar multiplication published so far, our technique shows an average improvement of up to 10.6%.