Preventing Distinguishability between Multiplication and Squaring Operations

TL;DR

This paper investigates vulnerabilities in elliptic curve cryptography's scalar multiplication to side-channel attacks and proposes two mitigation techniques involving data redirection and bus reloading.

Contribution

It introduces and analyzes two novel mitigation strategies to reduce distinguishability in multiplication and squaring operations in ECC implementations.

Findings

Energy consumption variations can reveal scalar multiplication details.

Data redirection and bus reloading mitigate side-channel distinguishability.

The mitigation techniques are effective regardless of the multiplication method.

Abstract

Scalar multiplication kP is a critical operation in Elliptic Curve Cryptosystems (ECC), often targeted by Side-Channel Analysis (SCA). Despite strategies based on atomic patterns to enhance security, the binary kP algorithms remain susceptible to simple SCA due to energy consumption variations in field multipliers during passing two different or two identical operands. This vulnerability arises independent of the multiplication method used. We implemented and analysed two mitigation techniques: one involving data redirection and another focusing on bus reloading.