Practical Investigation on the Distinguishability of Longa's Atomic Patterns

TL;DR

This study evaluates the distinguishability of Longa's atomic patterns in elliptic curve cryptography, implementing and analyzing electromagnetic side-channel traces to assess their effectiveness and identify areas for further security improvements.

Contribution

We implemented Longa's atomic patterns for elliptic curve point operations and analyzed electromagnetic traces, providing insights into their side-channel resistance and correcting the atomic patterns.

Findings

Significant differences in execution time and shape of atomic blocks were not observed.

Electromagnetic analysis offers limited distinguishability of atomic patterns under current conditions.

Corrections to Longa's atomic patterns were proposed based on experimental observations.

Abstract

This paper investigates the distinguishability of the atomic patterns for elliptic curve point doubling and addition operations proposed by Longa. We implemented a binary elliptic curve scalar multiplication kP algorithm with Longa's atomic patterns for the NIST elliptic curve P-256 using the open-source cryptographic library FLECC in C. We measured and analysed an electromagnetic trace of a single kP execution on a microcontroller (TI Launchpad F28379 board). Due to various technical limitations, significant differences in the execution time and the shapes of the atomic blocks could not be determined. Further investigations of the side channel analysis-resistance can be performed based on this work. Last but not least, we examined and corrected Longa's atomic patterns corresponding to formulae proposed by Longa.