Distinguishability Investigation on Longa's Atomic Patterns when used as a Basis for Implementing Elliptic Curve Scalar Multiplication Algorithms

TL;DR

This paper empirically investigates Longa's atomic patterns in elliptic curve scalar multiplication for side-channel attack resistance, identifying discrepancies and implementing the patterns on a microcontroller for practical analysis.

Contribution

First practical implementation and empirical analysis of Longa's atomic patterns in ECC scalar multiplication, including correction of original pattern discrepancies.

Findings

No significant differences in execution time or atomic block shapes found

Identified and corrected discrepancies in Longa's original atomic patterns

Provides a foundation for further SCA-resistance investigations

Abstract

In the evolving landscape of cryptographic security, the robustness of Elliptic Curve Cryptography (ECC) against side-channel analysis (SCA) attacks is of paramount importance due to the widespread use of ECC and the growing sophistication of SCAs. This thesis delves into the investigation of Longa's atomic patterns applied within Elliptic Curve scalar multiplication algorithms, assessing their resistance to horizontal SCAs. The research employs these atomic patterns in practical implementation on a microcontroller (Texas Instruments Launchpad F28379 board) using the open-source cryptographic library FLECC in C. In our analysis, we only focused on the distinguishability of the first atomic block in the Elliptic Curve point doubling and point addition patterns. Due to various technical limitations, we were unable to determine significant differences in the execution time and the shapes of the atomic blocks. Further investigations of the SCA-resistance can be performed based on this work. A significant contribution of this work is the identification and correction of several discrepancies in Longa's original atomic patterns. This thesis marks the first practical implementation of Longa's patterns, extending the theoretical research into empirical analysis.