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

Sze Hei Li

TL;DR

This thesis marks the first practical implementation of Longa's atomic patterns applied within Elliptic Curve scalar multiplication algorithms, extending the theoretical research into empirical analysis and assessing their resistance to horizontal SCAs.

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.

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

TL;DR

This thesis marks the first practical implementation of Longa's atomic patterns applied within Elliptic Curve scalar multiplication algorithms, extending the theoretical research into empirical analysis and assessing their resistance to horizontal SCAs.

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.
Paper Structure (47 sections, 4 equations, 35 figures, 22 tables, 2 algorithms)

This paper contains 47 sections, 4 equations, 35 figures, 22 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Motivation
  3. Contributions
  4. Structure of This Thesis
  5. Background
  6. Elliptic Curve Cryptosystem
  7. Binary Algorithms for EC Scalar Multiplication
  8. Side-Channel Analysis Attacks
  9. Vulnerabilities of kP Implementations to SCA
  10. Atomicity as a Countermeasure Against SSCA
  11. Vulnerabilities of the Atomic Patterns
  12. Key-dependent Data Processing
  13. Key-dependent Addressing of Registers
  14. State-of-the-art Literature Overview
  15. Analysis of MNAMNAA-based Algorithms
  16. ...and 32 more sections

Figures (35)

  • Figure 1: Number of published papers that referenced [2] over the years.
  • Figure 2: Distribution of themes of literature referencing [2].
  • Figure 3: Front side and back side of the board attacked.
  • Figure 4: The Integrated Circuit Scanner positioning the board and the EM-probe.
  • Figure 5: The oscilloscope connected to the probe showing the captured trace.
  • ...and 30 more figures