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Simple Power Analysis of Polynomial Multiplication in HQC

Pavel Velek, Tomáš Rabas, Jiří Buček

TL;DR

A single-trace Simple Power Analysis attack against HQC that exploits power consumption leakage that occurs during polynomial multiplication performed at the beginning of HQC decryption.

Abstract

The Hamming Quasi-Cyclic (HQC) cryptosystem was selected for standardization in the fourth round of the NIST Post-Quantum Cryptography (PQC) standardization project. The goal of the PQC project is to standardize one or more quantum-resistant public-key cryptographic algorithms. In this paper, we present a single-trace Simple Power Analysis (SPA) attack against HQC that exploits power consumption leakage that occurs during polynomial multiplication performed at the beginning of HQC decryption. Using the ChipWhisperer-Lite board, we perform and evaluate the attack, achieving a 99.69% success rate over 10 000 attack attempts. We also propose various countermeasures against the attack and evaluate their time complexity.

Simple Power Analysis of Polynomial Multiplication in HQC

TL;DR

A single-trace Simple Power Analysis attack against HQC that exploits power consumption leakage that occurs during polynomial multiplication performed at the beginning of HQC decryption.

Abstract

The Hamming Quasi-Cyclic (HQC) cryptosystem was selected for standardization in the fourth round of the NIST Post-Quantum Cryptography (PQC) standardization project. The goal of the PQC project is to standardize one or more quantum-resistant public-key cryptographic algorithms. In this paper, we present a single-trace Simple Power Analysis (SPA) attack against HQC that exploits power consumption leakage that occurs during polynomial multiplication performed at the beginning of HQC decryption. Using the ChipWhisperer-Lite board, we perform and evaluate the attack, achieving a 99.69% success rate over 10 000 attack attempts. We also propose various countermeasures against the attack and evaluate their time complexity.
Paper Structure (13 sections, 5 equations, 5 figures, 1 table)

This paper contains 13 sections, 5 equations, 5 figures, 1 table.

Table of Contents

  1. INTRODUCTION
  2. HQC
  3. HQC Key Generation and Decryption
  4. TARGET IMPLEMENTATION
  5. Multiplication Algorithm
  6. Implementation Analysis
  7. ATTACK SETUP
  8. ATTACK APPROACH
  9. ATTACK EVALUATION
  10. COUNTERMEASURES
  11. Masking
  12. MULTIPLICATION ALGORITHM COMPLEXITY
  13. CONCLUSION

Figures (5)

  • Figure 1: Figure of the ChipWhisperer-Lite board with a 32-bit STM32F303 target.
  • Figure 2: Power consumption trace used to recover the value of the first four bits of $a$, indicating a value of 10 based on the drop between peaks number 10 and 11.
  • Figure 3: Power consumption trace used to recover the value of the second set of four bits of $a$, indicating a value of 4 based on the drop between peaks number 4 and 5.
  • Figure 4: Normalized confusion matrix showing the actual correct values along with the values recovered by the single-trace SPA attack for the first 4 bits of $a$. The matrix is row-normalized and shows the distribution of the recovered values for each actual value.
  • Figure 5: Normalized confusion matrix showing the actual correct values along with the values recovered by the single-trace SPA attack for the last 60 bits of $a$. For this portion of the private key, all bits were recovered with 100% accuracy. The matrix is row-normalized and shows the distribution of the recovered values for each actual value.