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A Statistical Side-Channel Risk Model for Timing Variability in Lattice-Based Post-Quantum Cryptography

Aayush Mainali, Sirjan Ghimire

TL;DR

The paper proposes a scenario-driven statistical framework to quantify timing side-channel risk in lattice-based PQC, explicitly modeling environment noise (idle, jitter, loaded) and secret-dependent leakage with diverse leakage mechanisms. It generates synthetic timing traces for two secret classes and evaluates them with multiple metrics (Welch t, KS distance, Cliff's delta, mutual information, and distribution overlap), then combines these into a TLRI-style composite score for cross-scenario ranking. Across Kyber, Saber, and Frodo, idle conditions yield the strongest distinguishability while jitter and loaded conditions attenuate signals due to increased variance and overlap; cache-index and branch-style leakages emerge as the most informative channels, and faster schemes show higher peak risk under similar leakage assumptions. The framework offers an early-stage, reproducible tool to compare leakage risk across schemes and environments, guiding where to prioritize hardware measurements and countermeasures before platform-specific validation. The findings underscore the need to consider environment-driven variability in practical PQC deployments and support more robust, leakage-resilient designs in lattice-based KEMs.

Abstract

Timing side-channels are an important threat to cryptography that still needs to be addressed in implementations, and the advent of post-quantum cryptography raises this issue because the lattice-based schemes may produce secret-dependent timing variability with the help of complex arithmetic and control flow. Since also real timing measurements are affected by environmental noise (e.g. scheduling effects, contention, heavy tailed delays), in this work a scenario-based statistical risk model is proposed for timing leakage as a problem of distributional distinguishability under controlled execution conditions. We synthesize traces for two secret classes in idle, jitter and loaded scenarios and for multiple leakage models and quantify leakage with Welch's t-test, KS distance, Cliff's delta, mutual information, and distribution overlap to combine in a TLRI like manner to obtain a consistent score for ranking scenarios. Across representative lattice-based KEM families (Kyber, Saber, Frodo), idle conditions generally have the best distinguishability, jitter and loaded conditions erode distinguishability through an increase in variance and increase in overlap; cache-index and branch-style leakage tends to give the highest risk signals, and faster schemes can have a higher peak risk given similar leakage assumptions, allowing reproducible comparisons at an early design stage, prior to platform-specific validation.

A Statistical Side-Channel Risk Model for Timing Variability in Lattice-Based Post-Quantum Cryptography

TL;DR

The paper proposes a scenario-driven statistical framework to quantify timing side-channel risk in lattice-based PQC, explicitly modeling environment noise (idle, jitter, loaded) and secret-dependent leakage with diverse leakage mechanisms. It generates synthetic timing traces for two secret classes and evaluates them with multiple metrics (Welch t, KS distance, Cliff's delta, mutual information, and distribution overlap), then combines these into a TLRI-style composite score for cross-scenario ranking. Across Kyber, Saber, and Frodo, idle conditions yield the strongest distinguishability while jitter and loaded conditions attenuate signals due to increased variance and overlap; cache-index and branch-style leakages emerge as the most informative channels, and faster schemes show higher peak risk under similar leakage assumptions. The framework offers an early-stage, reproducible tool to compare leakage risk across schemes and environments, guiding where to prioritize hardware measurements and countermeasures before platform-specific validation. The findings underscore the need to consider environment-driven variability in practical PQC deployments and support more robust, leakage-resilient designs in lattice-based KEMs.

Abstract

Timing side-channels are an important threat to cryptography that still needs to be addressed in implementations, and the advent of post-quantum cryptography raises this issue because the lattice-based schemes may produce secret-dependent timing variability with the help of complex arithmetic and control flow. Since also real timing measurements are affected by environmental noise (e.g. scheduling effects, contention, heavy tailed delays), in this work a scenario-based statistical risk model is proposed for timing leakage as a problem of distributional distinguishability under controlled execution conditions. We synthesize traces for two secret classes in idle, jitter and loaded scenarios and for multiple leakage models and quantify leakage with Welch's t-test, KS distance, Cliff's delta, mutual information, and distribution overlap to combine in a TLRI like manner to obtain a consistent score for ranking scenarios. Across representative lattice-based KEM families (Kyber, Saber, Frodo), idle conditions generally have the best distinguishability, jitter and loaded conditions erode distinguishability through an increase in variance and increase in overlap; cache-index and branch-style leakage tends to give the highest risk signals, and faster schemes can have a higher peak risk given similar leakage assumptions, allowing reproducible comparisons at an early design stage, prior to platform-specific validation.
Paper Structure (52 sections, 36 equations, 5 figures, 3 tables)

This paper contains 52 sections, 36 equations, 5 figures, 3 tables.

Table of Contents

  1. Introduction
  2. Literature Review
  3. Timing Side-Channels: Foundations and Modern Threat Surfaces
  4. Side-Channel and Fault Attacks in the Post-Quantum Era
  5. Leakage in Lattice-Based Constructions: Encoding, NTT, and Algorithmic Structure
  6. Hardware and Accelerator Implementations: Performance--Security Trade-offs
  7. From Isolated Attacks to Risk Quantification Under Timing Variability
  8. Identified Gaps and Motivation for This Work
  9. Methodology
  10. Overview of the Experimental Design
  11. Scenario definition and experimental objective
  12. Trace structure and notation
  13. Secret Sampling and Baseline Timing Model
  14. Secret generation model
  15. Baseline cycles and scheme parameterisation
  16. ...and 37 more sections

Figures (5)

  • Figure 1: Scenario-to-score pipeline: scenario definition, trace generation, metric computation, and TLRI risk scoring
  • Figure 2: TLRI scores across all simulated scenarios (scheme $\times$ environment $\times$ leakage type). Higher TLRI indicates stronger timing distinguishability between secret classes.
  • Figure 3: Kyber worst-case scenario (idle + cache-index leakage). Left: histogram+KDE. Middle: ECDF. Right: violin plot.
  • Figure 4: Saber worst-case scenario (idle + cache-index leakage). Left: histogram+KDE. Middle: ECDF. Right: violin plot.
  • Figure 5: Frodo worst-case scenario (idle + cache-index leakage). Left: histogram+KDE. Middle: ECDF. Right: violin plot.