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Ciphertext Malleability in Lattice-Based KEMs as a Countermeasure to Side Channel Analysis

Pierre-Augustin Berthet

TL;DR

The paper addresses a Side Channel Analysis vulnerability arising from ciphertext malleability in lattice-based KEMs. It introduces a novel countermeasure that uses the same malleability to randomize leakage, enabling practical protection when combined with masking or shuffling. The work generalizes Ravi et al.'s targeted bit-flip attack to arbitrary parameter d and demonstrates how to apply and optimize the attack on FrodoKEM across multiple parameter sets, while also detailing extensions to decryption and decapsulation steps. Overall, the approach provides a low-overhead, compatible mechanism to bolster SCA resistance for multiple PQC primitives, with guidance on scalability and integration with existing defenses.

Abstract

Due to developments in quantum computing, classical asymmetric cryptography is at risk of being breached. Consequently, new Post-Quantum Cryptography (PQC) primitives using lattices are studied. Another point of scrutiny is the resilience of these new primitives to Side Channel Analysis (SCA), where an attacker can study physical leakages. In this work we discuss a SCA vulnerability due to the ciphertext malleability of some PQC primitives exposed by a work from Ravi et al. We propose a novel countermeasure to this vulnerability exploiting the same ciphertext malleability and discuss its practical application to several PQC primitives. We also extend the seminal work of Ravi et al. by detailing their attack on the different security levels of a post-quantum Key Encapsulation Mechanism (KEM), namely FrodoKEM. We also provide a generalisation of their attack to different parameters which could be used in future similar primitives.

Ciphertext Malleability in Lattice-Based KEMs as a Countermeasure to Side Channel Analysis

TL;DR

The paper addresses a Side Channel Analysis vulnerability arising from ciphertext malleability in lattice-based KEMs. It introduces a novel countermeasure that uses the same malleability to randomize leakage, enabling practical protection when combined with masking or shuffling. The work generalizes Ravi et al.'s targeted bit-flip attack to arbitrary parameter d and demonstrates how to apply and optimize the attack on FrodoKEM across multiple parameter sets, while also detailing extensions to decryption and decapsulation steps. Overall, the approach provides a low-overhead, compatible mechanism to bolster SCA resistance for multiple PQC primitives, with guidance on scalability and integration with existing defenses.

Abstract

Due to developments in quantum computing, classical asymmetric cryptography is at risk of being breached. Consequently, new Post-Quantum Cryptography (PQC) primitives using lattices are studied. Another point of scrutiny is the resilience of these new primitives to Side Channel Analysis (SCA), where an attacker can study physical leakages. In this work we discuss a SCA vulnerability due to the ciphertext malleability of some PQC primitives exposed by a work from Ravi et al. We propose a novel countermeasure to this vulnerability exploiting the same ciphertext malleability and discuss its practical application to several PQC primitives. We also extend the seminal work of Ravi et al. by detailing their attack on the different security levels of a post-quantum Key Encapsulation Mechanism (KEM), namely FrodoKEM. We also provide a generalisation of their attack to different parameters which could be used in future similar primitives.
Paper Structure (39 sections, 3 theorems, 9 equations, 5 figures, 10 tables, 3 algorithms)

This paper contains 39 sections, 3 theorems, 9 equations, 5 figures, 10 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Our contributions
  3. Preliminaries
  4. Notations
  5. Generic SCA countermeasures
  6. LWE/LWR PKE using lattices
  7. Fujisaki-Okamoto Transform
  8. FrodoKEM
  9. Parameters
  10. ML-KEM
  11. Parameters
  12. SABER
  13. Parameters
  14. Exploiting ciphertext malleability: existing work and generalisation
  15. Seminal work: Targeted message bit flip for d=1
  16. ...and 24 more sections

Key Result

Theorem 3.2

For any value of $d$, there exists a two-classes distinguisher that gives the value of at least one bit of the output of ($\alpha,d$) with absolute certainty, and this for each bit of the output.

Figures (5)

  • Figure 1: Sector representation of the decoding function for different parameters $d$, with the intervals on the circle boundary counter-clockwise and the sectors labeled with the corresponding outputs to the intervals
  • Figure 2: Bitflipping the output of the decoding for parameter $d=1$
  • Figure 3: Overlap issue with 8 decodings and their 24-bit long output split on 3 registers
  • Figure 4: Overlap issue with 16 decodings and their 48-bit long output split on 3 registers
  • Figure 5: Comparison of the number of biases required for a complete output recovery between Ravi et al. ravi2021exploiting and this work

Theorems & Definitions (15)

  • Remark 2.1
  • Remark 2.2
  • Remark 2.3
  • Remark 2.4
  • Remark 3.1
  • Theorem 3.2
  • Remark 3.3
  • Remark 3.4
  • Remark 3.5
  • Remark 3.6
  • ...and 5 more