Assessing and countering reaction attacks against post-quantum public-key cryptosystems based on QC-LDPC codes

TL;DR

This paper evaluates the vulnerability of QC-LDPC and QC-MDPC code-based post-quantum cryptosystems to reaction attacks, analyzing how secret key structure influences security and identifying conditions for resistance.

Contribution

It provides a comprehensive complexity analysis of reaction attacks on these cryptosystems and highlights the importance of secret code rate and decoding algorithms for security.

Findings

QC-LDPC systems can resist reaction attacks with proper decoding algorithms.

Higher secret code rate enhances resistance to reaction attacks.

The structure of the secret key significantly impacts attack complexity.

Abstract

Code-based public-key cryptosystems based on QC-LDPC and QC-MDPC codes are promising post-quantum candidates to replace quantum vulnerable classical alternatives. However, a new type of attacks based on Bob's reactions have recently been introduced and appear to significantly reduce the length of the life of any keypair used in these systems. In this paper we estimate the complexity of all known reaction attacks against QC-LDPC and QC-MDPC code-based variants of the McEliece cryptosystem. We also show how the structure of the secret key and, in particular, the secret code rate affect the complexity of these attacks. It follows from our results that QC-LDPC code-based systems can indeed withstand reaction attacks, on condition that some specific decoding algorithms are used and the secret code has a sufficiently high rate.