# Analysis of reaction and timing attacks against cryptosystems based on sparse parity-check codes

## TL;DR

This paper investigates reaction and timing attacks on cryptosystems based on sparse parity-check codes, revealing that such attacks are broadly applicable beyond QC codes and can exploit probabilistic decoding to leak information.

## Contribution

It introduces a new algorithm for attacking QC codes and characterizes new side-channel leakages, expanding understanding of vulnerabilities in sparse parity-check code cryptosystems.

## Key findings

- Attacks are effective beyond QC codes due to probabilistic decoding.
- A novel algorithm improves information recovery in attacks.
- Numerical simulations confirm attack effectiveness.

## Abstract

In this paper we study reaction and timing attacks against cryptosystems based on sparse parity-check codes, which encompass low-density parity-check (LDPC) codes and moderate-density parity-check (MDPC) codes. We show that the feasibility of these attacks is not strictly associated to the quasi-cyclic (QC) structure of the code but is related to the intrinsically probabilistic decoding of any sparse parity-check code. So, these attacks not only work against QC codes, but can be generalized to broader classes of codes. We provide a novel algorithm that, in the case of a QC code, allows recovering a larger amount of information than that retrievable through existing attacks and we use this algorithm to characterize new side-channel information leakages. We devise a theoretical model for the decoder that describes and justifies our results. Numerical simulations are provided that confirm the effectiveness of our approach.