A New Approach to Code Smoothing Bounds

TL;DR

This paper introduces a novel method for bounding the smoothing parameter in code-based cryptosystems using random walks and equitable partitions, providing a generalization of previous Fourier-based bounds.

Contribution

It presents an alternative approach to bounding the total variation distance, expanding the theoretical toolkit for analyzing code security.

Findings

Derived a new inequality for total variation distance of random walks

Generalized existing bounds for finite abelian groups

Provides a new perspective on code smoothing analysis

Abstract

To analyze the security of code-based cryptosystems, the smoothing parameter, which is closely related to the total variation distance of codes, has been investigated. While previous studies have bounded this distance using the Fourier transform on locally compact abelian groups, we take an alternative approach based on random walks. In this paper, we derive an inequality for the total variation distance of random walks using equitable partitions, and we show that our proposed bound generalizes existing results for finite abelian groups.