Improved Quantum Information Set Decoding

TL;DR

This paper introduces a generalized quantum walk framework for information set decoding algorithms, enabling the combination of Near Neighbour techniques with quantum algorithms to improve decoding efficiency for binary linear codes.

Contribution

It provides a new, more general quantum walk-based framework for ISD algorithms and integrates Near Neighbour search into this framework for enhanced decoding methods.

Findings

Generalized quantum walk framework for ISD algorithms

Combined Near Neighbour search with quantum walk techniques

Enhanced quantum decoding algorithm for binary linear codes

Abstract

In this paper we present quantum information set decoding (ISD) algorithms for binary linear codes. First, we give an alternative view on the quantum walk based algorithms proposed by Kachigar and Tillich (PQCrypto'17). It is more general and allows to consider any ISD algorithm that has certain properties. The algorithms of May-Meuer-Thomae and Becker-Jeux-May-Meuer satisfy these properties. Second, we translate May-Ozerov Near Neighbour technique (Eurocrypt'15) to an `update-and-query' language more suitable for the quantum walk framework. First, this re-interpretation makes possible to analyse a broader class of algorithms and, second, allows us to combine Near Neighbour search with the quantum walk framework and use both techniques to give a quantum version of Dumer's ISD with Near Neighbour.