Improved Quantum Information Set Decoding

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.

Decoding techniques applied to the compilation of CNOT circuits for NISQ architectures

“…for solving the syndrome decoding problem are e icient but could still be improved, both in circuit size and computational time. For instance, some quantum algorithms have been proposed for solving the syndrome decoding problem via the Information Set Decoding algorithm [5,17,18], which gives the possibility of designing a hybrid quantum/classical compiler for this particular synthesis problem.…”

A Quantum Circuit to Speed-Up the Cryptanalysis of Code-Based Cryptosystems

“…We highlight that a promising direction for future work is the realization of quantum ISD circuits concretizing the approaches of [14,15]. Indeed, the works evaluate only the expected asymptotic computation costs of two ISD approaches, highlighting that they have the potential to improve on the ones of Prange and Lee-Brickell.…”

Quantum Period Finding against Symmetric Primitives in Practice

“…Using Q#, we designed and implemented multiple quantum circuits of independent interest: an efficient reversible circuit to solve boolean linear equations, and optimized quantum circuits for Chaskey, PRINCE and the two permutations used in Elephant, spongent and Keccak. Solving boolean linear equations could be useful for information set decoding [Kir18] or in some multivariate crytpanalysis.…”