Improved Quantum Information Set Decoding

In this paper we present quantum information set decoding (ISD) algorithms for binary linear codes. First, we refine the analysis of the quantum walk based algorithms proposed by Kachigar and Tillich (PQCrypto'17). This refinement allows us to improve the running time of quantum decoding in the leading order term: for an n-dimensional binary linear code the complexity of May-Meurer-Thomae ISD algorithm (Asiacrypt'11) drops down from 2(0.05904n+o(n)) to 2(0.05806n+o(n)). Similar improvement is achieved for our quantum version of Becker-Jeux-May-Meurer (Eurocrypt'12) decoding algorithm. Second, we translate May-Ozerov Near Neighbour technique (Eurocrypt'15) to an `updateand-query' language more common in a similarity search literature. This re-interpretation allows us to combine Near Neighbour search with the quantum walk framework and use both techniques to improve a quantum version of Dumer's ISD algorithm: the running time goes down from 2(0.059962n+o(n)) to 2(0.059450+o(n)).