Information Set Decoding for Lee-Metric Codes using Restricted Balls

TL;DR

This paper introduces a novel approach to Lee-metric syndrome decoding by leveraging the expected distribution of errors to reduce problem size, resulting in more efficient generic decoders for cryptographic applications.

Contribution

It proposes a method to decrease decoding complexity by restricting the search space based on error distribution in the Lee metric.

Findings

Decoding cost is significantly reduced using restricted balls.

The approach exploits the error distribution to improve decoding efficiency.

Potential for more secure cryptographic schemes using Lee metric codes.

Abstract

The Lee metric syndrome decoding problem is an NP-hard problem and several generic decoders have been proposed. The observation that such decoders come with a larger cost than their Hamming metric counterparts make the Lee metric a promising alternative for classical code-based cryptography. Unlike in the Hamming metric, an error vector that is chosen uniform at random of a given Lee weight is expected to have only few entries with large Lee weight. Using this expected distribution of entries, we are able to drastically decrease the cost of generic decoders in the Lee metric, by reducing the original problem to a smaller instance, whose solution lives in restricted balls.