An Upper-Bound on the Decoding Failure Probability of the LRPC Decoder

TL;DR

This paper establishes theoretical upper bounds on the probability of decoding failure for Low Rank Parity Check (LRPC) codes, which are used in rank-metric error correction and cryptography.

Contribution

It provides the first theoretical upper bounds on LRPC decoding failure probability, enhancing understanding of their reliability in cryptographic applications.

Findings

Derived upper bounds on decoding failure probability

Applicable to parameter choices in cryptographic schemes

Improves confidence in LRPC code performance

Abstract

Low Rank Parity Check (LRPC) codes form a class of rank-metric error-correcting codes that was purposely introduced to design public-key encryption schemes. An LRPC code is defined from a parity check matrix whose entries belong to a relatively low dimensional vector subspace of a large finite field. This particular algebraic feature can then be exploited to correct with high probability rank errors when the parameters are appropriately chosen. In this paper, we present theoretical upper-bounds on the probability that the LRPC decoding algorithm fails.