On Decoding and Applications of Interleaved Goppa Codes

TL;DR

This paper introduces a collaborative decoding algorithm for interleaved Goppa codes, enhancing error correction capabilities and proposing a modified McEliece cryptosystem with security analysis and parameter recommendations.

Contribution

It presents a novel collaborative decoding method for interleaved Goppa codes and applies it to improve cryptographic systems based on wild Goppa codes.

Findings

Enhanced decoding radius beyond half the minimum distance

Corrects more errors than Patterson decoder for binary Goppa codes

Proposes a modified McEliece cryptosystem with security analysis

Abstract

Goppa Codes are a well-known class of codes with, among others, applications in code-based cryptography. In this paper, we present a collaborative decoding algorithm for interleaved Goppa codes (IGC). Collaborative decoding increases the decoding radius beyond half of the designed minimum distance. We consider wild Goppa codes and show that we can collaboratively correct more errors for binary Goppa codes than the Patterson decoder. We propose a modified version of the McEliece cryptosystem using wild IGC based on a recently proposed system by Elleuch et al., analyze attacks on the system and present some parameters with the corresponding key sizes.