Variations of the McEliece Cryptosystem

TL;DR

This paper introduces two variations of the McEliece cryptosystem, one controlling error weight through relaxed permutation and another using spatially coupled LDPC codes, aiming for improved efficiency and security.

Contribution

It presents novel modifications to the McEliece cryptosystem, including a permutation relaxation technique and the application of spatially coupled LDPC codes for enhanced performance.

Findings

Controlled error weight in encryption enables efficient decryption.

Spatially coupled LDPC codes reduce key size while maintaining security.

Both variants are analyzed for security against known attacks.

Abstract

Two variations of the McEliece cryptosystem are presented. The first one is based on a relaxation of the column permutation in the classical McEliece scrambling process. This is done in such a way that the Hamming weight of the error, added in the encryption process, can be controlled so that efficient decryption remains possible. The second variation is based on the use of spatially coupled moderate-density parity-check codes as secret codes. These codes are known for their excellent error-correction performance and allow for a relatively low key size in the cryptosystem. For both variants the security with respect to known attacks is discussed.