A McEliece cryptosystem using permutation codes

TL;DR

This paper explores a new cryptosystem based on permutation codes, extending the McEliece framework, but finds it insecure while proposing an improved version that generalizes the original system.

Contribution

It introduces a permutation code-based cryptosystem framework and an enhanced version that generalizes the McEliece cryptosystem using linear codes.

Findings

Initial permutation code cryptosystem is insecure.

The framework can incorporate any permutation error-correcting code.

An improved McEliece system based on linear codes is proposed.

Abstract

This paper is an attempt to build a new public-key cryptosystem; similar to the McEliece cryptosystem, using permutation error-correcting codes. We study a public-key cryptosystem built using two permutation error-correcting codes. We show that these cryptosystems are insecure. However, the general framework in these cryptosystems can use any permutation error-correcting code and is interesting. We present an enhanced McEliece cryptosystem which subsumes McEliece cryptosystem based on linear error correcting codes.