Code based Cryptography: Classic McEliece

TL;DR

This paper provides a comprehensive overview of code-based cryptography, focusing on the McEliece cryptosystem, its mathematical foundations, attacks, and a key encapsulation mechanism for secure communication.

Contribution

It offers a detailed explanation of the Classic McEliece cryptosystem, including implementation and analysis of attacks, and discusses its application in key encapsulation mechanisms.

Findings

Successful implementation of ISD attack on small parameters

Detailed mathematical foundation of code-based cryptography

Description of Classic McEliece KEM for secure key exchange

Abstract

This article addresses code-based cryptography and is designed to depict the complete outline of a code based public key cryptosystem. This report includes basic mathematics and fundamentals of coding theory which are useful for studying code-based cryptography. Here, we briefly describe the first scheme of code based public key cryptosystems given by R. J. McEliece in 1978 and its improved version given by H. Niederreiter in 1986. We discuss the hard problems of coding theory which are used in code based cryptography and some classic attacks on it like information-set decoding (ISD). Successful implementation of the ISD attack on McEliece cryptosystem for some small parameters set is executed and the code for the same is provided in the Appendix. This report elaborates a key encapsulation mechanism (KEM), namely Classic McEliece, based on algebraic coding theory to establish a symmetric key for two users.