McEliece Cryptosystem Based On Extended Golay Code

TL;DR

This paper explores the use of extended Golay codes in the McEliece cryptosystem as a post-quantum cryptography approach, analyzing its security, implementation, and practical advantages over traditional Goppa codes.

Contribution

It introduces a novel variant of the McEliece cryptosystem using extended Golay codes and provides MATLAB implementation and analysis of its error correction capabilities.

Findings

Extended Golay code enables high data rate transmission.

The cryptosystem can detect 7-bit errors and correct up to 3 errors.

Implementation demonstrates practical feasibility of the approach.

Abstract

With increasing advancements in technology, it is expected that the emergence of a quantum computer will potentially break many of the public-key cryptosystems currently in use. It will negotiate the confidentiality and integrity of communications. In this regard, we have privacy protectors (i.e. Post-Quantum Cryptography), which resists attacks by quantum computers, deals with cryptosystems that run on conventional computers and are secure against attacks by quantum computers. The practice of code-based cryptography is a trade-off between security and efficiency. In this chapter, we have explored The most successful McEliece cryptosystem, based on extended Golay code [24, 12, 8]. We have examined the implications of using an extended Golay code in place of usual Goppa code in McEliece cryptosystem. Further, we have implemented a McEliece cryptosystem based on extended Golay code using MATLAB. The extended Golay code has lots of practical applications. The main advantage of using extended Golay code is that it has codeword of length 24, a minimum Hamming distance of 8 allows us to detect 7-bit errors while correcting for 3 or fewer errors simultaneously and can be transmitted at high data rate.