PKC-PC: A Variant of the McEliece Public Key Cryptosystem based on Polar Codes

TL;DR

This paper introduces PKC-PC, a variant of the McEliece cryptosystem using polar codes, which reduces key sizes and enhances security, making it a promising candidate for post-quantum cryptography standardization.

Contribution

The paper presents a novel cryptosystem variant based on polar codes, with improved key size, information rate, and security features compared to traditional McEliece implementations.

Findings

Reduced public and private key sizes.

Increased information rate.

Enhanced security against conventional attacks.

Abstract

Polar codes are novel and efficient error correcting codes with low encoding and decoding complexities. These codes have a channel dependent generator matrix which is determined by the code dimension, code length and transmission channel parameters. This paper studies a variant of the McEliece public key cryptosystem based on polar codes, called "PKC-PC". Due to the fact that the structure of polar codes' generator matrix depends on the parameters of channel, we used an efficient approach to conceal their generator matrix. Then, by the help of the characteristics of polar codes and also introducing an efficient approach, we reduced the public and private key sizes of the PKC-PC and increased its information rate compared to the McEliece cryptosystem. It was shown that polar codes are able to yield an increased security level against conventional attacks and possible vulnerabilities on the code-based public key cryptosystems. Moreover, it is indicated that the security of the PKC-PC is reduced to solve NP-complete problems. Compared to other post-quantum public key schemes, we believe that the PKC-PC is a promising candidate for NIST post-quantum crypto standardization.