Estimating The Dimension Of The Subfield Subcodes of Hermitian Codes

TL;DR

This paper investigates the true dimension of subfield subcodes of Hermitian codes, aiming to enhance McEliece cryptosystem parameters and proposing an estimation method using extreme value distribution.

Contribution

It introduces a novel approach to estimate the true dimension of these codes, which is crucial for cryptographic applications, especially in quantum-resistant schemes.

Findings

True dimension can be effectively estimated by the extreme value distribution.

Analysis of computational data supports the estimation method.

Results suggest improved parameters for McEliece cryptosystem.

Abstract

In this paper, we study the behavior of the true dimension of the subfield subcodes of Hermitian codes. Our motivation is to use these classes of linear codes to improve the parameters of the McEliece cryptosystem, such that key size and security level. The McEliece scheme is one of the promising alternative cryptographic schemes to the current public key schemes since in the last four decades, they resisted all known quantum computing attacks. By analyzing computational data series of true dimension, we concluded that they can be estimated by the extreme value distribution function.