A Smart Approach for GPT Cryptosystem Based on Rank Codes

TL;DR

This paper introduces the Smart approach for GPT cryptosystems that enhances security against known structural attacks by carefully selecting the distortion matrix, enabling smaller public keys and improved robustness.

Contribution

The paper proposes a novel Smart approach that improves the security of GPT cryptosystems against existing attacks through strategic choice of the distortion matrix.

Findings

The Smart approach withstands all known structural attacks.

It allows for smaller public key sizes.

It enhances the cryptosystem's robustness against attacks.

Abstract

The concept of Public- key cryptosystem was innovated by McEliece's cryptosystem. The public key cryptosystem based on rank codes was presented in 1991 by Gabidulin -Paramonov-Trejtakov(GPT). The use of rank codes in cryptographic applications is advantageous since it is practically impossible to utilize combinatoric decoding. This has enabled using public keys of a smaller size. Respective structural attacks against this system were proposed by Gibson and recently by Overbeck. Overbeck's attacks break many versions of the GPT cryptosystem and are turned out to be either polynomial or exponential depending on parameters of the cryptosystem. In this paper, we introduce a new approach, called the Smart approach, which is based on a proper choice of the distortion matrix X. The Smart approach allows for withstanding all known attacks even if the column scrambler matrix P over the base field Fq.