On improving security of GPT cryptosystems

TL;DR

This paper reviews the security challenges of GPT cryptosystems based on rank codes, discusses various attacks, and explores modifications and tools to enhance their resistance against these attacks.

Contribution

It applies a known security enhancement approach to various GPT cryptosystem variants to improve their robustness against structural attacks.

Findings

Certain modifications can withstand Gibson's attack

Overbeck's attacks remain a significant threat

Tools exist to prevent Overbeck's attack in some variants

Abstract

The public key cryptosystem based on rank error correcting codes (the GPT cryptosystem) was proposed in 1991. Use of rank codes in cryptographic applications is advantageous since it is practically impossible to utilize combinatoric decoding. This enabled using public keys of a smaller size. Several attacks against this system were published, including Gibson's attacks and more recently Overbeck's attacks. A few modifications were proposed withstanding Gibson's attack but at least one of them was broken by the stronger attacks by Overbeck. A tool to prevent Overbeck's attack is presented in [12]. In this paper, we apply this approach to other variants of the GPT cryptosystem.