Code-Based Cryptosystems Using Generalized Concatenated Codes

TL;DR

This paper explores the use of generalized concatenated codes in the McEliece cryptosystem, analyzing vulnerabilities to existing attacks and proposing modifications to enhance quantum resistance.

Contribution

It investigates generalized concatenated codes for the McEliece cryptosystem, analyzes attack vulnerabilities, and suggests modifications for improved security against structural attacks.

Findings

Sendrier's attack can partially break generalized concatenated codes

Alternative methods for code structure recovery are proposed

Modifications to the cryptosystem increase resistance to attacks

Abstract

The security of public-key cryptosystems is mostly based on number theoretic problems like factorization and the discrete logarithm. There exists an algorithm which solves these problems in polynomial time using a quantum computer. Hence, these cryptosystems will be broken as soon as quantum computers emerge. Code-based cryptography is an alternative which resists quantum computers since its security is based on an NP-complete problem, namely decoding of random linear codes. The McEliece cryptosystem is the most prominent scheme to realize code-based cryptography. Many codeclasses were proposed for the McEliece cryptosystem, but most of them are broken by now. Sendrier suggested to use ordinary concatenated codes, however, he also presented an attack on such codes. This work investigates generalized concatenated codes to be used in the McEliece cryptosystem. We examine the application of Sendrier's attack on generalized concatenated codes and present alternative methods for both partly finding the code structure and recovering the plaintext from a cryptogram. Further, we discuss modifications of the cryptosystem making it resistant against these attacks.