A new class of convolutional codes and its use in the McEliece Cryptosystem

TL;DR

This paper introduces a novel convolutional code class with efficient decoding, exploring its properties and application in a convolutional McEliece cryptosystem variant, analyzing its security and potential vulnerabilities.

Contribution

It presents a new convolutional code class with algebraic decoding and proposes its integration into a convolutional McEliece cryptosystem, extending traditional block code-based schemes.

Findings

Efficient algebraic decoding for the new convolutional codes

Application of convolutional codes in a cryptosystem with sequence messages

Discussion of security considerations and attack resistance

Abstract

In this paper we present a new class of convolutional codes that admits an efficient al- gebraic decoding algorithm. We study some of its properties and show that it can decode interesting sequences of errors patterns. The second part of the paper is devoted to in- vestigate its use in a variant of the McEliece cryptosystem. In contrast to the classical McEliece cryptosystems, where block codes are used, we propose the use of a convolu- tional encoder to be part of the public key. In this setting the message is a sequence of messages instead of a single block message and the errors are added randomly throughout the sequence. We conclude the paper providing some comments on the security. Although there is no obvious security threats to this new scheme, we point out several possible adaptations of existing attacks and discuss the difficulties of such attacks to succeed in breaking this cryptosystem.