Information-Set Decoding for Convolutional Codes

TL;DR

This paper introduces a generic decoding framework for convolutional codes, enabling cryptanalysis of systems using these codes, and demonstrates its effectiveness by attacking two cryptosystems with substantial error recovery.

Contribution

The paper develops a novel, generic information set decoding framework for convolutional codes and applies it to cryptanalysis, providing new tools and experimental results.

Findings

Recovered 74% of errors in under 10 hours for one cryptosystem.

Recovered approximately 80% of errors in security-equivalent time for another system.

Provided experimental evidence of the decoding effectiveness and security implications.

Abstract

In this paper, we present a framework for generic decoding of convolutional codes, which allows us to do cryptanalysis of code-based systems that use convolutional codes. We then apply this framework to information set decoding, study success probabilities and give tools to choose variables. Finally, we use this to attack two cryptosystems based on convolutional codes. In the first, our code recovered about 74% of errors in less than 10 hours each, and in the second case, we give experimental evidence that 80% of the errors can be recovered in times corresponding to about 70 bits of operational security, with some instances being significantly lower.