Information-Set Decoding for Convolutional Codes

2024-08-14

arXiv.org

AI Summary

Cryptanalysis of convolutional code-based cryptosystems remains challenging due to their inherent temporal dependencies and state constraints, for which no systematic information-set decoding (ISD) framework has existed. Method: This work proposes the first ISD framework specifically tailored to convolutional codes, integrating their algebraic structure with classical ISD principles. It introduces an optimized variable-selection model and an exact error-recovery probability estimation mechanism, accompanied by a dedicated security evaluation tool. Contribution/Results: The framework pioneers the extension of the ISD paradigm from block codes to convolutional codes, overcoming key decoding bottlenecks imposed by sequential structure and state-space limitations. Experiments demonstrate that it recovers 74–80% of induced errors in two representative convolutional code cryptosystems within ten hours, reducing their effective security strength to approximately 60 bits—lower in some instances. This establishes the first verifiable, reproducible, and general-purpose analytical benchmark for assessing the security of convolutional code cryptography.

Technology Category

• Constraint Satisfaction and Optimization: Satisfiability
• Cognitive Modeling & Cognitive Systems: Neural Spike Coding
• Search and Optimization: Non-convex Optimization

Application Category

• Security and Privacy: Applications of cryptography
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Responsible Web: Measurement, analysis, and circumvention of Web censorship

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 60 bits of operational security, with some instances being significantly lower.

Problem

• Develop generic decoding framework for convolutional codes
• Apply information set decoding to analyze success probabilities
• Attack two convolutional code-based cryptosystems experimentally

Innovation

• Generic decoding framework for convolutional codes
• Information set decoding with success analysis
• Attacks on convolutional code-based cryptosystems