Length-based cryptanalysis: The case of Thompson's Group
Cryptography and Security
2010-08-02 v4 Computational Complexity
Group Theory
Abstract
The length-based approach is a heuristic for solving randomly generated equations in groups which possess a reasonably behaved length function. We describe several improvements of the previously suggested length-based algorithms, that make them applicable to Thompson's group with significant success rates. In particular, this shows that the Shpilrain-Ushakov public key cryptosystem based on Thompson's group is insecure, and suggests that no practical public key cryptosystem based on this group can be secure.
Keywords
Cite
@article{arxiv.cs/0607079,
title = {Length-based cryptanalysis: The case of Thompson's Group},
author = {Dima Ruinskiy and Adi Shamir and Boaz Tsaban},
journal= {arXiv preprint arXiv:cs/0607079},
year = {2010}
}
Comments
Final version, to appear in JMC