English

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

R2 v1 2026-07-22T12:26:10.869Z