Length-based cryptanalysis: The case of Thompson's Group
<|reference_start|>Length-based cryptanalysis: The case of Thompson's Group: 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.<|reference_end|>
@article{ruinskiy2006length-based,
    title={Length-based cryptanalysis: The case of Thompson's Group},
    author={Dima Ruinskiy, Adi Shamir, and Boaz Tsaban},
    journal={Journal of Mathematical Cryptology 1 (2007), 359--372},
    year={2006},
    doi={10.1515/jmc.2007.018},
    archivePrefix={arXiv},
    eprint={cs/0607079},
    primaryClass={cs.CR cs.CC math.GR}
}