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Length-based cryptanalysis: The case of Thompson's Group

Dima Ruinskiy·Adi Shamir·Boaz Tsaban
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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.

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Dima Ruinskiy, Adi Shamir, Boaz Tsaban. 2007-05-31. Length-based cryptanalysis: The case of Thompson's Group. https://doi.org/10.1515/jmc.2007.018

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