[Resource Topic] 2006/244: Length-based cryptanalysis: The case of Thompson's Group

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

Authors: Dima Ruinskiy, Adi Shamir, Boaz Tsaban


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.

ePrint: https://eprint.iacr.org/2006/244

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