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. (Preliminary version. Comments are welcome.)

• Type: Journal
• Year: 2006
• Where: CORR
• Authors: Dima Ruinskiy, Adi Shamir, Boaz Tsaban
• Keywords: CORR 2006, Education, Length-based Approach, Public Key Cryptosystem, Significant Success Rates