Thompson's group and public key cryptography

Authors:
Vladimir Shpilrain;Alexander Ushakov
Affiliations:
Department of Mathematics, The City College of New York, New York, NY;Department of Mathematics, CUNY Graduate Center, New York, NY
Venue:
ACNS'05 Proceedings of the Third international conference on Applied Cryptography and Network Security
Year:
2005

Citing 3
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Abstract

Recently, several public key exchange protocols based on symbolic computation in non-commutative (semi)groups were proposed as a more efficient alternative to well established protocols based on numeric computation. Notably, the protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al. exploited the conjugacy search problem in groups, which is a ramification of the discrete logarithm problem. However, it is a prevalent opinion now that the conjugacy search problem alone is unlikely to provide sufficient level of security no matter what particular group is chosen as a platform. In this paper we employ another problem (we call it the decomposition problem), which is more general than the conjugacy search problem, and we suggest to use R. Thompson's group as a platform. This group is well known in many areas of mathematics, including algebra, geometry, and analysis. It also has several properties that make it fit for cryptographic purposes. In particular, we show here that the word problem in Thompson's group is solvable in almost linear time.