Article

Thompson's group and public key cryptography

Authors:

Vladimir Shpilrain,

Alexander UshakovAuthors Info & Claims

ACNS'05: Proceedings of the Third international conference on Applied Cryptography and Network Security

Pages 151 - 163

https://doi.org/10.1007/11496137_11

Published: 07 June 2005 Publication History

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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.

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Published In

ACNS'05: Proceedings of the Third international conference on Applied Cryptography and Network Security

June 2005

528 pages

ISBN:3540262237

Editors:
John Ioannidis
AT&T Labs - Research
,
Angelos Keromytis
Computer Science Department, Columbia University
,
Moti Yung
Computer Science Department, Google Inc. and Columbia University, 1214 Amsterdam Avenue, New York, NY

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Springer-Verlag

Berlin, Heidelberg

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Published: 07 June 2005

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