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Thompson’s group and public key cryptography (2005)
| Venue: | In Third International Conference, ACNS 2005 |
| Citations: | 25 - 3 self |
BibTeX
@INPROCEEDINGS{Shpilrain05thompson’sgroup,
author = {Vladimir Shpilrain and Er Ushakov},
title = {Thompson’s group and public key cryptography},
booktitle = {In Third International Conference, ACNS 2005},
year = {2005},
pages = {151--163},
publisher = {Springer}
}
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Abstract
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. 1
Keyphrases
conjugacy search problem public key cryptography thompson group prevalent opinion particular group decomposition problem many area ko-lee et al numeric computation word problem linear time several property efficient alternative sufficient level several public key exchange protocol discrete logarithm problem symbolic computation cryptographic purpose
