Paper 2004/242 Original: eprint.iacr.org/2004/242 ↗
Combinatorial group theory and public key cryptography
Abstract
After some excitement generated by recently suggested public key exchange protocols due to Anshel-Anshel-Goldfeld and Ko-Lee et al., it is a prevalent opinion now that the conjugacy search problem is unlikely to provide sufficient level of security if a braid group is used as the platform. In this paper we address the following questions: (1) whether choosing a different group, or a class of groups, can remedy the situation; (2) whether some other ``hard" problem from combinatorial group theory can be used, instead of the conjugacy search problem, in a public key exchange protocol. Another question that we address here, although somewhat vague, is likely to become a focus of the future research in public key cryptography based on symbolic computation: (3) whether one can efficiently disguise an element of a given group (or a semigroup) by using defining relations.
Metadata
- Available format(s)
PDF- Category
- Cryptographic protocols
- Publication info
- Preprint.
- History
- 2004-09-20: last updated
- 2004-09-20: published
- Short URL
- https://ia.cr/2004/242
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2004/242,
author = {Vladimir Shpilrain and Gabriel Zapata},
title = {Combinatorial group theory and public key cryptography},
howpublished = {Cryptology {ePrint} Archive, Paper 2004/242},
year = {2004},
url = {https://eprint.iacr.org/2004/242}
}