Combinatorial Group Theory and Public Key Cryptography


DOI: 10.1007/s00200-006-0006-9

Cite this article as:
Shpilrain, V. & Zapata, G. AAECC (2006) 17: 291. doi:10.1007/s00200-006-0006-9


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.


Public key exchange Conjugacy search problem Commuting action Diffusion 

Copyright information

© Springer-Verlag 2006

Authors and Affiliations

  1. 1.Department of MathematicsThe City College of New YorkNew YorkUSA

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