Public key exchange using semidirect product of (semi)groups

Authors:
Maggie Habeeb;Delaram Kahrobaei;Charalambos Koupparis;Vladimir Shpilrain
Affiliations:
California University of Pennsylvania;CUNY Graduate Center and City Tech, City University of New York;CUNY Graduate Center, City University of New York;CUNY Graduate Center, The City College of New York
Venue:
ACNS'13 Proceedings of the 11th international conference on Applied Cryptography and Network Security
Year:
2013

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Abstract

In this paper, we describe a brand new key exchange protocol based on a semidirect product of (semi)groups (more specifically, on extension of a (semi)group by automorphisms), and then focus on practical instances of this general idea. Our protocol can be based on any group, in particular on any non-commutative group. One of its special cases is the standard Diffie-Hellman protocol, which is based on a cyclic group. However, when our protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. Here we also suggest a particular non-commutative semigroup (of matrices) as the platform and show that security of the relevant protocol is based on a quite different assumption compared to that of the standard Diffie-Hellman protocol.