Public key exchange using semidirect product of (semi)groups

2013/04/24 by Habeeb, Maggie, Kahrobaei, Delaram, Koupparis, Charalambos +1 · 1 citation
#20E22 #68P25 #94A60 #Cryptography and Security (cs.CR) #FOS: Computer and information sciences #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.1304.6572

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.

Cited by

• On the Classical Hardness of the Semidirect Discrete Logarithm Problem in Finite Groups

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• Cryptanalysis of Semidirect Product Key Exchange Using Matrices Over\n Non-Commutative Rings
• A remark on MAKE -- a Matrix Action Key Exchange