Abstract
In this survey, we describe a general key exchange protocol based on semidirect product of (semi)groups (more specifically, on extensions of (semi)groups by automorphisms), and then focus on practical instances of this general idea. This protocol can be based on any group or semigroup, 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 this protocol is used with a non-commutative (semi)group, it acquires several useful features that make it compare favorably to the Diffie-Hellman protocol. The focus then shifts to selecting an optimal platform (semi)group, in terms of security and efficiency. We show, in particular, that one can get a variety of new security assumptions by varying an automorphism used for a (semi)group extension.
Research of Delaram Kahrobaei was partially supported by a PSC-CUNY grant from the CUNY research foundation, as well as the City Tech foundation. Research of Delaram Kahrobaei and Vladimir Shpilrain was also supported by the ONR (Office of Naval Research) grant N000141512164.
Research of Vladimir Shpilrain was partially supported by the NSF grant CNS-1117675.
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Kahrobaei, D., Shpilrain, V. (2016). Using Semidirect Product of (Semi)groups in Public Key Cryptography. In: Beckmann, A., Bienvenu, L., Jonoska, N. (eds) Pursuit of the Universal. CiE 2016. Lecture Notes in Computer Science(), vol 9709. Springer, Cham. https://doi.org/10.1007/978-3-319-40189-8_14
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