Public Key Exchange Using Semidirect Product of (Semi)Groups

  • Maggie Habeeb
  • Delaram Kahrobaei
  • Charalambos Koupparis
  • Vladimir Shpilrain
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7954)


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.


Semidirect Product Group Ring Invertible Element Elliptic Curve Cryptography Practical Instance 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Maggie Habeeb
    • 1
  • Delaram Kahrobaei
    • 2
  • Charalambos Koupparis
    • 3
  • Vladimir Shpilrain
    • 4
  1. 1.California University of PennsylvaniaUSA
  2. 2.CUNY Graduate Center and City TechCity University of New YorkUSA
  3. 3.CUNY Graduate CenterCity University of New YorkUSA
  4. 4.CUNY Graduate CenterThe City College of New YorkUSA

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