On the power of commutativity in cryptography

  • Adi Shamir
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 85)


Every field needs some unifying ideas which are applicable to a wide variety of situations. In cryptography, the notion of commutativity seems to play such a role. This paper surveys its potential applications, such as the generation of common keys, challenge-and-response identification, signature generation and verification, key-less communication and remote game playing.


Commutative Diagram Unify Idea Encryption Function Modular Exponentiation Root Problem 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1980

Authors and Affiliations

  • Adi Shamir
    • 1
    • 2
  1. 1.Department of MathematicsMassachusetts Institute of TechnologyCambridgeU.S.A.
  2. 2.Department of MathematicsThe Weizmann Institute of ScienceRehovotIsrael

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