Information Theory without the Finiteness Assumption, I: Cryptosystems as Group-Theoretic Objects

  • G. R. Blakley
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 196)


This paper gives a definition of cryptosystem in terms of confusion, diffusion and replacement. This definition lends itself to infinite, as well as finite, structures, and the notion of group appears to play an essential role in it. We offer three theses for discussion. The first is that all known cryptosystems fit the definition. The second is that (Shannon) confusion amounts to left composition of a cryptographic relation with a message and left action of a cryptographic relation on a message, as well as that (Shannon) diffusion amounts to left composition of a message with a cryptographic relation and left action of a message on a cryptographic relatin. The third is what Shannon calls mixing cannot occur unless certain type of “nonassociativity”, or at least lack of adherence to some algebraic laws, is present in the description of a cryptosystem in accordance with this definition.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • G. R. Blakley
    • 1
  1. 1.Department of MathematicsTexas A&M UniversityCollege StationUSA

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