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Chasing Diagrams in Cryptography

  • Dusko Pavlovic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8222)

Abstract

Cryptography is a theory of secret functions. Category theory is a general theory of functions. Cryptography has reached a stage where its structures often take several pages to define, and its formulas sometime run from page to page. Category theory has some complicated definitions as well, but one of its specialties is taming the flood of structure. Cryptography seems to be in need of high level methods, whereas category theory always needs concrete applications. So why is there no categorical cryptography? One reason may be that the foundations of modern cryptography are built from probabilistic polynomial-time Turing machines, and category theory does not have a good handle on such things. On the other hand, such foundational problems might be the very reason why cryptographic constructions often resemble low level machine programming. I present some preliminary explorations towards categorical cryptography. It turns out that some of the main security concepts are easily characterized through diagram chasing, going back to Lambek’s seminal ‘Lecture Notes on Rings and Modules’.

Keywords

Boolean Function Category Theory Hiding Condition Security Parameter Follow Diagram Commute 
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 2014

Authors and Affiliations

  • Dusko Pavlovic
    • 1
  1. 1.Royal Holloway, University of LondonUK

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