2014/01/01 by Duško Pavlović, Dusko Pavlovic · 1 voice · 1 citation
Computer Science · Mathematics · #Categorical variable #Category theory #Computability, Logic, AI Algorithms #Computer science #Computer security #Cryptography #Encryption #Financial cryptography #Geometric and Algebraic Topology #Mathematics #Public-key cryptography #Pure mathematics #Theoretical computer science #semigroups and automata theory
paper · pdf · doi:10.1007/978-3-642-54789-8_19
published in Lecture notes in computer science, 353-367 (Springer Science+Business Media)
openalex publication_date 2014/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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 sometimes 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 the categorical technique of *diagram chasing*, which was first used Lambek's seminal `Lecture Notes on Rings and Modules'.