HoTT-Crypt : A Study in Homotopy Type Theory based on Cryptography

16 pages•Published: November 18, 2018

Abstract

This paper investigates a preliminary application of homotopy type theory in cryptography. It discusses specifying a cryptographic protocol using homotopy type theory which adds the notion of higher inductive type and univalence to Martin-Lo ̈f’s intensional type theory. A higher inductive type specification can act as a front-end mapped to a concrete cryptographic implementation in the universe. By having a higher inductive type front-end, we can encode domain-specific laws of the cryptographic implementation as higher-dimensional paths. The higher inductive type gives us a graphical computational model and can be used to extract functions from underlying concrete implementation. Us- ing this model we can extend types to act as formal certificates guaranteeing on correctness properties of a cryptographic implementation.

Keyphrases: functor, groupoid, higher inductive type, homotopy type theory, univalence

In: Gilles Barthe, Konstantin Korovin, Stephan Schulz, Martin Suda, Geoff Sutcliffe and Margus Veanes (editors). LPAR-22 Workshop and Short Paper Proceedings, vol 9, pages 75-90.

Links:	https://easychair.org/publications/paper/q2qC
	https://doi.org/10.29007/tvpp

BibTeX entry

@inproceedings{LPAR-IWIL2018:HoTT_Crypt_Study_Homotopy,
  author    = {Paventhan Vivekanandan},
  title     = {HoTT-Crypt : A Study in Homotopy Type Theory based on Cryptography},
  booktitle = {LPAR-22 Workshop and Short Paper Proceedings},
  editor    = {Gilles Barthe and Konstantin Korovin and Stephan Schulz and Martin Suda and Geoff Sutcliffe and Margus Veanes},
  series    = {Kalpa Publications in Computing},
  volume    = {9},
  publisher = {EasyChair},
  bibsource = {EasyChair, https://easychair.org},
  issn      = {2515-1762},
  url       = {/publications/paper/q2qC},
  doi       = {10.29007/tvpp},
  pages     = {75-90},
  year      = {2018}}

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