# Simple composition theorems of one-way functions -- proofs and presentations

Gaspar, Jaime and Boiten, Eerke Albert (2014) Simple composition theorems of one-way functions -- proofs and presentations. Technical report. IACR EPrints (The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided) (KAR id:52889)

 The full text of this publication is not currently available from this repository. You may be able to access a copy if URLs are provided. (Contact us about this Publication) Official URLhttps://eprint.iacr.org/2014/1006

## Abstract

One-way functions are both central to cryptographic theory and a clear example of its complexity as a theory. From the aim to understand theories, proofs, and communicability of proofs in the area better, we study some small theorems on one-way functions, namely: composition theorems of one-way functions of the form "if $f$ (or $h$) is well-behaved in some sense and $g$ is a one-way function, then $f \circ g$ (respectively, $g \circ h$) is a one-way function".

We present two basic composition theorems, and generalisations of them which may well be folklore. Then we experiment with different proof presentations, including using the Coq theorem prover, using one of the theorems as a case study.

Item Type: Monograph (Technical report) foundations/one-way functions, proof presentation, Coq Q Science > QA Mathematics (inc Computing science) Faculties > University wide - Teaching/Research Groups > Centre for Cyber Security ResearchFaculties > Sciences > School of ComputingFaculties > Sciences > School of Computing > Security Group Eerke Boiten 07 Dec 2015 17:45 UTC 29 May 2019 16:39 UTC https://kar.kent.ac.uk/id/eprint/52889 (The current URI for this page, for reference purposes) https://orcid.org/0000-0002-9184-8968