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Cryptography 2018, 2(2), 9; https://doi.org/10.3390/cryptography2020009

Kolmogorov One-Way Functions Revisited

1,2
,
1,2
and
3,4,5,†,*
1
Department Matemática, Instituto Superior Técnico, Avenida Rovisco Pais 1, 1049-001 Lisboa, Portugal
2
Centro de Matemática, Aplicações Fundamentais e Investigação Operacional (CMAF-CIO), Campo Grande 016, 1749-016 Lisboa, Portugal
3
Department Informática, Faculdade de Ciências, Campo Grande 016, 1749-016 Lisboa, Portugal
4
LASIGE, Faculdade de Ciências, U Lisboa, Portugal; Campo Grande 016, 1749-016 Lisboa, Portugal
5
Instituto de Telecomunicações, Avenida Rovisco Pais, 1, 1049-001 Lisboa, Portugal
Current address: Campo Grande 016, 1749-016 Lisboa, Portugal
*
Author to whom correspondence should be addressed.
Received: 29 March 2018 / Revised: 20 April 2018 / Accepted: 25 April 2018 / Published: 28 April 2018
Full-Text   |   PDF [289 KB, uploaded 28 April 2018]

Abstract

We study characterizations of one-way functions in terms of time-bounded Kolmogorov complexity. As the main contribution, we propose definitions for strong and weak Kolmogorov one-way functions and show that these are equivalent to classical strong and weak one-way functions, respectively. The new definitions were motivated by the fact that the expected value approach is not able to characterize strong one-way functions as we prove in the paper. View Full-Text
Keywords: Kolmogorov complexity; one-way functions; cryptography; complexity theory Kolmogorov complexity; one-way functions; cryptography; complexity theory
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).
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Casal, F.; Rasga, J.; Souto, A. Kolmogorov One-Way Functions Revisited. Cryptography 2018, 2, 9.

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