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MPF Problem over Modified Medial Semigroup Is NP-Complete

Department of Applied Mathematics, Kaunas University of Technology, LT-44249 Kaunas, Lithuania
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Symmetry 2018, 10(11), 571; https://doi.org/10.3390/sym10110571
Received: 21 September 2018 / Revised: 16 October 2018 / Accepted: 22 October 2018 / Published: 1 November 2018
(This article belongs to the Special Issue Interactions between Group Theory, Symmetry and Cryptology)
This paper is a continuation of our previous publication of enhanced matrix power function (MPF) as a conjectured one-way function. We are considering a problem introduced in our previous paper and prove that tis problem is NP-Complete. The proof is based on the dual interpretation of well known multivariate quadratic (MQ) problem defined over the binary field as a system of MQ equations, and as a general satisfiability (GSAT) problem. Due to this interpretation the necessary constraints to MPF function for cryptographic protocols construction can be added to initial GSAT problem. Then it is proved that obtained GSAT problem is NP-Complete using Schaefer dichotomy theorem. Referencing to this result, GSAT problem by polynomial-time reduction is reduced to the sub-problem of enhanced MPF, hence the latter is NP-Complete as well. View Full-Text
Keywords: cryptography; non-commutative cryptography; one-way functions; NP-Completeness; key agreement protocol cryptography; non-commutative cryptography; one-way functions; NP-Completeness; key agreement protocol
MDPI and ACS Style

Sakalauskas, E.; Mihalkovich, A. MPF Problem over Modified Medial Semigroup Is NP-Complete. Symmetry 2018, 10, 571. https://doi.org/10.3390/sym10110571

AMA Style

Sakalauskas E, Mihalkovich A. MPF Problem over Modified Medial Semigroup Is NP-Complete. Symmetry. 2018; 10(11):571. https://doi.org/10.3390/sym10110571

Chicago/Turabian Style

Sakalauskas, Eligijus; Mihalkovich, Aleksejus. 2018. "MPF Problem over Modified Medial Semigroup Is NP-Complete" Symmetry 10, no. 11: 571. https://doi.org/10.3390/sym10110571

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