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Symmetry 2017, 9(1), 9; doi:10.3390/sym9010009

Improved Asymmetric Cipher Based on Matrix Power Function with Provable Security

1
Faculty of Mathematics and Natural Sciences, Department of Applied Mathematics, Kaunas University of Technology, Studentu str. 50-324, Kaunas LT - 51368, Lithuania
2
Faculty of Informatics, Department of Computer Science, Kaunas University of Technology, Studentu str. 50-213, Kaunas LT - 51368, Lithuania
*
Author to whom correspondence should be addressed.
Academic Editors: Young-Sik Jeong, Laurence T. Yang and Stefanos Gritzalis
Received: 23 September 2016 / Revised: 2 December 2016 / Accepted: 28 December 2016 / Published: 7 January 2017
(This article belongs to the Special Issue Symmetry in Secure Cyber World)
View Full-Text   |   Download PDF [735 KB, 9 January 2017; original version 7 January 2017]

Abstract

The improved version of the author’s previously declared asymmetric cipher protocol based on matrix power function (MPF) is presented. Proposed modification avoids discrete logarithm attack (DLA) which could be applied to the previously declared protocol. This attack allows us to transform the initial system of MPF equations to so-called matrix multivariate quadratic (MMQ) system of equations, which is a system representing a subclass of multivariate quadratic (MQ) systems of equations. We are making a conjecture that avoidance of DLA in protocol, presented here, should increase its security, since an attempt to solve the initial system of MPF equations would appear to be no less complex than solving the system of MMQ equations. No algorithms are known to solve such a system of equations. Security parameters and their secure values are defined. Security analysis against chosen plaintext attack (CPA) and chosen ciphertext attack (CCA) is presented. Measures taken to prevent DLA attack increase the security of this protocol with respect to the previously declated protocol. View Full-Text
Keywords: cryptography; asymmetric encryption; embedded systems cryptography; asymmetric encryption; embedded systems
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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Sakalauskas, E.; Mihalkovich, A.; Venčkauskas, A. Improved Asymmetric Cipher Based on Matrix Power Function with Provable Security. Symmetry 2017, 9, 9.

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