Improved Asymmetric Cipher Based on Matrix Power Function with Provable Security

Eligijus Sakalauskas,Algimantas Venčkauskas,Aleksejus Mihalkovich

doi:10.3390/sym9010009

Eligijus Sakalauskas, Algimantas Venčkauskas + Show 1 more

Open Access

https://doi.org/10.3390/sym9010009

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Journal: Symmetry	Publication Date: Jan 7, 2017
Citations: 6	License type: CC BY 4.0

Affiliation: Kaunas University of Technology

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.

Highlights

In this paper we present the improvement of the matrix power function (MPF) asymmetric cipher published in [1]
We provide the security considerations by proving that the proposed algorithm is secure against chosen ciphertext attack (CCA) and chosen plaintext attack (CPA)
We have proved that enhanced Matrix Power Asymmetric Cipher (MPAC) is resistant to Chosen Plaintext Attack and Chosen

Summary

Introduction

In this paper we present the improvement of the matrix power function (MPF) asymmetric cipher published in [1]. The purpose of this improvement is the prevention of discrete logarithm attack (DLA), which allows us to transform the initial system of MPF equations to the matrix multivariate quadratic (MMQ) system of equations. MPF was previously used to construct cryptographic primitives in [2,3] Implementation of these primitives in computationally restricted environments was analyzed in [4,5]. The cryptographic protocols and algorithms constructed on the base of MPF (see [1,2]) belong to the branch of non-commutiative cryptography. The prevention of DLA attack is presented in subsequent sections

Our Previous Work

Previous Asymmetric Cipher Protocol

Improvements of the Asymmetric Cipher Protocol

Security Analysis

Discussion