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Improved Asymmetric Cipher Based on Matrix Power Function Resistant to Linear Algebra Attack
Volume 28, Issue 3 (2017), pp. 517–524
Pub. online: 1 January 2017      Type: Research Article      Open accessOpen Access
Received
1 May 2016
Accepted
1 August 2017
Published
1 January 2017

Abstract

In this paper we consider an improved version of earlier published asymmetric encryption protocol based on matrix power function (MPF). Recently, a linear algebra attack on earlier version of this protocol was found. This attack allows an attacker to break suggested protocol in polynomial time.
Here we show that the improved version of our encryption protocol is not vulnerable to the declared linear attack, while retaining its effective realization in embedded systems.

References

 
Diffie, W., Hellman, M. (1976). New directions in cryptography. IEEE Transactions on Information Theory, 22(6), 644–654.
 
Liu, J., Zhang, H., Jia, J. (2016). A linear algebra attack on the non-commuting cryptography class based on matrix power function. In: International Conference on Information Security and Cryptology. Springer, Cham, pp. 343–354.
 
Mihalkovich, A., Sakalauskas, E. (2012). Asymmetric cipher based on MPF and its security parameters evaluation. In: Proceedings of the Lithuanian Mathematical Society, Ser. A, Vol. 53, pp. 72–77.
 
Sakalauskas, E., Luksys, K. (2012). Matrix power function and its application to block cipher s-box construction. International Journal of Innovative Computing, 8(4), 2655–2664.
 
Sakalauskas, E., Mihalkovich, A. (2014). New asymmetric cipher of non-commuting cryptography class based on matrix power function. Informatica, 25(2), 283–298.
 
Sakalauskas, E., Listopadskis, N., Tvarijonas, P. (2008). Key agreement protocol (KAP) based on matrix power function. In: Advanced Studies in Software and Knowledge Engineering. Institute of Information Theories and Applications FOI ITHEA, pp. 92–96.
 
Sakalauskas, E., Mihalkovich, A., Venčkauskas, A. (2017). Improved asymmetric cipher based on matrix power function with provable security. Symmetry, 9(1), 9. https://doi.org/10.3390/sym9010009.

Biographies

Sakalauskas Eligijus

E. Sakalauskas received PhD degree from Kaunas Polytechnical Institute in 1983. Currently he is a professor in Department of Applied Mathematics in Kaunas University of Technology. The scope of scientific interests is system theory, identification and cryptography. Over 50 papers were published in these fields.

In recent time his research interests are focused in cryptography. Some results were obtained in the following fields: one way functions construction based on the hard problems in non-commutative algebraic structures. Using this approach two new candidate one-way functions were proposed. Two such functions were proposed: one based on matrix discrete logarithm problem together with conjugation problem and other on matrix power function. On this base several original cryptographic protocols were proposed. The main trend of investigations is concentrated on post-quantum cryptographic systems construction potentially being resistant to quantum cryptanalysis. The main research results in cryptography were published in 17 papers.

Mihalkovich Aleksejus
aleksejus.michalkovic@ktu.lt

A. Mihalkovich received PhD degree from Kaunas University of Technology in 2015. Currently he is a lecturer in Department of Applied Mathematics in Kaunas University of Technology. The main research interest is connected with non-commutative cryptography.


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Copyright
© 2017 Vilnius University
Open access article under the CC BY license.

Keywords
cryptography matrix power function asymmetric encryption linear algebra attack

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