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Tropical Cryptography and Two Variants of Implementation of the Original Matrix One-Way Function
| International Journal of Computer Applications |
| Foundation of Computer Science (FCS), NY, USA |
| Volume 147 - Number 13 |
| Year of Publication: 2016 |
| Authors: Richard P. Megrelishvili |
10.5120/ijca2016911132
|
Richard P. Megrelishvili . Tropical Cryptography and Two Variants of Implementation of the Original Matrix One-Way Function. International Journal of Computer Applications. 147, 13 ( Aug 2016), 7-9. DOI=10.5120/ijca2016911132
Abstract
In this article we first announced about two versions of the new matrix one-way function (With respect to the issue of relevance, we repeat, that the main advantage of the matrix one-way function is high speed operation). The first variant is the result of the natural development of cryptography and is associated with the use in the cryptography of new tropical arithmetic operations. The results their applications may be named as "Tropical Cryptography." But at the same time, regardless of the general algebraic values "Tropical Cryptography", it is fact, that the construction of multiplicative groups, based on the our tropical operations, may be accepted as an integral part of the realization of the matrix one-way function. Therefore, its adoption and an implementation can be associated with its recognition. The second option, at this stage, is the result of repeated analysis of matrix one-way function and is associated with the use of exponential one-way function within a certain time frame (Assuming the exponential one-way function, which Diffie-Hellman took from Number Theory). However it is obvious that the use of the degree (exponential) one-way function, in a certain time interval is not associated with loss of speed for the matrix one-way function, therefore, and - for the corresponding key exchange algorithm via an open channel communication or to perform other actions.
References
- R.Megrelishvili, M.Chelidsze, K.Chelidze, “On the construction of secret and public key cryptosystems,” Iv.Javakhishvili Tbilisi State University, I.Vekua Institute of Applied Mathematics, Informatics and Mechanics (AMIM), v. 11, No 2, 2006, pp. 29-36.
- R.Megrelishvili, A.Sikharulidze, “New matrix sets generation and the cryptosystems,” Proceedings of the European Computing Conference and 3rd International Conference on Computational Intelligence, Tbilisi, Georgia, June, 26-28, 2009, pp. 253-255.
- R.Megrelishvili, M.Chelidze, G.Besiashvili, “Investigation of new matrix-key function for the public cryptosystems”. Proceedings of The Third International Conference, Problems of Cybernetics and Information, v.1, September, 6-8, Baku, Azerbaijan, 2010, pp. 75-78.
- R.Megrelisvili, M.Chelidze, G.Besiashvili, “One-way matrix function - analogy of Diffie-Hellman protocol”, Proceedings of the Seventh International Conference, IES-2010, 28 September-3 October, Vinnytsia, Ukraine, 2010, pp. 341-344.
- R.Megrelishili, M.Jinjikhadze, Matrix one-way function for the exchange of cryptographic keys and method for the generation of multiplicative matrix groups ", in Proceedings of The International Conference SAIT 2011, May 23-28, Kyiv, Ukraine, in 2011. p. 472.
- W.P.Wardlaw, Matrix Reprezentacion of Finite Fields, U.S. Navy, March 12, 1992, pp. 1-10, NRL/MR/5350.1-92-6953.
- R.P.Megrelishvili, New Direction in Construction of Matrix One-Way Function and Tropical Ctyptography, Archil Eliashvili Institute of Control Systems of The Georgian Technical University, Proceedings, N 16, 2012, pp.244-248.
- T.ElGamal. “A Public-Key Cryptosystem and a Signature Scheme Based on Discrete Logarithms,” IEEE Transaction on Information Theory, v. IT-31, n. 4, 1985, pp. 469-472.
- W.Diffie and M.E.Hellman. New Direction in Cryptography, IEEE Transaction on Information Theory, IT-22, n.6, Nov. 1976, pp. 644-654.
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