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Two New Versions of Numbers Fast Multiplication and Tropical Cryptography

by Richard P. Megrelishvili
Communications on Applied Electronics
Foundation of Computer Science (FCS), NY, USA
Volume 7 - Number 8
Year of Publication: 2017
Authors: Richard P. Megrelishvili

Richard P. Megrelishvili . Two New Versions of Numbers Fast Multiplication and Tropical Cryptography. Communications on Applied Electronics. 7, 8 ( Oct 2017), 12-15. DOI=10.5120/cae2017652699

@article{ 10.5120/cae2017652699,
author = { Richard P. Megrelishvili },
title = { Two New Versions of Numbers Fast Multiplication and Tropical Cryptography },
journal = { Communications on Applied Electronics },
issue_date = { Oct 2017 },
volume = { 7 },
number = { 8 },
month = { Oct },
year = { 2017 },
issn = { 2394-4714 },
pages = { 12-15 },
numpages = {9},
url = { },
doi = { 10.5120/cae2017652699 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
%0 Journal Article
%1 2023-09-04T20:01:39.170404+05:30
%A Richard P. Megrelishvili
%T Two New Versions of Numbers Fast Multiplication and Tropical Cryptography
%J Communications on Applied Electronics
%@ 2394-4714
%V 7
%N 8
%P 12-15
%D 2017
%I Foundation of Computer Science (FCS), NY, USA

This article discusses the rapid multiplication of two numbers. But first considered [1] the work that created the foundation of [1]. In this article [1] is took into consideration and used the fact that the leading countries in cryptography used the ElGamal algorithmic method (Digital Signature). This method is used, just like in an algorithm, for performing certain actions in a certain period of time. Our new one-way matrix function [1] is a protected algorithm that meets the known qualities of asymmetric cryptography, i.e. it is not directly related of Number Theory to the exponential functions of ax = y (mod p) and Euler's Theorem. That is why it [1] (2013) is distinguished with high speed, i.e. connected to of vector and of matrix multiplication operations with simplicity (This article also discusses protection issues of algorithm). Naturally, the question is: do use more Diffie-Hellman algorithm (as well as the RSA algorithm) for the same period of time? This important fast realizing is considered in the present article. Get a new results multiplication of numbers in high speed with module considering. It is when the two vectors (as two numbers) are multiplied to each other.

  1. R.P.Megrelishvili, Analysis of the Matrix one-Way Function and Two Variants of Its Implementation, International Journal of Multidisciplinary Research and Advances in Engineering (IJMRAE), Vol. 5, No. IV (Octomber2013), pp. 99-105.
  2. R. Megrelishvili, M.Chelidsze, K.Chelidze, Construction of Secret and Public Key Cryptosystems, Iv.Javakhishvili Tbilisi State University, of I.Vekua Institute of Applied Mathematics, Informatics and Mechanics (AMIM), v. 11, No 2, 2006, pp. 29-36.
  3. 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.
  4. Richard P. Megrelishvili, Tropical Cryptography and Analysis of Implementation of New Matrix One-Way Function, Proceedings of the 2014 International Conference on Mathematical Models and Methods in Appled Sciences (MMAS ’14). Saint Peterburg, Russia, September 23-25, 2014, pp. 273-275.
  5. R.Megrelishvili, A.Sikharulidze, New matrix sets generation and the cryptosystems, Proceedings of the European Computing Conference and 3th International Conference on Computational Intelligence, Tbilisi, Georgia, June, 26-28, 2009, pp. 253-255.
  6. R. Megrelishvili, M.Chelidze, G.Besiashvili, Investigation of New Matrix-Key Function for the Public Cryptosystems, Proceedings of Third International Conference, Problems of Cybernetics and Information, v.1, September, 6-8, Baku, Azerbaijan, 2010, pp. 75-78.
  7. R .Megrelisvili, M.Chelidze, G.Besiashvili, One-way matrix function - analogy for Diffie-Hellman protocol, Proceedings of the Seventh International Conference, IES-2010, 28 September-3 October, Vinnytsia, Ukraine, 2010, pp. 341-344.
  8. W.P.Wardlaw, Matrix Reprezentacion of Finite Fields, U.S. Navy, March 12, 1992, pp. 1-10, NRL/MR/5350.1-92-6953.
  9. 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.
  10. W.Diffie and M.E. Hellman. New Direction in Cryptography, IEEE Transaction on Information Theory, IT-22, n. 6, Nov. 1976, pp. 644-654.
  11. R.L.Rivest, A. Shamir and I.M. Adleman, A Method for Obtaining Digital Signature and Public-Key Cryptosystems, Communications of the ASM, v. 21, n. 2, Feb. 1978, pp. 120-126.
Index Terms

Computer Science
Information Sciences


Digital signature matrix one-way function key exchange algorithm Tropical cryptography.