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A new public key cryptography using $M_{q}$ matrix | ||
| Journal of Mathematical Modeling | ||
| مقاله 6، دوره 11، شماره 4، اسفند 2023، صفحه 681-693 اصل مقاله (163.73 K) | ||
| نوع مقاله: Research Article | ||
| شناسه دیجیتال (DOI): 10.22124/jmm.2023.23982.2142 | ||
| نویسندگان | ||
| Azadeh Ramezanpour Naseri1؛ Ahmad Abbasi* 2؛ Reza Ebrahimi Atani3 | ||
| 1Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran | ||
| 2Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran & Center of Excellence for Mathematical Modeling Optimization and Combinatorial Computing (MMOCC), University of Guilan, Rasht, Iran | ||
| 3Department of Computer Engineering, University of Guilan, Rasht, Iran | ||
| چکیده | ||
| We consider a new class of square Fibonacci $(q+1)\times(q+1)$-matrices in public key cryptography. This extends previous cryptography using generalized Fibonacci matrices. For a given integer $q$, a $(q+1)\times(q+1)$ binary matrix $M_{q}$ is a matrix which nonzero entries are located either on the super diagonal or on the last row of the matrix. In this article, we have proposed a modified public key cryptography using such matrices as key in Hill cipher and key agreement for encryption-decryption of terms of $M_{q}$-matrix. In this scheme, instead of exchanging the whole key matrix, only a pair of numbers needed to be exchanged, which reduces the time complexity as well as the space complexity of the transmission and has a large key space. | ||
| کلیدواژهها | ||
| Cryptography؛ Hill cipher؛ key exchange Elgamal؛ Fibonacci sequence and $M_{q}$-matrix | ||
| مراجع | ||
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[1] D.S. Dummit, R.M. Foote, Abstract Algebra, Wiley Hoboken, 2004. [2] H.W. Gould, A history of the Fibonacci Q-matrix and a higher-dimensional problem, Fibonacci Quart. 19 (1981) 250-257. [3] R.K. Hasoun, S.F. Khlebus, H.K. Tayyeh, A new approach of classical Hill cipher in public key cryptography, Intern. J. Nonlinear Anal. Appl. 12 (2021) 1071-1082. [4] L.S. Hill, Cryptography in an algebraic alphabet, The American Mathematical Monthly 36 (1929) 306-312. [5] F.E. Hoha, Elementary Matrix Algebra, New York: Macmillan Co., 1973. [6] I.A. Ismail, M. Amin, H. Diab, How to repair the Hill cipher, J. Zhejiang Univ. Sci. 7 (2006) 2022-2030. [7] T. Koshy, Fibonacci and Lucas Numbers with Applications, New York, NY: John Wiley and Sons, 2001. [8] S.S.M. Noor, N.M. Tahir, I.A. Yassin, A.M. Samad, Cryptosystem for secure Parking, 2011 IEEE 7th International colloquium on signal Processing and its Applications. [9] J. Overbey, W. Traves, J. Wojdylo, On the key space of the Hill Cipher, Cryptologia. 29 (2005) 59-72. [10] K. Prasad, H. Mahato, Cryptography using generalized Fibonacci matrices with Affine-Hill cipher, J. Discrete Math. Sci. Cryptogr. 25 (2022) 2341-2352. [11] W. Stallings, Cryptography and Network Security: Principles and Practice, 7th Ed, Pearson Education Limited, 2017. [12] A.P. Stakhov, A generalization of the Fibonacci Q-matrix, Rep. Natl. Acad. Sci. Ukraine. 9 (1999) 46-49. [13] A.P. Stakhov, Fibonacci matrices, a generalization of the Cassini formula and a new coding theory, Chaos Solitons Fractals 30 (2006) 56-66. [14] D.R. Stinson, Cryptography: Theory and Practice, 3rd Ed, Chapman and Hall/CRC, Taylor & Francis Group, 2006. [15] M. Viswanath, M.R. Kumar, A public key cryptosystem using Hill's cipher, J. Discrete Math. Sci. Cryptogr. 18 (2015) 129-138. [16] M. Zeriouh, A. Chillali, A. Boua, Cryptography based on the matrices, Boletim Da Sociedade Paranaense De Matematica. 37 (2019) 75-83. | ||
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