Algebraic Coding Theory Using Pell Equation x2 − 8y2 = 1

Janaki G, Gowri Shankari A

Abstract


An interdisciplinary field with significant practical use is cryptography. The difficulty of specific mathematical computing tasks affects
a public key cryptosystem’s security. The technique for coding and
decoding the messages was described in this work, utilising the solutions of Pell equation x2 - 8y2 = 1 and matrix Q8∗. It was noted
that messages can be turned into an even size that is then divided into
slabs.

Keywords


Pell equation; Encryption-decryption algorithm; Q8∗ matrix; Cryptography

Full Text:

PDF

References


C. Berges. A history of the fibonacci q-matrix and a higher- dimensional problem.

Fibonacci Quart, 19(3):250–257, 1981.

R. Carmichael. The Theory of Numbers and Diophantine Analysis. Dover Publications Co., New York, 1950.

L. Disckson. History of The Theory of Numbers, Volume II. Chelsia Publishing

Co., New York, 1952.

H. Gould. A history of the fibonacci q-matrix and a higher- dimensional problem.

Fibonacci Quart, 19(3):250–257, 1981.

G. Janaki and C. Saranya. Observations on the binary quadratic diophantine equation x2−2xy−y2+2x+14y = 72. International Journal of Scientific Research

in Mathematical and Statistical sciences, 7(2):152–155, 2020.

C. Saranya and G. Janaki. Solutions of pell’s equation involving jarasandha numbers. International Journal of Scientific Research in Mathematical and Statistical sciences, 6(1):234–236, 2019.

U. Sumeyra, T. Nihal, and N. Ozgur. new application to coding theory via fibonacci and lucas numbers. Mathematical Sciences and Applications E-Notes,

(1):62–70, 2019.

N. Tas, S. Ucar, N. Ozgur, and O. Kaymak. A new coding/ decoding algoirithm

using fibonacci numbers. Discrete Mathematics, Algorithms and Applications,

(2), 2018.

A. Tekcan. Continued fractions expansion of pD and pell equation x2 −dy2 = 1.

Mathematica Moravica, 15(2):19–27, 2011.

W. Trappe and L. Washington. Introduction to Cryptography. Prentice Hall,2006




DOI: http://dx.doi.org/10.23755/rm.v46i0.1062

Refbacks

  • There are currently no refbacks.


Copyright (c) 2023 Janaki G, Gowri Shankari A

Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.

Ratio Mathematica - Journal of Mathematics, Statistics, and Applications. ISSN 1592-7415; e-ISSN 2282-8214.