We apologize for a recent technical issue with our email system, which temporarily affected account activations. Accounts have now been activated. Authors may proceed with paper submissions. PhDFocusTM
CFP last date
20 December 2024
Call for Paper
January Edition
IJCA solicits high quality original research papers for the upcoming January edition of the journal. The last date of research paper submission is 20 December 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

Cryptosystem with Redei Rational Functions via Pellconics

by P. Anuradha Kameswari, R. Chaya Kumari
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 54 - Number 15
Year of Publication: 2012
Authors: P. Anuradha Kameswari, R. Chaya Kumari
10.5120/8639-2054

P. Anuradha Kameswari, R. Chaya Kumari . Cryptosystem with Redei Rational Functions via Pellconics. International Journal of Computer Applications. 54, 15 ( September 2012), 1-6. DOI=10.5120/8639-2054

@article{ 10.5120/8639-2054,
author = { P. Anuradha Kameswari, R. Chaya Kumari },
title = { Cryptosystem with Redei Rational Functions via Pellconics },
journal = { International Journal of Computer Applications },
issue_date = { September 2012 },
volume = { 54 },
number = { 15 },
month = { September },
year = { 2012 },
issn = { 0975-8887 },
pages = { 1-6 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume54/number15/8639-2054/ },
doi = { 10.5120/8639-2054 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T20:55:43.785597+05:30
%A P. Anuradha Kameswari
%A R. Chaya Kumari
%T Cryptosystem with Redei Rational Functions via Pellconics
%J International Journal of Computer Applications
%@ 0975-8887
%V 54
%N 15
%P 1-6
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

In this paper, two cryptosystems are constructed using the fact that Rédei rational functions are permutation polynomials and exploiting the multiplicative properties of Rédei rational functions and the inverse property of Dickson polynomial extended to Rédei rational functions. The encryptions are based on evaluating Rédei rational functions with the values connected to the solutions of the Pell's equation in . The connection between these evaluations and the convergents of solutions of Pell's equation are used in the construction of the second cryptosystem.

References
  1. A. K. Bhandari, The public key cryptography. Proceedings of the advanced instructional workshop on Algebraic number theory, HBA (2003)287-301.
  2. J. Buchmann, Introduction to cryptography , Springer-Verlag 2001.
  3. W. S. Chou, The factorization Dickson polynomials over finite fields, Finite fields Appl. 3,1997.
  4. S. D. Cohen, Dickson permutations in Number-theoritic and Algebraic methods in computer science. Moscow, 1993.
  5. M. Fried-R. Lidl, On Dickson Polynomials And Rédei Function, Contributions to general algebra 5, Proceedings of the Salzburg conferene, Mai29-june1,1986.
  6. Hans Lausch and Wilfried Nobauer, Algebra of Polynomials, North Holland publishing company-1973.
  7. M. jacobson, W. Hugh, Solving the pell equation, CMS Books in mathematics, canadian mathematical society, 2009.
  8. F. Lemmermeyer, Higher descent on Pellconics. III. The first 2-descent, available on http://arxiv. org/abs/math/0311310v1,2003.
  9. Lenstra H. W Jr. Solving the pell equation. Notice of AMS v. 49 no. 2 186-192 (2002).
  10. Neal Koblitz, A course in number theory and cryptography. ISBN 3-578071-8,SPIN 10893308 .
  11. Nobauer Wilfried, Uber Permutationspolynome und Permutationsfunktionen fur Primzahlpotenzen.
  12. Rudolf Lidl and Winfried B. Muller, Permutation polynomials in RSA cryptosystems, Springer-Verlag(1998).
  13. Sahadeo Padhye, A Public key cryptosystem based on pell equation.
  14. Stefano Barbero, Umberto Cerruti and Nadir Murru, Solving the Pell Equation via Rédei rational functions.
  15. Wilfried B. Muller and Rupert Nobauer, Cryptanalysis of the dickson scheme.
Index Terms

Computer Science
Information Sciences

Keywords

Pell conics Redei Rational function Permutation Polynomial Cryptosystem

Powered by PhDFocusTM