Call for Paper - March 2023 Edition
IJCA solicits original research papers for the March 2023 Edition. Last date of manuscript submission is February 20, 2023. Read More

A Method for Recovering a Key in the Key Exchange Cryptosystem by Diophantine Equations

Print
PDF
International Journal of Computer Applications
© 2014 by IJCA Journal
Volume 100 - Number 14
Year of Publication: 2014
Authors:
P. Anuradha Kameswari
L. Praveen Kumar
10.5120/17592-8302

Anuradha P Kameswari and Praveen L Kumar. Article: A Method for Recovering a Key in the Key Exchange Cryptosystem by Diophantine Equations. International Journal of Computer Applications 100(14):11-13, August 2014. Full text available. BibTeX

@article{key:article,
	author = {P. Anuradha Kameswari and L. Praveen Kumar},
	title = {Article: A Method for Recovering a Key in the Key Exchange Cryptosystem by Diophantine Equations},
	journal = {International Journal of Computer Applications},
	year = {2014},
	volume = {100},
	number = {14},
	pages = {11-13},
	month = {August},
	note = {Full text available}
}

Abstract

The Diophantine equations define an algebraic curve or an algebraic surface and ask about lattice points on it. A Diophantine equation may either possess no non trivial solution or finite number of solutions or infinite number of solutions. Therefore, computing lattice points is difficult in general for Diophantine equations of order greater than one. This ambiguity regarding the solutions of a Diophantine equation is another source for trapdoor functions in Public key cryptography. In this paper we analyze the potentiality of Diophantine equations in the key exchange cryptosystem and propose a method for recovering a key in the key exchange cryptosystem by Diophantine equations.

References

  • J. Buchmann "Introduction to cryptography" , Springer-Verlag 2001
  • D. Burton, "Elementary Number Theory" Sixth ed, Mc Graw Hill, New York, 2007.
  • H. Davenport's, "The Higher Arithmetic", Eighth edition, Cambridge University Press, ISBN-13 978-1-107-68854-4.
  • G. H. Hardy, E. M. Wright, D. R. Heath-Brown and J. H. Silverman, "An Introduction to the Theory of Numbers", Oxford University Press, 1965.
  • Harry Yosh, Heco Ltd, Canberra, Australia "The Key Exchange Cryptosystem Used With Higher Order Diophantine Equations" , IJNSA journal Vol. 3, No 2, March 2011}
  • Jacobson. M and W. Hugh, "Solving the Pell equation", CMS books in Mathematics, Canadian Mathematical society, 2009.
  • Neal Koblitz "A course in number theory and cryptography ISBN 3-578071-8,SPIN 10893308 "
  • Lawrence C. Washington, Wade Trappe "Introduction to Cryptography with Coding Theory" 2nd edition, Pearson.
  • A. J. Menezes, P. C. van Oorschot and S. A. Vanstone. , "Handbook of Applied Cryptography," CRC Press Series on Discrete Mathematics and its Applications. Boca Raton, FL, 1997.
  • I. Niven, H. S. Zuckerman, and H. L. Montgomery, "An Introduction to the Theory of Numbers", Fifth edition, John Wiley $&$ Sons, New York, 1991.
  • K. H. Rosen"Elementary Numbertheory and Its Applications" 3rd ed. , Addison-Wesley,1993
  • D. R. Stinson, "Cryptography Theory and Practice", Second Edition, Chapman Hall/CRC, 2002.