Encryption with Key stream via Short vectors

P. Anuradha Kameswari¹ , S B T Sundari Katakam²

Section:Research Paper, Product Type: Isroset-Journal
Vol.6 , Issue.3 , pp.115-120, Jun-2019

CrossRef-DOI:   https://doi.org/10.26438/ijsrmss/v6i3.115120

Online published on Jun 30, 2019

Copyright © P. Anuradha Kameswari , S B T Sundari Katakam . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper we describe a cryptosystem with keystream for Encryption, based on concatenation of short vectors of lattices corresponding to quadratic forms, that are good rational approximations of √z, for z a non-perfect square number. This cryptosystem is employed by both Symmetric key and Public key cryptosystem that is based on the hard mathematical problem of retrieving an irrational number from the convergents obtained as short vectors.

Key-Words / Index Term :
Encryption, key stream, short vector, LLL algorithm, Lattice reduction, quadratic form

References :
[1] Tom M. Apostol, Introduction to Analytical Number Theory, Springer-Verlag, New York, 1976.
[2] J. Buchmann, Introduction to cryptography , Springer-Verlag , New York, 2004
[3] David M. Burton, Elementary Number Theory , Sixth Edition, Tata McGraw-Hill Publishing company limited, New Delhi, India, 2008.
[4] H.Cohen, A course in Computational Algebraic Number Theory, Graduate Texts in Math.138. Springer ,1996.
[5] S.C. Coutinho, The Mathematics of Ciphers, University Press (India) Private Limited, 2003.
[6] H. Davenport, The Higher Arithmetic, Eighth edition, Cambridge University Press, United Kingdom, 2008.
[7] Jeffery Hoftstein, Jill Pipher, Joseph H. Silverman, An Introduction to Mathematical Cryptography, Second edition, Springer.
[8] P. Anuradha Kameswari, L. Praveen Kumar, Encryption on Elliptic Curves over Z_pq with Arithmetic on E(Z_pq) via E(Z_p) and E(Z_q), IOSR Journal of Mathematics (IOSR-JM), e-ISSN: 2278-5728, p-ISSN: 2319-765X. Volume 10, Issue 6 Ver. V (Nov - Dec. 2014), 21-29.
[9] P. Anuradha Kameswari, B. Ravitheja, "Encryption Using Lucas sequences L(Δ,pq) With Arithmetic on L(Δ,pq) via L(Δ,p) and L(Δ,q), International Journal of Scientific Research in Mathematical and Statistical Sciences Volume 6, No.1, pp.178-186, 2019
[10] A. M. Kane, "On the use of Continued Fractions for Stream Ciphers", In Proceedings of Security and Management, Las Vegas, USA , 2009.
[11] Neal Koblitz, A course in Number Theory and cryptography, Graduate Texts in Mathematics, second edition, Springer.
[12] A.K.Lenstra, H.W. Lenstra and L. Lovasz, Factoring Polynomials with Rational coefficients, Math.Ann.261, Springer - Verlag , pp. 515-534, 1982.
[13] Phong Q. Nguyen, Brigitte Valléee (Eds.), The LLL Algorithm, Survey and Applications, Springer, 2010.
[14] Nigel P.Smart, The Algorithmic Resolution of Diophantine Equations, London Mathematical Society, Student Texts 41, 1998.