A CRYPTOSYSTEM BASED ON HILBERT
MATRIX USING CIPHER BLOCK CHAINING
MODE

Penmetsa V Krishna Raja; A S N Chakravarthy; Prof. P S Avadhani

doi:https://doi.org/10.14445/22315373/IJMTT-V2I1P506

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 2 | Issue 1 | Year 2011 | Article Id. IJMTT-V2I1P506 | DOI : https://doi.org/10.14445/22315373/IJMTT-V2I1P506

A CRYPTOSYSTEM BASED ON HILBERT MATRIX USING CIPHER BLOCK CHAINING MODE

Penmetsa V Krishna Raja , A S N Chakravarthy , Prof. P S Avadhani

Citation :

Penmetsa V Krishna Raja , A S N Chakravarthy , Prof. P S Avadhani, "A CRYPTOSYSTEM BASED ON HILBERT MATRIX USING CIPHER BLOCK CHAINING MODE," International Journal of Mathematics Trends and Technology (IJMTT), vol. 2, no. 1, pp. 17-22, 2011. Crossref, https://doi.org/10.14445/22315373/IJMTT-V2I1P506

Abstract

Cryptography is the science of using mathematics to encrypt and decrypt data. Cryptography enables you to store sensitive information or transmit it across insecure networks so that it cannot be read by anyone except the intended recipient. While cryptography is the science of securing data, cryptanalysis is the science of analyzing and breaking secure communication. Classical cryptanalysis involves an interesting combination of analytical reasoning, application of mathematical tools and pattern finding. The objectives of the proposed work are to propose a new cryptographic method based on the special matrix called the Hilbert matrix for authentication and confidentiality and to propose a model for confidentiality and authentication using a combination of symmetric and public cryptosystems. Further, it is extended to shared key cryptosystems with the concept of digital enveloping using a session key. In the present work an algorithm for shared key encryption is developed using Hilbert matrix cryptosystem. In this the block chaining modes of operation have been used to tackle the issues of confusion and diffusion. Keywords— Crypto System, Hilbert Matrix, Cipher Block Chain Encryption,Decryption.

Keywords

Crypto System, Hilbert Matrix, Cipher Block Chain Encryption,Decryption.

References

[1] JE Andersen and C Berg,“Quantum Hilbert matrices and orthogonal polynomials”, Journal of computational and applied mathematics, 2009.
[2] I Gohberg and V Olshevsky, Numerische Mathematik, ”Fast inversion of Chebyshev-Vandermonde matrices”, Springer Publications,New York, 1994.
[3] V Mani and RE Hartwig, “Some properties of the q-adic vandermonde matrix”, Electron. J. Linear Algebra, emis.ams.org, 1996.
[4] R Alvarez, FM Martinez and JF Vicent A, “A New Public Key Cryptosystem based on Matrices”, WSEAS Information Security and Privacy (2007) 36-39 2007.
[5] Y Matsuo, “Matrix Theory, Hilbert Scheme and Integrable System” Arxiv preprint hep-th /9807085, 1998.
[6] Beckermann, Bernhard, "The condition number of real Vandermonde, Krylov and positive definite Hankel matrices". Numerische Mathematik 85 (4): 553–577, 2000.
[7] C Li, D Zhang, G Chen,” Cryptanalysis of an image encryption scheme based on the Hill cipher”, Journal of Zhejiang University-Science A, Springer Publications, New york, 2008.
[8] S. Suresh Babu, “A symmetric cryptographic model for authentication and confidentiality using Hilbert matrix”, Ph.D thesis, Andhra University, Visakhapatnam, 2010.
[9] E Diamantopoulos and AG Siskakis, “Composition Operators and the Hilbert Matrix”, Studia Math, 2000.
[10] Garrettt, P. "Making , Breaking Codes : An Introduction to Cryptology" , Upper Saddle River,NJ:Prentice Hall ,2001.
[11] A., Herzberg A., “Protecting (even naïve) web users from spoofing and phishing attacks”, Bar-Ilan (Israel), 2004.
[12] A. F. Al Shahri, D. G. Smith and J. M. Irvine, “Implementation of Secret Sharing to Increase Network Security and Reliability.”, ESPRC Postgraduate Research in Electronics and Photonics (PREP), Nottingham University, UK. April 2002.
[13] A. F. Al Shahri, D. G. Smith and J. M. Irvine, “Mobile distributed authentication protocol”, ISWSN’03 Dhahran, Saudi Arabia, March 24-26, 2003.
[14] A. Juels and S.A. Weis, “Authenticating Pervasive Devices with Human Protocols,” Proc. 25th Ann. Int’l Cryptology Conf. (CRYPTO ’05), pp. 293-308, 2005.
[15] A.K.Awasthi and S.Lal, “A remote user authentication scheme using smart cards with forward secrecy”, IEEE Trans. Consumer Electronics, Vol. 49, pp.1246-1248, 2003.
[16] A Klein, “Attacks on the RC4 stream cipher”, Designs, Codes and Cryptography, Springer Publications, New York, 2008.
[17] A. Menezes, P. Oorschot, S. Vanstone, “Handbook of Applied Cryptogtaphy”, CRC Press LLC 1997.
[18] A. Paul and U. Ramachandran. “Computation communication tradeoff for power and bandwidth savings in remote authentication over wireless networks”, Technical Report GIT-CERCS-04-01, Georgia Institute of Technology, 2004.