IJPAM: Volume 116, No. 2 (2017)




M.K. Viswanath$^1$, M. Ranjith Kumar$^2$
$^1$Department of Mathematics
Rajalakshmi Engineering College, Thandalam
Chennai, 602 105, Tamil Nadu, INDIA
$^2$Department of Mathematics
Research and Development Centre
Bharathiar University
Coimbatore, 641 046, Tamil Nadu, INDIA


The main object of this paper is to develop a mutual authentication protocol that guarantees security, integrity and authenticity of messages, transferred over a network system. In this paper a symmetric key cryptosystem, that satisfies all the above requirements, is developed using the decimal expansion of an irrational number.


Received: 2017-05-01
Revised: 2017-06-15
Published: October 7, 2017

AMS Classification, Key Words

AMS Subject Classification: 11T71, 14G50, 68P25, 68R01, 94A60
Key Words and Phrases: Vinogradov's theorem, Chen's theorem, RSA algorithm, Pseudo inverse

Download Section

Download paper from here.
You will need Adobe Acrobat reader. For more information and free download of the reader, see the Adobe Acrobat website.


Man Young Rhee, Cryptography and Secure Communications, McGraw-Hill Series on Computer Communications, Singapore (1994).

M. Eisenberg Hill ciphers and Modular Linear Algebra, Mimeographed Notes, University of Massachusetts, USA (1998).

I.A. Ismail, M. Amin and H. Diab, How to repair the Hill cipher, Journal of Zhejiang University Science, 7, No. 12 (1998), 2022-2030.

S. Lester Hill, Cryptography in an algebraic alphabet, The American Mathematical Monthly, 36 No. 6 (1929), 306-312.

M.K. Viswanath and M. Ranjithkumar, A secure cryptosystem using the decimal expansion of an Irrational number, Applied Mathematical Sciences, 9, No. 106 (2015), 5293-5303.

J.R. Chen, On the representation of a large even integer as the sum of a prime and the product of atmost two primes, Kexue Tongbao (Chinese), 17 (1966), 365-386.

J.R. Chen, On the representation of a large even integer as the sum of a prime and the product of atmost two primes, Sci. Sinica, 16 (1973), 157-176.

I.M. Vinogradov, The representation of an odd number as a sum of three primes, Dokl. Akad. Nauk. SSSR, 16 (1937), 139-142.

R.L. Rivest, A. Shamir and L. Adleman, A method for obtaining digital signatures and public key cryptosystems, Communications of the ACM, 21, No. 2 (1978), 120-126.

A.J. Menezes , P.C. Van Oorchot and S.A. Vanstone Handbook of Applied Cryptography, CRC Press, USA (2000).

Neal Koblitz, A course in Number Theory and Cryptography, Springer, USA (1994).

T.L. Boullion and P.L. Odell, Generalized Inverse Matrices, Wiley, New York (1971).

R. Penrose, A generalized Inverse for matrices, Pvoc. Cambridge Phil. SOC, 51 (1955), 406-413.

Predrag Stanimirovic and Miomir Stankovic, Determinants of rectangular matrices and Moore-Penrose inverse, Novi sad J.Math., 27, No. 1 (1997), 53-69.

J. Pintz and I.Z. Puzsa, On Linnik's approximation to Goldbach's problem, I. Acta Arithmatica, 109, No. 2 (2003), 169-194.

M.K. Viswanath and M. Ranjithkumar, A Public Key Cryptosystem Using Hill’s Cipher, Journal of Discrete Mathematical Sciences and Cryptography, 18, No. 1-2 (2015), 129-138.

How to Cite?

DOI: 10.12732/ijpam.v116i2.12 How to cite this paper?

International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2017
Volume: 116
Issue: 2
Pages: 403 - 413

Google Scholar; DOI (International DOI Foundation); WorldCAT.

CC BY This work is licensed under the Creative Commons Attribution International License (CC BY).