**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**30184

##### Modified Diffie-Hellman Protocol By Extend The Theory of The Congruence

**Authors:**
Rand Alfaris,
Mohamed Rushdan MD Said,
Mohamed Othman,
Fudziah Ismail

**Abstract:**

**Keywords:**
Extended theory of the congruence,
modified Diffie-
Hellman protocol.

**Digital Object Identifier (DOI):**
doi.org/10.5281/zenodo.1059825

**References:**

[1] Burton, D. M. The Theory of Congruences. In Elementary Number Theory, 4th ed. Boston, MA: Allyn and Bacon, pp. 80-105, 1989.

[2] Conway, J. H. and Guy, R. K. Arithmetic Modulo. In The Book of Numbers. New York: Springer-Verlag, pp. 130-132, 1996.

[3] Cormen, T. H., Leiserson, C. E., Rivest, R. and Stein, C. Greatest common divisor. In Introduction to Algorithms, MIT Press and McGraw-Hill, 2nd edn., pp. 856-862, 2001.

[4] Diffie, W. and Hellman, M. New Directions in Cryptography. IEEE Transactions on Information Theory IT-22: pp. 472-492, 1976.

[5] Hejhal, D. A., Friedman, J., Gutzwiller, M. C. and Odlyzko, A. M. Emerging Applications of Number Theory. New York: Springer. 2nd edn., 1999.

[6] Hrbacek, K. and Jech, T. Finite, Countable, and Uncountable Sets. In Introduction to Set Theory. New York, 3rd edn., pp. 65-93. 1999.

[7] Gilbert, J. and Gilbert, L. Elements of Modern Algebra. 6th ed. Thomson, brooks/cole, pp. 57-117, 2005.

[8] Nagell, T. Theory of Congruences. In Introduction to Number Theory. New York: Wiley, pp. 68-131, 1951.

[9] Niven, I. and Zuckerman, H. S. An Introduction to the Theory of Numbers. New York: John Wiley and Sons. 4th edn., 1980.

[10] Rand Alfaris. Modified Diffie-Hellman Protocol. In A New Decimal Cryptosystem Based on Decimal Numbers. Ph.D. Thesis, University Putra Malaysia, pp. 55-81, 2008.

[11] Rand Alfaris, Muhamad Rezal Kamel Ariffin and Mohamed Rushdan Md Said. Rounding Theorem the Possibility of Applying Cryptosystems on Decimal Numbers. Journal of Mathematics and Statistics, Vol. 4(1), pp. 15-20, 2008.

[12] S'eroul, R. Congruences. In Programming for Mathematicians. Berlin: Springer-Verlag, pp. 11-12, 2000.