Hardening the ElGamal cryptosystem in the setting of the second group of units. (c2011)

Abstract

The purpose of this thesis is to give up to date discussion of the principles, techniques and algorithms of interest in cryptographic practice. We choose to emphasize on the most practical and applied cryptographic system, El-Gamal scheme. This thesis discusses modifications we made on El-Gamal scheme, mainly extending the scheme to work on the second group of units of Zn and the second group of units of the quotient ring of polynomials over a field with cyclic second group of units. The arithmetic needed in this new setting is described. Algorithms are given. Advantages and efficiency of the new method are pointed out. Finally the security of the new scheme is studied and suggestions for further work are introduced.