الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
Signcryption is a new paradigm in public key cryptography. A remarkable property of a signcryption scheme is that it full fills both the functions of public key encryption and digital signature, with a cost significantly smaller than that required by signature~then-encryption. The purposes of this thesis are to demonstrate how to specify partial signcryption scheme before and after applying elliptic curve over finite fields, and to examine the efficiency of such schemes. The analysis shows that when compared with signcryption, partial signcryption represents 50.2% saving in communication overhead, partial signcryption represents 83.8% saving in communication overhead.
Then, I explained a modification on Zheng elliptic curve signcryption scheme. The modifications of Zheng elliptic curve signcryption scheme are called quadruple elliptic curve signcryption scheme (QECSS).it is very easy to modify existing software to use QECSS. The purposes of this thesis are to demonstrate how to specify Quadruple signcryption schemes on curves over finite fields, and to examine the efficiency of such schemes. The analysis shows that when compared with signature-then-encryption on elliptic curves, Quadruple signcryption on the curves represent a 58% saving in computational cost and a 40% saving in communication overhead.