36 Quadruple Elliptic Curves Signcryption Schemes (QECSS)
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Signcryption is a new paradigm in public key cryptography. A remarkable property of a signcryption scheme is that it fulfills both the functions of public key encryption and digital signature, with a cost significantly smaller than that required by signature-then-encryption. Zheng elliptic curve signcryption is a new paradigm in public key cryptography that uses two keys for signcryption. In this paper, we explain a new signcryption schemes on elliptic curves. Our new signcryption schemes are modifications of Zheng elliptic curve signcryption schemes are called Quadruple elliptic curve signcryption schemes. The procedure for encryption of Quadruple elliptic curve signcryption schemes is exactly the same as regular Zheng elliptic curve signcryption schemes, but repeated three times and uses another one key for signature. Hence the name Quadruple Zheng Elliptic Curve Signcryption Schemes (QECSS). QECSS is based on Zheng ECS algorithm; it is very easy to modify existing software to use QECSS. The purposes of this paper are to demonstrate how to specify Quadruple signcryption schemes on curves over finite fields, and to examine the efficiency of such schemes. Our 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.