Distributed Signcryption Scheme on Hyperelliptic Curve

I. Gupta, N.R. Pillai, and P.K. Saxena (India)


Hyperelliptic curve, divisor, signcryption, Lagrange’s in terpolation, distributed signcryption.


The notion of signcryption was introduced by Zheng [15] in 1997. He showed that it was possible to combine the operations of signature generation/verification and en cryption/decryption and thereby achieving better efficiency over performing the two operations separately. He also showed that the ElGamal protocols over Z∗ p admit this ef ficient combination methodology. A distributed signcryp tion scheme was proposed by Mu and Varadharajan [11] in 2000. But the complexity of their scheme was dependent on the number of users in the communicating group. In this paper, we present an efficient distributed sign cryption scheme on hyperelliptic curve (HEC) with the help of Lagrange’s interpolation polynomial over prime field in which complexity of scheme is independent of the number of users in the communicating group. To do this, we first obtain a signcryption scheme based on HEC and then de rive signcryption scheme in a distributed environment. It is also shown that there are technical advantages of signcryp tion based on HEC over such schemes on Z∗ p . Finally, we analyze the cost of the signcryption scheme and the distributed signcryption scheme on HEC.

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