Threshold Signcryption Based on Elliptic Curve

Abstract

The signcryption scheme presented by Zheng uses hash function and symmetrical cipher to encrypt message. The first protocol for threshold generation of Zheng's signcryption scheme couldn't support multiple public verifiers. In this paper, we proposed a new signcryption scheme based on EC-ELGamal type encryption. Message to be transmitted is embedded in Elliptic Curve as a point P(m) and encrypted by point addition which is efficient and secure as well as exiting schemes. By using verifiable secret sharing and secure multiparty computation, we propose a protocol for threshold generation of the signcryption. Because point addition couldn't map coordinate addition directly, we introduce a linear sum of coordinates to reconstruct the private coordinate. The protocol supports k out of n senders and the public verifier. The specific receiver can verify the validity of the signature before decrypting the cipher. The proposed protocol is a perfect threshold scheme. Thus, it can defend the attack launched by k-1 players. Complexity of them is less than the same schemes based on DLP (Discrete Logarithm Problem).