基于双线性的无可信中心可验证秘密共享方案

Verifiable Secret Sharing Scheme Based on Bilinear-pairs without Distribution Center

针对一般秘密共享方案或可验证秘密共享方案存在的缺点,结合椭圆曲线上双线性对性质和运用双线性Diffie-Hellman问题,构造了一个基于双线性对的无可信中心可验证秘密共享方案。在该方案中,共享秘密S是素数阶加法群G1上的一个点,在秘密分发过程中所广播的承诺Cj是与双线性有关的值。利用双线性对的双线性就可以实现共享秘密的可验证性,有效地防止参与者之间的欺诈行为,而不需要参与者之间执行复杂的交互式证明,因而该方案避免了为实现可验证性而需交互大量信息的通信量和计算量,通信效率高,同时该方案的安全性等价于双线性Diffie-Hellman假设的困难性。

NDBP-VSS based on bilinear-pairings is proposed in combination with the properties of bilinear-pairs on elliptic curve and bilinear Diffie-Hellman problem to overcome the disadvantages of the general＇secret sharing schemes and verifiable secret sharing schemes, in which the sharing secret S is a point on additive cyclic group Gj and the commitment Cj is the value relative to bilinear-pairs. The verifiableness of the sharing secret can be implemented by the properties of bilinear-pairs without implementation of complex interaction proofs of participants and numerous calculation. The communication efficiency was improved by the scheme. The security of this scheme is equivalent to the bilinear Diffie-Hellman assumption.