Pairings In The Elliptic Curve Cryptosystem Computing And Applications

In this paper, by the use of the relations between bilinear pairing and threshold signature, first of all, through analyzing the method of computing Weil and Tate pairings in the literature, the thesis gives two improvements on the basis of it. The algorithms are analyzed. The improved algorithms are much better than the original algorithm. The two methods may easily realize with low computation. In addition, the two algorithms are examined by means of examples.Second, a new threshold signature scheme without a trusted party is presented by use of bilinear pairings. This scheme supposes PKG is not a trusted dealer. If the users in the scheme trust PKG unconditionally, dishonest PKG can forge any user's signature because all users' secret key can be produced by PKG In new scheme it isn't feasible that dishonest PKG try to forge signature by calculating the users' secret key. In the process of the keys'generation all members'discussion achieves the key. Group's public key and private key are generated by the common members. It can prevent member's secret key from leaking, and solve the problems that the past scheme depended on the trusted party excessively and the rights of trusted party were too collective. At last the properties of robustness and unforgeability are proved in the proposed scheme.