Secure Distributed Key Generation on Vector Space Access Structures in Bilinear Groups

Distributed key generation is a method for a set of players to generate a pair of public key and private key together, such that the public key is output publicly while the private key is distributed among the players by a secret sharing method. Secure distributed key generation in finite field for discrete-log based cryptosystems has been studied for many year and many protocols have been proposed and widely used in threshold cryptosystems and distributed cryptographic computing. In this paper we focus on secure distributed key generation in bilinear groups and propose such protocol on vector space access structures. The new proposed distributed key generation protocol is secure and has a wide application. We give detailed proof for its security.