A Forward Secure Threshold Signature Scheme Based on the Structure of Binary Tree

Forward secure threshold signature plays an important role in distributed signature. Based on binary tree structure, a new forward secure threshold signature from bilinear pairings is proposed in this paper. In this scheme, each cost of key generation algorithm, key update algorithm, signing algorithm and verifying algorithm is independent of the total number of time periods. At the same time, the scheme needs very few interactions. Because the bilinear pairing used in this scheme is operating over a certain elliptic curve, the scheme inherits the property of short signature, that is, it has short secret key, public key and signature. We formalize the definition of the security model of forward secure threshold signature and prove the proposed scheme is forward secure under the computation Diffie-Hellman assumption in the random oracle model.