A New Directed-Threshold Multi-signature Scheme without Trusted Share Distribution Center

This paper combines the ideas of (t; n) threshold signature schemes and multisignature schemes with directed signature scheme and propose a new type of digital signature scheme named as Directed-Threshold Multi-Signature scheme. Most (t, n) threshold schemes are based on the Lagrange interpolation or Chinese Remainder Theorem. The scheme proposed is based on Multivariate Linear Polynomial. In this scheme, there is a common trusted center (CTC) for determining the group secret parameters of the group and the secret shares all members, and a designated combiner DC who takes the responsibility to collect and verify each partial signature and then produce a group signature, but no secret information associated with the DC. Any malicious set of signers cannot impersonate any other set of signers to forge the signatures. In case of forgery, it is possible to trace the signing set. Any t or more share holds act in collusion cannot conspire to reconstruct the congruences the multivariate linear polynomial f_S(u₁, u₂,⋯, u_t) by providing their own secret shares and hence they can not recover the group secret key.