Threshold Signature Scheme without Using Polynomial Interpolation

In a (t, n) secret sharing scheme (SS), the secret is shared among n shareholders in such a way that (a) with t or more than t shares can recover the secret, and (b) with fewer than t shares cannot obtain the secret. The threshold signature scheme is an application that extends the SS to a digital signature scheme. In a threshold signature scheme, any t or more than t group members can represent the group to generate a group signature; but fewer than t group members cannot generate a group signature. So far, most threshold signature schemes are based on the linear polynomial. In other words, these threshold signature schemes need to overcome the problem of polynomial interpolation. In this paper, we propose a threshold signature scheme based on the Chinese Remainder Theorem (CRT). We describe how to set up the system by a trusted group manager initially and generate pairs of public and private keys for group members. Since our proposed scheme is based on the CRT, there is no polynomial interpolation. The security of our proposed threshold signature scheme is based on the difficulty of solving the discrete logarithm problem.