Group-oriented signature schemes based on Chinese remainder theorem

In this paper two group signature schemes are developed using the Chinese remainder theorem, the first work is based on exponentiation of primitive root of a prime field and the second work is based on elliptic curves. A trusted authority is involved in the schemes for the construction of the group key and individual participant keys. The constructed keys are used as long run keys. The group signature generated by the trusted authority from the partial signatures of the participants. The security of the proposed schemes depends on the NP-hard problems integer factorization, discrete logarithm and elliptic curve discrete logarithm. The signature schemes are illustrated using Mathematica 6.0 and MATLAB 7.0.