Abstract: Two blinded variants of signatures of knowledge, are described in this paper, including blind signature of knowledge protocols for the double discrete logarithm, and for the root of the discrete logarithm. Then a new group blind digital signature scheme is presented, which involves taking the group signature scheme of Jan Camenisch as basis, and combining with the above two blind signatures of knowledge. The scheme has some good properties, such as unforgeability, and blindness properties, etc. And computational, space, and communication complexities of the scheme are linear in the security parameterl.