This paper introduces a new type of signature called a group signature, which has the following properties: 1. Only members of the group can sign messages. 2. The receiver can verify that a signature is valid but cannot identify the specific member who signed it. 3. The signature can be "opened" to reveal the identity of the signer if necessary. The authors present four different group signature schemes, each based on different cryptographic assumptions: - Scheme 1 uses a public key system and requires a trusted authority (Z) for setup and signature opening. - Scheme 2 uses RSA and discrete logarithms, with no trusted authority needed after setup. - Scheme 3 uses RSA and a trusted public directory, with no trusted authority needed. - Scheme 4 uses discrete logarithms and a trusted public directory, with no trusted authority needed. Each scheme is designed to protect the signer's anonymity and includes protocols for verification and disavowal. The paper also discusses the implementation details, security proofs, and potential improvements. Open problems and future research directions are outlined, including the possibility of creating digital group signatures and optimizing the confirmation protocol.This paper introduces a new type of signature called a group signature, which has the following properties: 1. Only members of the group can sign messages. 2. The receiver can verify that a signature is valid but cannot identify the specific member who signed it. 3. The signature can be "opened" to reveal the identity of the signer if necessary. The authors present four different group signature schemes, each based on different cryptographic assumptions: - Scheme 1 uses a public key system and requires a trusted authority (Z) for setup and signature opening. - Scheme 2 uses RSA and discrete logarithms, with no trusted authority needed after setup. - Scheme 3 uses RSA and a trusted public directory, with no trusted authority needed. - Scheme 4 uses discrete logarithms and a trusted public directory, with no trusted authority needed. Each scheme is designed to protect the signer's anonymity and includes protocols for verification and disavowal. The paper also discusses the implementation details, security proofs, and potential improvements. Open problems and future research directions are outlined, including the possibility of creating digital group signatures and optimizing the confirmation protocol.