This paper introduces a new privacy primitive called "Traceable Signatures" and presents an efficient, provably secure implementation. Traceable signatures offer an extended set of fairness mechanisms compared to traditional group signatures, allowing for the tracing of all signatures of a single party without revealing identities of other users. The authors develop several basic tools, zero-knowledge proofs, and protocols to support efficient implementation, including the concept of "traceable (anonymous) identification." The security model includes definitions for correctness and security properties, addressing misidentification, anonymity, and framing attacks. The construction is based on mathematical assumptions and cryptographic primitives, ensuring robustness and efficiency. The paper also discusses the application of traceable signatures in transforming anonymous systems into those with "fair privacy" and the implementation of CRL-based revocation.This paper introduces a new privacy primitive called "Traceable Signatures" and presents an efficient, provably secure implementation. Traceable signatures offer an extended set of fairness mechanisms compared to traditional group signatures, allowing for the tracing of all signatures of a single party without revealing identities of other users. The authors develop several basic tools, zero-knowledge proofs, and protocols to support efficient implementation, including the concept of "traceable (anonymous) identification." The security model includes definitions for correctness and security properties, addressing misidentification, anonymity, and framing attacks. The construction is based on mathematical assumptions and cryptographic primitives, ensuring robustness and efficiency. The paper also discusses the application of traceable signatures in transforming anonymous systems into those with "fair privacy" and the implementation of CRL-based revocation.