This paper presents a new and efficient signature scheme based on the LRSW assumption and bilinear maps, which is provably secure in the plain model. The scheme is used to construct efficient anonymous credential systems, group signature schemes, and identity escrow schemes. The signature scheme allows for zero-knowledge proofs of knowledge of a signature on a committed message and the issuance of a signature on a committed message. The scheme is efficient and secure under the LRSW assumption, which is a discrete-logarithm-based assumption that holds for generic groups and is independent of the decisional Diffie-Hellman assumption. The paper also describes how the signature scheme can be extended to support block-based messages and how it can be used to construct group signatures and anonymous credential systems. The paper further discusses the security of the proposed schemes and their applications in cryptographic protocols. The work is compared to other schemes, including those based on the strong RSA assumption and the recent work by Boneh, Boyen, and Shacham. The paper concludes with a discussion of the implications of the proposed schemes for cryptographic applications.This paper presents a new and efficient signature scheme based on the LRSW assumption and bilinear maps, which is provably secure in the plain model. The scheme is used to construct efficient anonymous credential systems, group signature schemes, and identity escrow schemes. The signature scheme allows for zero-knowledge proofs of knowledge of a signature on a committed message and the issuance of a signature on a committed message. The scheme is efficient and secure under the LRSW assumption, which is a discrete-logarithm-based assumption that holds for generic groups and is independent of the decisional Diffie-Hellman assumption. The paper also describes how the signature scheme can be extended to support block-based messages and how it can be used to construct group signatures and anonymous credential systems. The paper further discusses the security of the proposed schemes and their applications in cryptographic protocols. The work is compared to other schemes, including those based on the strong RSA assumption and the recent work by Boneh, Boyen, and Shacham. The paper concludes with a discussion of the implications of the proposed schemes for cryptographic applications.