Abstract. A credential system is a system in which users can obtain credentials from organizations and demonstrate possession of these credentials. Such a system is anonymous when transactions carried out by the same user cannot be linked. An anonymous credential system is of significant practical relevance because it is the best means of providing privacy for users. In this paper we propose a practical anonymous credential system that is based on the strong RSA assumption and the decisional Diffie-Hellman assumption modulo a safe prime product and is considerably superior to existing ones: (1) We give the first practical solution that allows a user to unlinkably demonstrate possession of a credential as many times as necessary without involving the issuing organization. (2) To prevent misuse of anonymity, our scheme is the first to offer optional anonymity revocation for particular transactions. (3) Our scheme offers separability: all organizations can choose their cryptographic keys independently of each other. Moreover, we suggest more effective means of preventing users from sharing their credentials, by introducing allor-nothing sharing: a user who allows a friend to use one of her credentials once, gives him the ability to use all of her credentials, i.e., taking over her identity. This is implemented by a new primitive, called circular encryption, which is of independent interest, and can be realized from any semantically secure cryptosystem in the random oracle model.

Abstract. We propose a new and efficient signature scheme that is provably secure in the plain model. The security of our scheme is based on a discrete-logarithm-based assumption put forth by Lysyanskaya, Rivest, Sahai, and Wolf (LRSW) who also showed that it holds for generic groups and is independent of the decisional Diffie-Hellman assumption. We prove security of our scheme under the LRSW assumption for groups with bilinear maps. We then show how our scheme can be used to construct efficient anonymous credential systems as well as group signature and identity escrow schemes. To this end, we provide efficient protocols that allow one to prove in zero-knowledge the knowledge of a signature on a committed (or encrypted) message and to obtain a signature on a committed message.

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