In this paper, we introduce updatable anonymous credential systems (UACS) and use them to construct a new privacy-preserving incentive system. In a UACS, a user holding a credential certifying some attributes can interact with the corresponding issuer to update his attributes. During this, the issuer knows which update function is run, but does not learn the user's previous attributes. Hence the update process preserves anonymity of the user. One example for a class of update functions are additive updates of integer attributes, where the issuer increments an unknown integer attribute value v by some known value k. This kind of update is motivated by an application of UACS to incentive systems. Users in an incentive system can anonymously accumulate points, e.g. in a shop at checkout, and spend them later, e.g. for a discount.

We present CLARC (Cryptographic Library for Anonymous Reputation and Credentials), an anonymous credentials system (ACS) combined with an anonymous reputation system. Using CLARC, users can receive attribute-based credentials from issuers. They can efficiently prove that their credentials satisfy complex (access) policies in a privacy-preserving way. This implements anonymous access control with complex policies. Furthermore, CLARC is the first ACS that is combined with an anonymous reputation system where users can anonymously rate services. A user who gets access to a service via a credential, also anonymously receives a review token to rate the service. If a user creates more than a single rating, this can be detected by anyone, preventing users from spamming ratings to sway public opinion. To evaluate feasibility of our construction, we present an open-source prototype implementation.