Reduction of authentication time in an anonymous credential system with proofs for monotone formulas on attributes

An anonymous credential system allows a user to convince a service provider anonymously that he/she owns certified attributes. Previously, an anonymous credential system was proposed to prove user´s attributes to satisfy a monotone formula, i.e., a logic relation with any combination of AND/OR relations. However, this system has a problem of requiring large authentication time which depends on the number of attributes in the proved formula. In this paper, we propose methods to accelerate the authentication time by reducing the exponentiation costs for the calculations of accumulator and the witness which are used in the system. We implemented the accelerated system using a fast pairing library, and measured the authentication times, while changing the size of the proved relation.