An Efficient Blacklistable Anonymous Credential System with Reputation Using Pairing-Based Accumulator

To achieve the privacy-enhancing authentications without any TTP (Trusted Third Party), blacklistable anonymous credential systems have been proposed. In conventional blacklistable anonymous credential systems, a user is blacklisted after the user misbehaves once. Since it is too harsh to be of practical use, extended blacklistable anonymous credential systems based on reputation have been proposed. In the reputation-based system, each behavior of a user is given a score. The service provider publishes a reputation list of correspondences between session ID and the score. In the authentication, a user can anonymously prove the total of his own scores. However, the previously proposed systems have the efficiency problem: The authentication data size is O(|L|) or O(K), where |L| is the size of the reputation list L, and K is the size of the following window. In the window type of systems, the authentication is based on a window with most recent K authentications of the user. When a past authentication becomes outside the window, the misbehaving of the authentication is forgiven. Thus, K should be as large as possible. Therefore, the previous systems suffer from O(|L|) or O(K)-size data in each authentication. In addition, in the previous systems, the authentication needs the computation of O(|L|) or O(K) exponentiations, which is heavy. In this paper, an efficient blacklistable anonymous credential system with reputation is proposed. In our system, the data size of the authentication does not depend on parameters such as |L| and K, and is O(1). Furthermore, although the computational costs in the authentication depend on some parameters, the parameter-related costs are only multiplications instead of exponentiations. For constructing our system, we newly introduce the concept of an accumulator for reputation, and show an efficient pairing-based construction. Using the accumulator, we construct the efficient blacklistable anonymous credential system with reputation.