Threshold Anonymous Counting Tokens with Batch Proofs for Online Paywalls
Yanqi Zhao, Minghong Sun, Min Xie, Xiaoyi Yang, Yong Hong Yu · 2025
As online application services evolve, an increasing number of users are opting for subscription-based or paywall models to access high-quality content. Anonymous counting tokens (ACTs), which regulate user access while protecting user privacy, are widely adopted in the online paywall model. However, the centralized server of ACT may lead to a single point of failure, thereby exposing users’ privacy. To address this challenge, in this paper, we propose threshold anonymous counting tokens with batch proofs (ThrACT) that balance privacy preservation and access count limitation for online paywalls. We define the system model for ThrACT and provide its concrete construction. We utilize the threshold Boneh-Boyen signature to facilitate distributed issuance of anonymous tokens and enable batch issuance. In addition, our ThrACT employs non-interactive zero-knowledge proofs to verify the label and token requests while allowing the correctness of multiple blind token shares to be validated simultaneously. We also prove that ThrACT satisfies unforgeable and unlinkable security properties. Finally, we evaluate the computational cost of our ThrACT and compare it with other schemes. The experiment result demonstrates that ThrACT not only supports distributed issuance, batch verification, and counting functionalities but also achieves computational overhead in milliseconds. In particular, when the threshold is set to (3,5), the token issuance time is approximately 9 milliseconds.