Anonymous credentials (ACs) are fundamental to privacy-preserving authentication, allowing users to prove possession of attributes without revealing their identities. State-of-the-art ACs distribute credential issuance across multiple authorities, typically employing techniques such as Shamir's secret sharing or aggregate signatures. While this approach enhances system robustness and eliminates a single point of failure, it treats all authorities equally in the credential issuance phase. This uniform treatment disregards the varying levels of trustworthiness or stake held by different authorities. Such a limitation has become particularly problematic in modern decentralized systems like Proof-of-Stake networks, where the inherent trust differentiation among nodes cannot be leveraged in the credential issuance process. To address this limitation, we propose the notion of Multi-Authority Anonymous Credentials with Epoch-Based Weights (MA-ACEW), the first Multi-Authority Anonymous Credential (MA-AC) model that considers authorities' weight distribution in credential issuance. Crucially, MA-ACEW enables efficient credential updates when authority weight distributions change across epochs. The core of MA-ACEW is our novel Epoch-Bound Pointcheval-Sanders Signature (EB-PS) primitive, which binds signatures to specific time epochs. This temporal binding enables both weight-based credential issuance within epochs and efficient non-interactive credential updates across epochs. We formalize the EUF-eCMA unforgeability requirement for EB-PS and prove our construction satisfies it under a novel STB-GPS assumption. We then prove that our MA-ACEW construction achieves unforgeability, anonymity, and blindness. Finally, we present benchmarks demonstrating the efficiency of EB-PS and MA-ACEW. Remarkably, presenting a credential aggregated from 128 partial ones takes only 10.68 ms on average.

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