ACS-DTWI: An anonymous credential scheme with dual-threshold weighted issuers

Consortium identity and cross-institutional authorization require anonymous credentials to reflect both institutional diversity and differentiated authority. Count-threshold issuance captures a minimum participation requirement, whereas cumulative-weight authorization captures an authority requirement; applying either condition alone leaves the other governance dimension unspecified. We present ACS-DTWI, a same-set dual-threshold anonymous credential scheme whose authorized sets satisfy | S | ≥ t and W ( S ) ≥ T . ACS-DTWI realizes this policy through two independent sharp reconstruction layers under a shared threshold PS key, a trusted identity–coordinate registry produced at setup, subset-independent blind-signing bundles, and post-collection selection of a qualifying issuer set. Any successful reconstruction induces a registered provenance set satisfying both conditions, while the resulting credential is verified under one fixed key and supports re-randomized, unlinkable presentation without revealing the issuer subset, its cardinality, or its cumulative weight. We formalize provenance-bound unforgeability and establish unforgeability, blindness, and unlinkability under the stated assumptions. In a representative minimum-coalition setting, exact enumeration identifies 86.67% of count-qualified coalitions as weight-insufficient. Implementation measurements over 𝑛 = 3 –50 issuers keep 𝖵 𝖾 𝗋 𝗂 𝖿 𝗒 𝖢 𝗋 𝖾 𝖽 between 10.17 and 12.43 ms, indicating a stable presentation-time verification path over the measured scale.