Master-Trapdoor-Free Post-Quantum Multi-Authority Authentication via User-Local Lattice Capability Aggregation

Cross-organizational authentication often requires credentials from several authorities. We construct a lattice-based protocol with independently issued capabilities bound to a periodic pseudonym authenticated by a trusted user registry and aggregated locally into one proof. Setup requires no system-wide lattice master trapdoor or cross-authority joint lattice secret. Repartitioning a fixed witness among authorities preserves the aggregate relation and proof dimensions. We prove fixed-witness selective unforgeability of the ideal protocol under honest issuance, authentication-signature security, normal-form module learning with errors (Module-LWE), and homogeneous module short-integer solution (Module-SIS). The proof uses classical random oracles, a programmable extendable-output function (XOF), an integer norm certificate, and a reference sampler with quantified error. A C++17 research prototype was evaluated in 23 configurations. Its 78,522-byte token becomes smaller than the per-attribute Module-Lattice-Based Digital Signature Algorithm (ML-DSA)-44 reference at 33 attributes and is 49.51% smaller at 64 attributes. With 64 attributes and 64 authorities, online signing and prepared verification took 56.038 and 8.729 ms, respectively. Complete local cold signing took 370.050 ms, and public matrices for 64 capabilities occupied 29.75 mebibytes (MiB). Aggregation reduces repeated token communication for larger witnesses, at the cost of preparation, public-state storage, and higher measured computation than the ML-DSA references.