The Forest Analogy: Full Specification of the MRS-AUTH Cryptographic Framework

This work presents MRS-AUTH, a hybrid post-quantum and coercion-resistant authentication framework built around a structured Diophantine witness space defined by N = 19A + 9B. Its mathematical core is expressed through three Crown Equations: A₀ = dr(N) = 1 + ((N − 1) mod 9) B₀ = (N − 19·A₀) / 9 dr(B) = dr(2, dr(N)) Together, these equations provide deterministic anchoring, exact boundary reconstruction, and structural filtering for constant-time witness sampling without exhaustive enumeration. MRS-AUTH uses a three-layer witness chain in which the authentic witness is cryptographically bound to an identity, while alternative mathematically valid witnesses can be generated as coercion-resistant alibis. The framework combines ML-KEM-1024, HKDF-SHA256, AES-256-GCM, HMAC-SHA256, Shamir Secret Sharing with commitment verification, and Merkle commitments. Its mathematical model and security games are formally specified in EasyCrypt, alongside a Rust implementation with an automated test suite. MRS-AUTH is an active research prototype and requires independent security review before production deployment.