MRS: A Universal Framework with Recursive Depth

This paper introduces MRS-AUTH (Multiple Representation Systems Authentication), a novel framework for deniable authentication based on recursive decomposition within the linear Diophantine system N = 19A + 9B. The central innovation is the Matryoshka structure: coefficients in any valid representation can themselves be recursively decomposed, generating a theoretically infinite hierarchy of equally valid authentication credentials — referred to as "alibis." Each recursive layer contributes approximately 125 bits of entropy. With N ≈ 10⁴² and three layers, the total entropy exceeds 370 bits, providing post-quantum security against Grover's algorithm without requiring exponentially large parameters. The digital root invariant dr(A) = dr(N) serves as a natural verification mechanism across all recursive layers. The framework is integrated with Kyber-KEM through a formal security reduction, establishing that the hybrid system is at least as hard to break as Kyber itself. Unlike prior approaches to deniable authentication — including simulation-based and distribution-based methods — MRS-AUTH achieves information-theoretic deniability grounded in mathematical multiplicity rather than computational assumptions. Applications are demonstrated across public-key cryptography, symmetric authentication, physical access control, IoT, two-factor authentication, and secure messaging. A reference implementation in Python is inc