MRS‑AUTH — Multi‑Representation System for Authentication

MRS-AUTH — Multi-Representation System for Authentication MRS-AUTH is a proposed cryptographic authentication primitive based on a multi-representation system arising from linear Diophantine equations. The construction uses the equation [ aA+bB=N ] with the concrete parameter pair (a,b)=(19,9), to generate multiple valid representations of a public parameter. These representations are recursively nested into layered credential chains, forming a structured forest of alternative witnesses. The central objective is to investigate whether this multi-representation structure can provide authentication with index anonymity and deniability properties. Rather than relying on a single distinguished witness, MRS-AUTH constructs a committed set containing an authentic chain and structurally valid aliases. An active-verifier game is used to model an adversary with adaptive verification access and to formalize the indistinguishability of the authentic index. The core construction and its principal security arguments are formalized in EasyCrypt. The formal development includes the Diophantine kernel, Forest Symmetry property, Merkle commitment model, Active-Verifier Game, and an index-anonymity reduction based on the binding properties of the underlying hash construction. The paper also investigates efficient sampling of the recursively generated forest. An exact weighted sampler provides uniform sampling over the defined chain space for the formal model. For larger parameter sizes, a continuum-volume approximation is studied using Ehrhart-theoretic analysis. This approximation is supported by mathematical derivation and numerical validation; its complete formalization and the determination of the associated bounding constant remain open tasks. The work therefore distinguishes between properties established in the formal model and properties that remain subjects for further analysis. In particular, the Diophantine layer is presented as post-quantum-oriented rather than proven post-quantum secure. A dedicated quantum analysis of the structured search space remains future work. A constant-time Rust implementation is also described, including branch-free operations, rejection sampling, memory zeroization, and timing barriers. These implementation properties are considered within an abstract execution model and should not be interpreted as a complete physical side-channel security evaluation. MRS-AUTH is presented as a research-stage, mechanically oriented cryptographic primitive, rather than a ready-to-deploy authentication protocol. The work focuses on the interaction between Diophantine multi-representation structures, recursive witness spaces, formal verification, and cryptographic index anonymity. Research status: Research phase. Cryptographic status: Proposed primitive; not standardized or certified by NIST, IETF, or another standards body.