Stochastic Verification Architectures: ZK-FRS Protocols with Polynomial Blinding, Worst-Case Cryptographic Bounds, and Complete Resolution of the MCA Decoding Limit

This paper presents a formal soundness and privacy analysis for polynomial In-teractive Oracle Proofs (IOPs) utilizing Folding Reed-Solomon (FRS) schemes augmentedwith zero-knowledge polynomial blinding. We combine an explicit worst-case cryptographicreduction with the multivariate interpolation paradigm of Guruswami and Rudra (2008) toestablish protocol stability in high-error regimes. Specifically, we prove that integrating lin-ear polynomial masking for privacy preserves the underlying algebraic structure required tobound candidate list sizes in the Mutual Correlated Agreement (MCA) region where the er-ror radius lies strictly between one minus the square root of the code rate and one minusthe code rate. By modeling the verifier’s challenge as a formal variable within a trivariateideal and proving generic non-degeneracy via Jacobian determinant bounds over restrictedevaluation surfaces, we demonstrate that list growth remains strictly bounded by an asymp-totic order proportional to the inverse capacity gap raised to the power of one less than thefolding parameter, preventing superpolynomial explosion without sacrificing zero-knowledgeguarantees. Furthermore, we derive a combined soundness metric incorporating both foldingand query bounds to enforce concrete one-hundred-and-twenty-eight-bit security levels underadversarial error distributions.