Paper 2025/1529

UC-Security of the ZK-NR Protocol under Contextual Entropy Constraints: A Composable Zero-Knowledge Attestation Framework

Abstract

The CRO Trilemma formalizes the inherent incompatibility between confidentiality, reliability, and legal opposability in proof systems. This paper provides the complete Universal Composability (UC) security proof for the ZK-NR protocol, a layered architecture designed to approach this bound. We model each dialectical layer (Iron, Gold, Clay) as an ideal functionality with erasure semantics and prove indistinguishability between real and ideal executions under post-quantum assumptions. The results establish the composable security of ZK-NR and formally achieve a CRO index Γ_CRO < 0.4 + negl(λ) against adaptive contextual adversaries.

Note: This manuscript is the second article in a series of four, delivering the formal security proofs for the ZK-NR protocol. It assumes familiarity with the protocol's design, detailed in Article A.1 (ePrint 2025/1422), which is built upon the Q2CSI framework (ePrint 2025/1380) and the CRO Trilemma formalization (ePrint 2025/1348). The core contribution is a complete UC security analysis under contextual entropy constraints. This includes: The construction of UC simulators for each dialectical layer (Iron, Gold, Clay). Formal proofs of layer-specific properties (temporal integrity, hybrid unforgeability, contextual zero-knowledge). A novel formalization of erasure semantics within the UC model. A formal proof resolving the CRO Trilemma for the ZK-NR instantiation. This submission is entirely theoretical and contains no implementation details or performance metrics, which are reserved for Article A.3. All contributions are original. This manuscript is not under submission or review elsewhere.