Cryptographic Legal Opposability (CLO) Framework: Confidentiality-Reliability-Opposability Trade-Offs in Institutional Cryptography

Cryptographic evidence systems exhibit a fundamental tension: increased cryptographic strength often induces institutional opacity. We present the Cryptographic Legal Opposability (CLO) framework, which establishes an information-theoretic foundation for institutional cryptography via rigorous definitions of confidentiality (Conf), reliability (Rel), and opposability (Opp), where Opp is a novel metric capturing the extent to which institutional actors can effectively interpret and operationalize cryptographic proofs. Our main contributions are as follows: (1) a complete mathematical formalization of the framework, including proven bounds on the properties of the measures and on fundamental feasibility constraints; (2) the introduction of the Semantic One-Time Pad construction, which is shown to achieve provably optimal (Conf, Rel, Opp) trade-offs within its class; (3) theoretical insights suggesting inherent limitations on the joint optimization of these three quantities, with context entropyH(C) emerging as a critical bottleneck; and (4) theoretical case studies of deployed systems (Helios voting, zk-SNARKs, and ECDSA) revealing consistent trade-off structures. Our formal analysis indicates that the studied protocols realize substantially different regimes of joint optimization (with Conf · Rel · Opp values ranging from 0.27 to 0.57), providing preliminary evidence for underlying, possibly universal, trade-off phenomena. Overall, the CLO framework shows that institutional cryptography must be designed not only for mathematical security but also for principled interpretability by institutional stakeholders. Establishing rigorous impossibility bounds on achievable trade-offs remains the central open theoretical problem.