The Mazari Bidirectional Architecture: Mathematical Foundations of Secure Ordering in Privacy-Preserving Computation

Abstract

We present the Mazari Bidirectional Architecture, a cryptographic framework providing end-to-end privacy guarantees for computation systems employing homomorphic encryption (HE), differential privacy (DP), and zero-knowledge proofs (ZK). The architecture comprises two complementary orderings: Y.I.N. Mazari Ordering (DP→ZK→HE) for secure data submission and Y.A.N.G. Mazari Ordering (VERIFY→DISAGGREGATE→DECRYPT→DENOISE) for secure result retrieval. Through exhaustive permutation analysis, we prove that among all possible orderings for each direction, exactly one ordering in each direction is secure—and these orderings are mathematical duals. The Y.I.N. ordering prevents information leakage during data submission, while the Y.A.N.G. ordering prevents timing side-channel attacks during result retrieval. This paper provides comprehensive coverage of all implementation variations, security proofs, and robustness analysis to establish technical foundations for privacy-preserving computation research.