The A-Scheme for Information-Theoretic Covert Transport

This paper introduces the A-scheme—a scalable additively homomorphic encryption framework for attribute-driven access control in distributed environments. At its core is a knapsack-inspired Base-3 packing technique, providing a mathematically optimal method for emulating bitwise XOR operations within additively homomorphic scalar rings. We prove that a ternary radix ($b=3$) is the unique integer optimum for carry-free homomorphic containers, yielding a $1.58\times$ improvement in information density over binary encodings. Practical scalability is achieved by adapting the Gaudry–Schost algorithm with equivalence class optimizations for the short-interval Elliptic Curve Discrete Logarithm Problem (ECDLP).

To ensure security, we provide a formal reliance on the Decisional Diffie–Hellman (DDH) assumption and integrate steganographic uniform string mappings to eliminate algebraic invariants.

Finally, our framework introduces ``homomorphic blind decoding,'' grounded in the Information-theoretic underdetermination and fortified against MDS puncturing to ensure robust security against advanced algebraic cryptanalysis. The operational integrity and architectural viability of all core A-scheme elements are empirically validated through comprehensive Magma prototyping.