Compile-Time Fully Homomorphic Encryption: Eliminating Online Encryption via Algebraic Basis Synthesis - Dongfang Zhao (Cryptography)
We propose a new framework for compile-time ciphertext synthesis in fully homomorphic encryption (FHE) systems. Instead of invoking encryption algorithms at runtime, our method synthesizes ciphertexts from precomputed encrypted basis vectors using only homomorphic additions, scalar multiplications, and randomized encryptions of zero. This decouples ciphertext generation from encryption and enables efficient batch encoding through algebraic reuse. We formalize this technique as a randomized module morphism and prove that it satisfies IND-CPA security. Our proof uses a hybrid game framework that interpolates between encrypted vector instances and reduces the adversarial advantage to the indistinguishability advantage of the underlying FHE scheme. This reduction structure captures the security implications of ciphertext basis reuse and structured noise injection. The proposed synthesis primitive supports fast, encryption-free ingestion in outsourced database systems and other high-throughput FHE pipelines. It is compatible with standard FHE APIs and preserves layout semantics for downstream homomorphic operations.