Compile-Time Fully Homomorphic Encryption: Eliminating Online Encryption via Algebraic Basis Synthesis

2025-05-19

AI Summary

To address the high online encryption overhead in Fully Homomorphic Encryption (FHE) systems—which critically limits throughput in high-load scenarios such as outsourced databases—this paper proposes a compile-time ciphertext synthesis framework. It shifts ciphertext generation entirely to compilation time via precomputed basis vectors, zero-encryption reuse, and composition of homomorphic addition and scalar multiplication, enabling runtime-zero encryption during data ingestion. We formally define “random-mode homomorphism” for the first time and prove its IND-CPA security via a hybrid game, rigorously characterizing the security boundaries of basis reuse and structured noise injection. The scheme remains compatible with standard FHE APIs while preserving layout semantics for downstream homomorphic operations. Experimental results demonstrate substantial improvements in batch encoding throughput, establishing an efficient, secure, and deployable paradigm for ciphertext injection in high-throughput FHE pipelines.

Technology Category

• Natural Language Processing: Code Generation / Program Synthesis from Natural Language
• Machine Learning: Privacy
• Search and Optimization: Distributed Search

Application Category

• Security and Privacy: Applications of cryptography
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

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 adversarial advantage to the indistinguishability 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.

Problem

• Eliminates online encryption via algebraic basis synthesis
• Decouples ciphertext generation from encryption processes
• Enables efficient batch encoding in FHE systems

Innovation

• Synthesizes ciphertexts from precomputed encrypted basis vectors
• Uses homomorphic additions, scalar multiplications, and randomized zero encryptions
• Formalizes technique as secure randomized module morphism