Ciphertext- and Polynomial-Level Optimization for Fully Homomorphic Encryption

2026-07-20 · Source: cs.SE updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Software Development & Engineering, Cybersecurity & Data Privacy · Depth: Expert, long

Summary

Recifhe is a new multi-level compiler designed to optimize Fully Homomorphic Encryption (FHE) programs, specifically RNS-CKKS schemes, by operating at both ciphertext and polynomial levels. Unlike existing FHE compilers that primarily optimize at the coarse-grained ciphertext level, Recifhe introduces fine-grained polynomial-level optimizations to eliminate redundant computations across ciphertext operations. At the ciphertext level, Recifhe transforms non-FHE input programs and applies global optimizations like Rescale hoisting. At the polynomial level, it employs common subexpression elimination, performance-aware ModDown hoisting, and operation fusion. Recifhe also incorporates liveness-driven operation scheduling to mitigate memory growth. This approach achieves a 1.25x speedup over ciphertext-level-only optimization and a 1.36x speedup with a 0.93x smaller memory footprint compared to manually optimized polynomial sequences in existing FHE libraries. It uses a polynomial modulus degree N=2^16 and L=27 with 32-bit moduli.

Key takeaway

For AI Architects designing privacy-preserving machine learning systems with FHE, Recifhe demonstrates that fine-grained, multi-level compilation is crucial. You should consider compilers that integrate polynomial-level optimizations, like performance-aware ModDown hoisting and liveness-driven scheduling, to achieve significant speedups and reduce memory footprint. This approach can yield a 1.25x speedup and 0.93x memory usage compared to current methods, making FHE more practical for complex applications.

Key insights

Multi-level FHE compilation, optimizing at both ciphertext and polynomial granularities, significantly boosts performance and reduces memory.

Principles

• Optimize at appropriate granularity levels.
• Profile operations to guide performance-aware decisions.
• Liveness-driven scheduling reduces memory overhead.

Method

Recifhe transforms non-FHE programs, applies global ciphertext-level optimizations, then decomposes operations for polynomial-level common subexpression elimination, performance-aware ModDown hoisting, and operation fusion, followed by liveness-driven scheduling.

In practice

• Implement multi-level FHE compilers for RNS-CKKS.
• Use profiling to validate optimization profitability.
• Apply liveness analysis for memory-efficient FHE.

Topics

• Fully Homomorphic Encryption
• FHE Compilers
• RNS-CKKS
• Polynomial Optimization
• Ciphertext Optimization
• Privacy-Preserving AI

Best for: Research Scientist, AI Scientist, AI Architect

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Editorial summary, takeaway, and curation by AIssential. Original article published by cs.SE updates on arXiv.org.