Ciphertext- and Polynomial-Level Optimization for Fully Homomorphic Encryption

2026-07-17

AI Summary

Existing fully homomorphic encryption (FHE) compilers perform optimizations only at the ciphertext level, which is insufficient to eliminate polynomial-level redundant computations across ciphertexts, thereby limiting performance gains. This work proposes Recifhe, a multi-level FHE compiler that introduces, for the first time, polynomial-level optimization. Recifhe transforms conventional programs into FHE-compatible ones while integrating the RNS-CKKS scheme, achieving finer-grained computation reduction through ciphertext management, global program transformation, and cross-ciphertext polynomial redundancy elimination. Compared to approaches restricted to ciphertext-level optimization, Recifhe delivers an average speedup of 1.25×.

Abstract

Fully homomorphic encryption (FHE) schemes such as RNS-CKKS enable privacy-preserving services by allowing direct computation on encrypted data. While recent FHE compilers optimize FHE programs, they operate at the coarse-grained ciphertext level, where each ciphertext operation comprises a sequence of polynomial operations. At this granularity, the compilers miss optimization opportunities across ciphertext operations. This work presents Recifhe, a new multi-level compiler that supports not only ciphertext-level but also polynomial-level optimization. At the ciphertext level, Recifhe transforms a non-FHE input program into an FHE program by inserting ciphertext management operations and applies global optimizations. At the polynomial level, Recifhe eliminates redundant polynomial computations across ciphertext operations. Recifhe achieves a 1.25x speedup over ciphertext-level-only optimization.

Problem

• Fully Homomorphic Encryption
• Compiler Optimization
• Ciphertext-Level Optimization
• Polynomial-Level Optimization
• RNS-CKKS

Innovation

• fully homomorphic encryption
• multi-level compiler
• polynomial-level optimization
• ciphertext optimization
• RNS-CKKS