Paper 2025/1594

Practical Dense-Key Bootstrapping with Subring Secret Encapsulation

Abstract

Bootstrapping remains the primary bottleneck in most FHE schemes, significantly impacting their efficiency. To enhance both the speed and precision of bootstrapping, sparse secrets have been widely adopted, particularly in SIMD-style FHE schemes such as BGV, BFV, and CKKS. However, the security of sparse LWE secrets is not well understood, leading to their exclusion from standardization efforts. To address this gap between the potential security risks of sparse secrets and the inefficiency of dense-secret bootstrapping, we introduce the subring secret encapsulation method. This approach involves switching to a dense secret in a subring before bootstrapping, thereby improving bootstrapping performance while still basing security on dense secret LWE. The EvalMod and digit removal steps are accelerated due to the smaller Hamming weight of the subring secret. Furthermore, the algebraic structure of the subring secret enables faster CoeffsToSlots and SlotsToCoeffs operations through hoisted key switchings. When applied to the CKKS scheme, our method achieves a bootstrapping throughput increase of 46%–51% compared to state-of-the-art dense secret bootstrapping techniques. For BGV/BFV schemes, our approach demonstrates a 2.48x improvement in throughput when bootstrapping $2^{15}$ slots modulo $65537$.