<scp>ReSBM:</scp> Region-based Scale and Minimal-Level Bootstrapping Management for FHE via Min-Cut

The RNS-CKKS scheme in Fully Homomorphic Encryption (FHE) supports crucial features for privacy-preserving machine learning, such as fixed-point arithmetic and SIMD-style vectorization. Yet, managing the escalation of ciphertext scales from homomorphic multiplications, which risks capacity overflow, along with bootstrapping, presents significant challenges. These complexities are exacerbated by the need to efficiently handle scale and bootstrapping at compile time while ensuring rapid encrypted inference.