The Hydra-FHE Architecture: Accelerating Homomorphic Large-Integer Arithmetic via Determinant-Locked Shift Operations

Fully Homomorphic Encryption (FHE) schemes, such as BGV and CKKS, are currently bottlenecked by the computational cost of modular multiplication over large cyclotomic rings. This technical report introduces "Hydra-FHE," a specialized arith- metic core designed to bypass generic multipliers by exploiting the structural rigidity of Fermat-based moduli (Fn = 22n + 1). By replacing expensive O(N log N ) multiplication circuits with determinant-locked, zero-cost bit-shift operations, we demonstrate a determin- istic reduction in latency and power consumption. Software benchmarks on 8192-bit integers confirm a 20.5x speedup compared to standard arithmetic libraries. This architecture is proposed as a highly efficient IP core for next-generation FPGA and ASIC-based FHE accelerators