RNS Base Conversion Using Optimized Multiword Multipliers for Approximate Modulus Switching

초록

Modulus switching is a critical step in approximate homomorphic encryption schemes such as Residue Number System (RNS)-CKKS. At its heart lies RNS base conversion (BConv), which involves repeated large-integer modular multiplications and additions across multiple moduli. This paper proposes a base conversion core for approximate modulus switching using an optimized multiword multiplication strategy mapped to DSP blocks, coupled with Barrett reduction for efficient modular arithmetic. Our architecture includes a memory-buffered datapath coupled with a shift-register-based stream controller that enables efficient partial result reuse and deeply pipelined execution. We compare full-parallel (FP) and datapath-serialized (DS) implementations, leveraging our optimized modular multiplier to achieve 50 % lower latency compared to the baseline. Our proposed DS design, utilizing the Residue Digit Computation Unit (RDCU), provides improved throughput as the polynomial degree increases, making it particularly suitable for low-latency key-switching in RNS-CKKS accelerators. © 2025 IEEE.

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