Comparison of Barrett Modular Reduction with Various Multipliers in the Context of BFV/BGV Homomorphic Encryption

초록

Homomorphic Encryption (HE) enables data to be processed while still encrypted, which is crucial for protecting privacy in cloud computing and sensitive fields such as healthcare and finance. However, HE is still slow and uses a significant amount of memory, especially due to complex operations such as multiplying encrypted data. These operations rely on polynomial arithmetic, which involves modular arithmetic operations, including additions, subtractions, and multiplications. Among these, integer modular multiplication is the most challenging to implement. In this work, we focus on improving the whole process of Barrett Modular Multiplication (BMM), which includes multiplying two numbers and reducing the result. We examine various methods to enhance the key steps of BMM: multiplication, estimating the quotient, reducing the result, and handling overflows. We test these methods in hardware and compare them based on their speed and efficiency, using area-time-performance (ATP) and throughput-per-second (TPS) metrics. © 2025 IEEE.

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