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Fully homomorphic encryption (FHE) is a novel encryption method that can perform operations on encrypted data. The performance of applications based on FHE is still low due to the high computational complexity of operations on the ciphertext. In this paper, we proposed an efficient FHE radix-2 addition algorithm in BGV scheme, called Optimized Cheon’s SIMD Adder. It is an optimization of Cheon’s SIMD Adder. The proposed adder uses the previously calculated results as much as possible to calculate the new result, so that it can keep the circuit depth as  0(log(μ))  and reduce the number of homomorphic multiplications. We also compared the weighted computational complexity (WCC) between this work and Cheon’s. The WCC of this work is only  O (μ) , while Cheon’s is 0( μ· log (μ )). At the end of the paper, we implemented the proposed addition, which improves the calculation speedup by 1.3 ~ 1.4 times for 8 ~ 512- bit adders compared with Cheon’s SIMD Adder.

An Efficient FHE Radix-2 Addition Algorithm in BGV Scheme