30 research outputs found
Accelerating BGV Bootstrapping for Large Using Null Polynomials Over
No full textThe BGV scheme is one of the most popular FHE schemes for computing homomorphic integer arithmetic. The bootstrapping technique of BGV is necessary to evaluate arbitrarily deep circuits homomorphically. However, the BGV bootstrapping performs poorly for large plaintext prime due to its digit removal procedure exhibiting a computational complexity of at least . In this paper, we propose optimizations for the digit removal procedure with large by leveraging the properties of null polynomials over the ring . Specifically, we demonstrate that it is possible to construct low-degree null polynomials based on two observations of the input to the digit removal procedure: 1) the support size of the input can be upper-bounded by ; 2) the size of the lower digits to be removed can be upper-bounded by . Here can be controlled within a narrow interval in our parameter selection, making the degree of these null polynomials much smaller than for large values of . These low-degree null polynomials can significantly reduce the polynomial degrees during homomorphic digit removal, thereby decreasing both running time and capacity consumption. Theoretically, our optimizations reduce the computational cost of extracting a single digit from (by Chen and Han) or (by Geelen et al.) to for some . We implement and benchmark our method on HElib with and . With our optimized digit removal, we achieve a bootstrapping throughput times that in HElib, with the speedup increasing with the value of . For , we accelerate the digit removal step by 80 times and reduce the bootstrapping time from more than 12 hours to less than 14 minutes
Searching for the parallel growth of cities
No full textThree urban growth theories predict parallel growth of cities. The endogenous growth theory predicts deterministic parallel growth; the random growth theory implies that city growth follows Gibrat’s law with a steady-state distribution; and the hybrid growth theory suggests the co-movement of random city growth. This paper uses the Chinese city size data from 1984-2006 and time series econometric techniques to test for parallel growth. The results from various types of stationarity tests on pooled heterogeneous cities show that city growth is random. However, once growth trend and structural change are taken into account, certain groups of cities with common group characteristics, such as similar natural resource endowment or policy regime, grow parallel.Urban growth; Parallel growth; Zipf’s law; Unit root; Structural change
Notice of Retraction: Optimization research on spiral case reinforcement based on the computer simulation
No full textTorque ripple reduction of brushless DC motor based on optimal control with adaptive compensation
No full textAnalysis of a free boundary problem for tumor growth with Gibbs-Thomson relation and time delays
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Research on disassembly sequence of products based on connected element hierarchy network graph
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