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• W2556975971 abstract "We present an efficient hardware prime generator that generates a prime p by combining trial division and Fermat test in parallel. Since the execution time of this parallel combination is greatly influenced by the number k of the smallest odd primes used in the trial division, it is important to determine the optimal k to create the fastest parallel combination. We present probabilistic analysis to determine the optimal k and to estimate the expected running time for the parallel combination. Our analysis is conducted in two stages. First, we roughly narrow the range of optimal k by using the expected values for the random variables used in the analysis. Second, we precisely determine the optimal k by using the exact probability distribution of the random variables. Our experiments show that the optimal k and the expected running time determined by our analysis are precise and accurate. Furthermore, we generalize our analysis and propose a guideline for a designer of a hardware prime generator to determine the optimal k by simply calculating the ratio of M to D, where M and D are the measured running times of a modular multiplication and an integer division, respectively." @default.
• W2556975971 created "2016-11-30" @default.
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• W2556975971 date "2016-10-30" @default.
• W2556975971 modified "2023-09-27" @default.
• W2556975971 title "Design and Analysis of Efficient Parallel Hardware Prime Generators" @default.
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• W2556975971 doi "https://doi.org/10.5573/jsts.2016.16.5.564" @default.
• W2556975971 hasPublicationYear "2016" @default.
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