An Extended Quadratic Frobenius Primality Test with Average and Worst Case Error Estimates
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چکیده
منابع مشابه
An Extended Quadratic Frobenius Primality Test with Average Case Error Estimates
We present an Extended Quadratic Frobenius Primality Test (EQFT), which is related to the Miller-Rabin test and the Quadratic Frobenius test (QFT) by Grantham. EQFT is well-suited for generating large, random prime numbers since on a random input number, it takes time about equivalent to 2 Miller-Rabin tests, but has much smaller error probability. EQFT extends QFT by verifying additional algeb...
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The publication of the quadratic Frobenius primality test [6] has stimulated a lot of research, see e.g. [4, 10, 11]. In this test as well as in the Miller-Rabin test [13], a composite number may be declared as probably prime. Repeating several tests decreases that error probability. While most of the above research papers focus on minimising the error probability as a function of the number of...
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Consider a procedure that chooses fe-bit odd numbers independently and from the uniform distribution, subjects each number to t independent iterations of the strong probable prime test (Miller-Rabin test) with randomly chosen bases, and outputs the first number found that passes all t tests. Let pfc , denote the probability that this procedure returns a composite number. We obtain numerical upp...
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Definition: CCρ(f) ≥ s if s-sized circuits can compute f with probability at most ρ for a random input. That is, for every circuit family {Cn} with |Cn| ≤ s(n), Prx←R{0,1}n [Cn(x) = f(x)] < ρ. If CC1−1/(100n)(f) ≥ s we say that f is “mildly hard on the average” for s-sized circuits (every circuit will fail on a 1/(100n) fraction of the inputs) and if CC1(f) ≥ s we say that f is “worst-case hard...
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ژورنال
عنوان ژورنال: BRICS Report Series
سال: 2003
ISSN: 1601-5355,0909-0878
DOI: 10.7146/brics.v10i9.21780