Rabin-Miller primality test: composite numbers which pass it
نویسندگان
چکیده
منابع مشابه
Rabin-miller Primality Test: Composite Numbers Which Pass It
The Rabin-Miller primality test is a probabilistic test which can be found in several algebraic computing systems (such as Pari, Maple, ScratchPad) because it is very easy to implement and, with a reasonable amount of computing, indicates whether a number is composite or "probably prime" with a very low probability of error. In this paper, we compute composite numbers which are strong pseudopri...
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Using the HOL theorem prover, we apply our formalization of probability theory to specify and verify the Miller–Rabin probabilistic primality test. The version of the test commonly found in algorithm textbooks implicitly accepts probabilistic termination, but our own verified implementation satisfies the stronger property of guaranteed termination. Completing the proof of correctness requires a...
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The Fermat and Solovay–Strassen tests are each based on translating a congruence modulo prime numbers, either Fermat’s little theorem or Euler’s congruence, over to the setting of composite numbers and hoping to make it fail there. The Miller–Rabin test uses a similar idea, but involves a system of congruences. For an odd integer n > 1, factor out the largest power of 2 from n− 1, say n− 1 = 2e...
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Currently, even the fastest deterministic primality tests run slowly, with the AgrawalKayal-Saxena (AKS) Primality Test runtime Õ(log(n)), and probabilistic primality tests such as the Fermat and Miller-Rabin Primality Tests are still prone to false results. In this paper, we discuss the accuracy of the Miller-Rabin Primality Test and the number of nonwitnesses for a composite odd integer n. We...
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In the light of information security it is highly desirable to avoid a “single point of failure” because this would be an attractive target for attackers. Cryptographic protocols for distributed computations are important techniques in pursuing this goal. An essential module in this context is the secure multiparty multiplication of two polynomially shared values over Zq with a public prime num...
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1995
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1995-1260124-2