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Generalized Strong Pseudoprime Tests and Applications

✍ Scribed by Pedro Berrizbeitia; T.G. Berry

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
270 KB
Volume
30
Category
Article
ISSN
0747-7171

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✦ Synopsis

We describe probabilistic primality tests applicable to integers whose prime factors are all congruent to 1 mod r where r is a positive integer; r = 2 is the Miller-Rabin test. We show that if Ξ½ rounds of our test do not find n = (r + 1) 2 composite, then n is prime with probability of error less than (2r) -Ξ½ . Applications are given, first to provide a probabilistic primality test applicable to all integers, and second, to give a test for values of cyclotomic polynomials.

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