The Miller–rabin Test
نویسنده
چکیده
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 = 2ek where e ≥ 1 and k is odd. This meaning for e and k will be used throughout. The polynomial xn−1 − 1 = x2ek − 1 can be factored repeatedly as often as we have powers of 2 in the exponent:
منابع مشابه
Improving the Speed and Accuracy of the Miller-Rabin Primality Test
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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