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Proving primality in essentially quartic random time
 Math. Comp
, 2003
"... Abstract. This paper presents an algorithm that, given a prime n, finds and verifies a proof of the primality of n in random time (lg n) 4+o(1). Several practical speedups are incorporated into the algorithm and discussed in detail. 1. ..."
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Abstract. This paper presents an algorithm that, given a prime n, finds and verifies a proof of the primality of n in random time (lg n) 4+o(1). Several practical speedups are incorporated into the algorithm and discussed in detail. 1.
Abstract Uncertainty can be Better than Certainty: Some Algorithms for Primality Testing ∗
"... For many years mathematicians and computer scientists have searched for a fast and reliable primality test. This is especially relevant nowadays, because the popular RSA publickey cryptosystem requires very large primes in order to generate secure keys. I will describe some efficient randomised alg ..."
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For many years mathematicians and computer scientists have searched for a fast and reliable primality test. This is especially relevant nowadays, because the popular RSA publickey cryptosystem requires very large primes in order to generate secure keys. I will describe some efficient randomised algorithms that are useful, but have the defect of occasionally giving the wrong answer, or taking a very long time to give an answer. In 2002, Agrawal, Kayal and Saxena (AKS) found a deterministic polynomialtime algorithm for primality testing. I will describe the original AKS algorithm and some improvements by Bernstein and Lenstra. As far as theory is concerned, we now know that “PRIMES is in P”, and this appears to be the end of the story. However, I will explain why it is preferable to use randomised algorithms in practice.