Primality testing using elliptic curves

@article{Goldwasser1999PrimalityTU,
  title={Primality testing using elliptic curves},
  author={Shafi Goldwasser and Joe Kilian},
  journal={J. ACM},
  year={1999},
  volume={46},
  pages={450-472}
}
We present a primality proving algorithm—a probablistic primality test that produces short certificates of primality on prime inputs. We prove that the test runs in expected polynomial time for all but a vanishingly small fraction of the primes. As a corollary, we obtain an algorithm for generating large certified primes with distribution statistically close to uniform. Under the conjecture that the gap between consecutive primes is bounded by some polynomial in their size, the test is shown to… 

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