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Goldwasser S., Kilian J. — Primality testing using elliptic curves
Goldwasser S., Kilian J. — Primality testing using elliptic curves



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Название: Primality testing using elliptic curves

Авторы: Goldwasser S., Kilian J.

Аннотация:

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 run in expected polynomial time for all primes, yielding a Las Vegas primality test.Our test is based on a new methodology for applying group theory to the problem of prime certification, and the application of this methodology using groups generated by elliptic curves over finite fields.We note that our methodology and methods have been subsequently used and improved upon, most notably in the primality proving algorithm of Adleman and Huang using hyperelliptic curves and in practical primality provers using elliptic curves.


Язык: en

Рубрика: Математика/

Тип: Статья

Статус предметного указателя: Неизвестно

ed2k: ed2k stats

Год издания: 1999

Количество страниц: 23

Добавлена в каталог: 22.09.2009

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