NDLI: Primality testing using elliptic curves

Content Provider	ACM Digital Library
Author	Goldwasser, Shafi Kilian, Joe
Copyright Year	1999
Abstract	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.
Starting Page	450
Ending Page	472
Page Count	23
File Format	PDF
ISSN	00045411
e-ISSN	1557735X
DOI	10.1145/320211.320213
Journal	Journal of the ACM (JACM)
Volume Number	46
Issue Number	4
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1999-07-01
Publisher Place	New York
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Las Vegas algorithms Distribution of primes Elliptic curves Group theory Prime certification Prime generation Primes
Content Type	Text
Resource Type	Article
Subject	Hardware and Architecture Information Systems Control and Systems Engineering Artificial Intelligence Software

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