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- Elliptic_curve_primality abstract "Elliptic curve primality testing techniques are among the quickest and most widely used methods in primality proving. It is an idea forwarded by Shafi Goldwasser and Joe Kilian in 1986 and turned into an algorithm by A. O. L. Atkin the same year. The algorithm was altered and improved by several collaborators subsequently, and notably by Atkin and François Morain, in 1993. The concept of using elliptic curves in factorization had been developed by H. W. Lenstra in 1985, and the implications for its use in primality testing (and proving) followed quickly.Primality testing is a field that has been around since the time of Fermat, in whose time most algorithms were based on factoring, which become unwieldy with large input; modern algorithms treat the problems of determining whether a number is prime and what its factors are separately. It enjoys a great deal of interest with the advent of modern cryptography. Although many current tests result in a probabilistic output (N is either shown composite, or probably prime, such as with the Baillie–PSW primality test or the Miller–Rabin test), the elliptic curve test proves primality (or compositeness) with a quickly verifiable certificate.Elliptic curve primality proving provides an alternative to (among others) the Pocklington primality test, which can be difficult to implement in practice. Interestingly, the elliptic curve primality tests are based on criteria which is analogous to the Pocklington criterion, on which that test is based, where the groupis replaced by , and E is a properly chosen elliptic curve. We will now state a proposition on which to base our test, which is analogous to the Pocklington criterion, and gives rise to the Goldwasser–Kilian–Atkin form of the elliptic curve primality test.".
- Elliptic_curve_primality wikiPageExternalLink prove4_2.html.
- Elliptic_curve_primality wikiPageExternalLink gmp-ecpp.
- Elliptic_curve_primality wikiPageExternalLink LiDIA.
- Elliptic_curve_primality wikiPageExternalLink S0025-5718-1993-1199989-X.
- Elliptic_curve_primality wikiPageExternalLink index.html.
- Elliptic_curve_primality wikiPageExternalLink ecpp.english.html.
- Elliptic_curve_primality wikiPageID "25904365".
- Elliptic_curve_primality wikiPageRevisionID "600636958".
- Elliptic_curve_primality title "Elliptic Curve Primality Proving".
- Elliptic_curve_primality urlname "EllipticCurvePrimalityProving".
- Elliptic_curve_primality subject Category:Primality_tests.
- Elliptic_curve_primality comment "Elliptic curve primality testing techniques are among the quickest and most widely used methods in primality proving. It is an idea forwarded by Shafi Goldwasser and Joe Kilian in 1986 and turned into an algorithm by A. O. L. Atkin the same year. The algorithm was altered and improved by several collaborators subsequently, and notably by Atkin and François Morain, in 1993. The concept of using elliptic curves in factorization had been developed by H. W.".
- Elliptic_curve_primality label "Elliptic curve primality".
- Elliptic_curve_primality sameAs m.0b74403.
- Elliptic_curve_primality sameAs Q5365795.
- Elliptic_curve_primality sameAs Q5365795.
- Elliptic_curve_primality wasDerivedFrom Elliptic_curve_primality?oldid=600636958.
- Elliptic_curve_primality isPrimaryTopicOf Elliptic_curve_primality.