Elliptic curves and primality proving

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Abstract

The aim of this paper is to describe the theory and implementation of the Elliptic Curve Primality Proving algorithm. Problema, numeros primos a compositis dignoscendi, hosque in factores suos primos resolvendi, ad gravissima ac utilissima totius arithmeticae pertinere, et geometrarum tum veterum tum recentiorum industriam ac sagacitatem occupavisse, tam notum est, ut de hac re copiose loqui superfluum foret.

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Authors

A. O. L. Atkin

Pennsylvania State University

François Morain

Université Claude Bernard Lyon 1

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Mathematics of Computation

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Direction Générale de l'Armement

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Atkin et al. (Fri,) studied this question.

synapsesocial.com/papers/6a1e5f9e40bc8a3dd768d055 — DOI: https://doi.org/10.1090/s0025-5718-1993-1199989-x

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Die Klassenkörper der komplexen Multiplikation· 1958 · 50 citations
The Art of Computer Programming, Vol. 2· 1981 · 862 citations
Implementation of the Atkin-Goldwasser-Kilian primality testing algorithm· 1988 · 17 citations
Small Class Numbers and Extreme Values of L-Functions of Quadratic Fields· 1977 · 10 citations
Factorizations of 𝑏ⁿ±1, 𝑏=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers· 1988 · 143 citations

Also consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

Die Klassenkörper der komplexen Multiplikation· 1958 · 50 citations
The Art of Computer Programming, Vol. 2· 1981 · 862 citations
Implementation of the Atkin-Goldwasser-Kilian primality testing algorithm· 1988 · 17 citations
Small Class Numbers and Extreme Values of L-Functions of Quadratic Fields· 1977 · 10 citations
Factorizations of 𝑏ⁿ±1, 𝑏=2, 3, 5, 6, 7, 10, 11, 12 Up to High Powers· 1988 · 143 citations

Elliptic curves and primality proving

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Abstract

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Cite this study

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