Elliptic Curves and Primality Proving
نویسندگان
چکیده
منابع مشابه
Elliptic Curves and Primality Proving
The aim of this paper is to describe the theory and implementation of the Elliptic Curve Primality Proving algorithm. Problema, números primos a compositis dignoscendi, hosque in factores suos primos resolvendi, ad gravissima ac utilissima totius arithmeticae pertinere, et geometrarum turn veterum turn recentiorum industriam ac sagacitatem occupavisse, tarn notum est, ut de hac re copióse loqui...
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Elliptic curves are fascinating mathematical objects. In this paper, we present the way they have been represented inside the COQ system, and how we have proved that the classical composition law on the points is internal and gives them a group structure. We then describe how having elliptic curves inside a prover makes it possible to derive a checker for proving the primality of natural number...
متن کاملPrimality Proving Using Elliptic Curves: An Update
In 1986, following the work of Schoof on counting points on elliptic curves over finite fields, new algorithms for primality proving emerged, due to Goldwasser and Kilian on the one hand, and Atkin on the other. The latter algorithm uses the theory of complex multiplication. The algorithm, now called ECPP, has been used for nearly ten years. The purpose of this paper is to give an account of th...
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We give an overview of a method for using elliptic curves with complex multiplication to give efficient deterministic polynomial time primality tests for the integers in sequences of a special form. This technique has been used to find the largest proven primes N for which there was no known significant partial factorization of N − 1 or N + 1.
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We describe how to generate large primes using the primality proving algorithm of Atkin. Figure 1: The Titanic .
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ژورنال
عنوان ژورنال: Mathematics of Computation
سال: 1993
ISSN: 0025-5718
DOI: 10.2307/2152935