The Probability that the Number of Points on an Elliptic Curve over a Finite Field is Prime | Zendy

Galbraith Steven D. | Zendy; McKee James | Zendy

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The Probability that the Number of Points on an Elliptic Curve over a Finite Field is Prime

Author(s) -

Galbraith Steven D.,

McKee James

Publication year - 2000

Publication title -

journal of the london mathematical society

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 1.441

H-Index - 62

eISSN - 1469-7750

pISSN - 0024-6107

DOI - 10.1112/s0024610700001502

Subject(s) - schoof's algorithm , mathematics , finite field , elliptic curve , prime (order theory) , supersingular elliptic curve , field (mathematics) , modular elliptic curve , counting points on elliptic curves , finite set , hessian form of an elliptic curve , division polynomials , discrete mathematics , pure mathematics , combinatorics , mathematical analysis , quarter period

The paper gives a formula for the probability that a randomly chosen elliptic curve over a finite field has a prime number of points. Two heuristic arguments in support of the formula are given as well as experimental evidence. The paper also gives a formula for the probability that a randomly chosen elliptic curve over a finite field has kq points where k is a small number and q is a prime.

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