THE PROBABILITY THAT THE NUMBER OF POINTS ON AN ELLIPTIC CURVE OVER A FINITE FIELD IS PRIME

STEVEN D. GALBRAITH; JAMES McKEE

doi:10.1112/S0024610700001502

Abstract

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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THE PROBABILITY THAT THE NUMBER OF POINTS ON AN ELLIPTIC CURVE OVER A FINITE FIELD IS PRIME

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THE PROBABILITY THAT THE NUMBER OF POINTS ON AN ELLIPTIC CURVE OVER A FINITE FIELD IS PRIME

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