Let E be an elliptic curve defined over the field of rationals Q(sqrt(-d)) having equation y^2 = x^3 + a x + b with a and b integers. Let P be a point on E with integer coordinates and having infinite order in the additive group of rational points of E, and let n be a composite natural number such that (-d/n) = - 1, where (-d/n) is the Jacobi symbol. Then if (n + 1) P congruent 0 (mod n), n is called an elliptic pseudoprime for (E, P).

Atkin-Goldwasser-Kilian-Morain certificate | elliptic curve primality proving | strong elliptic pseudoprime