METHOD FOR THE CONSTRUCTION OF ELLIPTIC CURVES OVER FINITE FIELDS

摘要

The invention relates to a method for constructing elliptic curves E over finite fields based on the equation M = P + 1 + x (where ||x|| <= 2√P; P represents a prime power while E represents an elliptic curve over the field Fp comprising P elements), accordingly 4P = x<2> + y<2>||D|| (where y ϵ N and the discriminant D = f<2>D0 of the order of conductor f in the imaginary quadratic number field K of discriminant D0), by using module functions g so as to have access to large discriminant values ||D||. According to the invention, the module functions g are characterized in that the degree of g(alpha) is a real divisor of h (h being the ideal class number of the order of K to the discriminant D) while the coefficients of the associated minimal polynomials are small.