Constructing Supersingular Elliptic Curves Depending on the Coefficients of Weierstrass Equation (Journal of the College of Basic Education, 2022)
In the use of elliptic curves in its applications (especially in cryptography), one often needs to construct elliptic curves with a known type (number of points) over a given finite field Fp, where some types are more secure than others. So we introduce a simple way to construct a supersingular elliptic curve by computing the coefficient of xp-1 in f(x)(p-1)/2 wheref(x)= x3+ax+b. And we give an algorithm that compute that coefficient and construct the required curve.