The author incorrectly calling them "elliptical curves" is like nails on a chalkboard. An "elliptical" is an exercise machine or an adjective used to describe something shaped like an ellipse. The set of points in a field satisfying an equation of the form y^2 = x^3 + ax + b (which set, when enlarged to include the point at infinity and associated with the point addition group law, forms an abelian group) is an "elliptic curve".