How is the elliptic curve chosen?
First of all, a finite field is chosen, see (9) If the field is GF(p) where p is a large prime, the x·y term is omitted, leaving us with y^2 = x^3 + a·x^2 + b There is a requirement that 4·a^3 + 27·b^2 is non-zero. If the field is GF(2^m) then we include the x·y term to get y^2 + x·y = x^3 + a·x^2 + b There is a requirement that b is non-zero. Fields GF(p^m) with both p>2 and m>1 are not considered here.
