We have researched on the systematic generation of irreducible cubic polynomials for use in elliptic curve cryptosystem. But we couldn't make it clear that the number of irreducible cubic polynomials whose coefficient of degree 1 is a quadratic ersidue. In this paper, we show that this number is given with the number of quadratic residues in the set {X^2+3|X⋴F_p}, then we give the number of quadratic residues in the set.