In constructing pairingfriendly ellitpic curves

the curve parameters are often represented by polynomials with rational coefficients. For efficiently generating the curves parameters

the degree of the complex multipliction polynomial must be less than 3. A method is proposed to constructed suitable polynomials which will make the degree of the complex multipliction polynomial less than 3. Some examples are given

especially when embedding degree is 8. It is generally believed that when embedding degree is 8 the complex multipliction polynomial whose degree is less than 3 does not exist.