The generation of suitable EC parameters is the major obstacle in an elliptic curve environment. Advanced mathematics seems to be required in order to obtain curve E and base point G which are not vulnerable to attacks on the discrete logarithm problem.
In IEEE P1363 annex A, one approach is suggested involving mathematical topics such as Class Group calculations, algebra in the finite field Zp[x]/m(x) and evaluations of infinite series.
Please enter the size in bits of the prime modulus (for certain high bit size values, the execution time can take about a minute). Please note, that the parameters generated are for demonstration only.