I am doing my academic project on ELLIPTIC CURVE CRYPTOGRAPHY for image encryption over prime field F(p) and Binary field GF(2^m), I am doing my project by own in my college. I am implementing my intended project using MATLAB. Now i am struck at some point in project. Hence i need your help. Problems what i am facing are listed below.Please, help me by solving my problems.

1. Problem in choosing / generating base points/generator points in both [F(p) and GF(2^m)] fields.

2. Problem in generating all possible points over GF(2^m).

I am coding in MATLAB.If i get solutions to above my problems, i am greatly thank full to you. Please help me, i searched solutions for above mentioned problems, but i filed. I hope you understand my problem and kindly help me soon.

Thank you