Galois fields - F2^n

Elliptic curves over F2^n:
characteristic: 2 expansion degree: n
Elements in F2^4
0000, 0001, 0010, 0011, 0100, 0101, 0110, 0111, 1000, 1001, 1010, 1011, 1100, 1101, 1110, 1111
characteristic 2, expansion degree 4
Other fields:
Elements in F3^2
00,01,02,10,11,,12,20,21,22
characteristic 3, expansion degree 2
suitable for cryptography:
y^2 + xy = x^3 + ax^2 + b
b cannot be zero, a may be zero.

Supersingular curve not suitable for cryptography:
y^2 + y = x^3 + ax + b
points (x,y) are variables in F2^n and plus operations is the just XOR of x bits with y bits.

...to be tested!