Elliptic curve in Binary Field implementation For Elliptic curves defined over $GF(2^n)$, by adding any two points P and Q over $GF(2^n)$ we get the third point over $GF(2^n)$.
In Elliptic Curve Digital Signature Algorithm (ECDSA) https://en.wikipedia.org/wiki/Elliptic_Curve_Digital_Signature_Algorithm
, there is a usage of prime numbers, particularly for the calculation of multiplicative inverse. It works fine for the Weierstrass form of Elliptic curve over $GF(P)$.
Now, I want to implement ECDSA using a binary form of Elliptic curve (like Hessian curve), but every time I am doing it, it is giving the wrong answer. My question is, is it not possible to use any curve over $GF(2^n)$ for an implementation like this?
Yes it can. The only variation from the wikipedia article is in step 5 where it states to calculate $r\equiv x_1\pmod{n}$. This does not make sense when $x_1$ isbn element of a binary field. Instead binary field elements are converted to integers by a standards prescribed process (see ANSI X9.62-1984 section 4)