is there the way how to generate new Koblitz curves (over F2n and Fp as well)? I found that "The recommended parameters associated with a Koblitz curve were chosen by repeatedly selecting parameters admitting an efficiently computable endomorphism until a prime order curve was found." here. What means "efficiently computable endomorphism"? Maybe it means that trace of the Frobenius map should be equal 1? I am confused about all the Frobenius maps, endomorphisms, traces etc.

So, is there the way to generate Koblitz curves (or compute efficient endomorphism)?

Thanks a lot for every advice.

Is there the way to generate new Koblitz curves, over $\mathbb F_{2^n}$ and $\mathbb F_p$?

The Certicom SEC 2 standard says:

The recommended parameters associated with a Koblitz curve were chosen by repeatedly selecting parameters admitting an efficiently computable endomorphism until a prime order curve was found.

What does "efficiently computable endomorphism" mean? Maybe it means that trace of the Frobenius map should be equal 1? I am confused about all the Frobenius maps, endomorphisms, traces, etc.

So, is there the way to generate Koblitz curves, or find efficiently computable endomorphisms?