Although the computation for scalar multiplications for Koblitz curve can be efficiently executed by TNAF method, but it still need to compute the multiplicative inverse for each point addition.


Koblitz curves are still (convertible to) elliptic curves with a short Weierstrass equation.

Therefore you can use the standard projective / Jacobian coordinate systems as you'd use for more generic curves, though I think (variants of) Jacobian coordinates tend to perform best. All of these coordinate systems only require a single modular inversion at the end of the scalar multiplication, in an operation often called "rescaling".

If your curve is additionally of the form $y^2=x^3+b$ further optimizations seem to be possible using a special case of Jacobian coordinates.

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