Efficient $(3,3)$-isogenies on fast Kummer surfaces

We give an alternative derivation of $(N,N)$-isogenies between fast Kummer surfaces which complements existing works based on the theory oftheta functions. We use this framework to produce explicit formulae for the case of $N=3$, and show that the resulting algorithms are more efficient than all prior $(3,3)$-isogeny algorithms.