The main idea is that computing public keys as fast as possible is even faster if they're not moving around blindly, like what happens in Kangaroo. But no one tried to use this effectively. I think this is because on a CPU there's basically zero performance difference, but on a GPU... the speed rockets (not that it wasn't already freaking fast) because the unknown dynamics disappear. Hence, a speed 3 to 4 times higher.
Very nice! I think the biggest bottleneck in computing public keys or (better said) in adding two public keys, which we usually only need, is the modular multiplicative inverse. If we find some low level optimizations, that can speed up the computation as well very much.
In the addition of two public keys (or two points on an elliptic curve), modular multiplicative inversion is the heaviest step.
By implementing fast inversion algorithms (such as Montgomery), using coordinate systems that eliminate or minimize inversion (such as projective or Jacobian), or employing batch inversion techniques, the computation speed can be dramatically increased.
Another approach is batch inversion: if multiple inversions are required, they can all be obtained with a single division and a few simple multiplications, resulting in a lower overall cost.