  A low storage algorithm for constructing isogenies between ordinary elliptic
curves was proposed by Galbraith, Hess and Smart (GHS). We give an improvement
of this algorithm by modifying the pseudorandom walk so that lower-degree
isogenies are used more frequently. This is motivated by the fact that high
degree isogenies are slower to compute than low degree ones. We analyse the
running time of the parallel collision search algorithm when the partitioning
is uneven. We also give experimental results. We conclude that our algorithm is
around 14 times faster than the GHS algorithm when constructing horizontal
isogenies between random isogenous elliptic curves over a 160-bit prime field.
  The results apply to generic adding walks and the more general group action
inverse problem; a speed-up is obtained whenever the cost of computing edges in
the graph varies significantly.
