Testing set proportionality and the Ádám isomorphism of circulant graphs

Given two k   element subsets S,T⊆ZnS,T⊆Zn, we give a quasi-linear algorithm to either find λ∈Zn∗ such that S=λTS=λT or prove that no such λ exists.This question is closely related to isomorphism testing of circulant graphs and has recently been studied in the literature.