Collision-resistant hash-shuffles on the reals
George Barmpalias, Xiaoyan Zhang
TL;DR
A oneway real function is constructed which is collision-resistant: the probability of effectively producing distinct reals with the same image is zero, and each real has uncountable inverse image.
Abstract
Oneway real functions are effective maps on positive-measure sets of reals that preserve randomness and have no effective probabilistic inversions. We construct a oneway real function which is collision-resistant: the probability of effectively producing distinct reals with the same image is zero, and each real has uncountable inverse image.