Collision-resistant hash-shuffles on the reals

TL;DR

This paper introduces a new collision-resistant one-way real function that preserves randomness and has uncountably many preimages, advancing the understanding of cryptographic functions on real numbers.

Contribution

It constructs the first known collision-resistant one-way function on the reals with uncountable inverse images, expanding cryptographic theory into continuous domains.

Findings

Constructed a collision-resistant one-way real function

Proved the function preserves randomness and has uncountable preimages

Showed the probability of effective collisions is zero

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.