Hush Functions Extended to Any Size Input versus Any Size Output
Traditional hush functions map a large number to a small number such that the reverse-hush has infinity of solutions, and nonetheless a collision is hard to come by. This primitive is so abundantly useful that one is tempted to extend it such that any number large or small may be mapped to any number larger, or smaller while maintaining the above conditions. This extension would increase the flexibility of the commodity hush primitive, expand its current applications, and likely suggest new ones. Additional generality may be achieved by allowing the input to determine the computational burden, and involving Turing's Entscheidungs-problem.