1. A method for embedding a digital message into a digital representation of an original digital object having a smoothness utilizing a computer, the method comprising: at the computer, identifying a first portion of the original digital object that can be modified with at least one bit of data while preserving a perceptual quality of the original digital object; generating a representation of the first portion at the computer; losslessly compressing the representation of the first portion at the computer; generating a bit stream comprising the compressed representation of the first portion and a digital message at the computer; generating a modified digital object at the computer by modifying the first portion with the bit stream by permuting at least one subset of values in the first portion to simulate addition of invertible noise, wherein the modified digital object has a smoothness corresponding to a smoothness of the original digital object, and wherein the smoothness of one or more pixel groups of the original digital object is classified, such that perceptual representations of classified pixel groups of the one or more pixel groups have a bias between classifications; and storing the modified digital object using the computer.