a method of embedding auxiliary information into the digital representation of host data containing noise in the low - order bits . the method applies to digital data representing analog signals , for example digital images . the method reduces the error introduced by other methods that replace the low - order bits with auxiliary information . by a substantially reverse process , the embedded auxiliary data can be retrieved easily by an authorized user through use of a digital key . the modular error embedding method includes a process to permute the order in which the host data values are processed . the method doubles the amount of auxiliary information that can be added to host data values , in comparison with bit - replacement methods for high bit - rate coding . the invention preserves human perception of the meaning and content of the host data , permitting the addition of auxiliary data in the amount of 50 % or greater of the original host data .