A system for watermarking an image file selects coefficients using a selection procedure that is kept secret, and assigns the selected coefficients to coefficient pairs. The difference between the coefficients of the pairs is biased by a value that varies, preferably in a pseudo-random manner, and the biased differences are used to generate signature bits that characterize the authentic image at different locations. To detect an unauthorized alteration after the image file has been watermarked, coefficient pairs are selected using the same secret procedure that was originally used to generate the signature bits. The difference between the coefficients of the pairs is then biased and checked against the signature bits. Using a varying bias value permits a tolerance band for reducing false alarms to be used without the risk that would otherwise exist that evidence of an attack on the original image might be hidden in the tolerance band.