Cryptanalysis of correlation based watermark using single copy

In invisible digital watermarking, given an image I, a signal s_i is added, which produces a watermarked copy I⁽ⁱ⁾ = I + s⁽ⁱ⁾, such that I, I⁽ⁱ⁾ are visually indistinguishable. The addition means the element wise addition in the image matrix. This image I⁽ⁱ⁾ is given to the i-th buyer. In the detection stage, the available image (may be attacked using image processing. or cryptanalytic techniques) I^(#) is compared to the original image I and a signal s^(#) = I^(#) - I is recovered. The buyer i is suspected if s⁽ⁱ⁾ possesses significant correlation with s^(#). For successful cryptanalysis, one has to mount an attack to construct I^(#) from I⁽ⁱ⁾ (both visually indistinguishable) such that there is no significant correlation between s^(#) = I^(#) - I and s⁽ⁱ⁾. Thus, the buyer i will not be identified. To the attacker, only I⁽ⁱ⁾ is available, but I, s⁽ⁱ⁾ are not known. Thus there is no facility for the attacker to test the correlation between s⁽ⁱ⁾ and s^(#). However, the attacker needs to be convinced indirectly that the correlation between s⁽ⁱ⁾ and s^(#) has been removed. We use the CKLS scheme to demonstrate the success of the attack. The paradigm of attack needs only a single copy in contrast to the collusion attack, which needs more than one copy.