Digital Watermarking under a Filtering and Additive Noise Attack Condition - Computer Network Security - page 371

Digital Watermarking under a Filtering
and Additive Noise Attack Condition

Valery Korzhik 1 , Guillermo Morales-Luna 2 ,
Irina Marakova 3 , and Carlos Patino-Ruvalcaba 4

1 Specialized Center of Program System “SPECTR”
Kantemirovskaya str. 10, St. Petersburg 197342, Russia
[e-mail]
2 Computer Science, CINVESTAV-IPN, Av. IPN 2508, Mexico City, Mexico
[e-mail]
3 Institute of Radio Electronics and Telecommunication Systems
Odessa National Polytechnic University, Ukraine
[e-mail]
4 Computer Science, CINVESTAV-IPN, Guadalajara, Mexico
[e-mail]

Abstract. We consider a private zero-bit watermark (WM) system in
which an unauthorized removal of the WM is restricted by a linear filter-
ing of the watermarked message combined with additive noise attack. It
is assumed that a WM detector knows both the original cover message
(CM) and the pulse (or frequency) response of the attack filter. The for-
mulas to calculate the WM- missing and WM- false alarm probabilities are
developed and proved. We conclude that whenever some filtering of the
watermarked message is yet acceptable with respect to CM quality then
there results in a degradation of the WM system even if the designer of
the WM uses an optimal signal. This fact is different than most that can
be found at current WM literature. The main properties of a WM sys-
tem under a filtering and additive noise attack condition are confirmed
by simulations of the watermarked images.
Keywords. Watermark, Linear Filtering, Correlation Detector, Error
Probability, White and Colored Additive Noise.

1 Introduction

It is rather well known that any WM system is the practice of imperceptible
modification of the given CM to embed an additional message. WM can be used
in a wide variety of applications [1] but in the current paper we will keep in mind
predominantly the copyright ownership , where WM should be protected against
unauthorized removal only. In other words: no unauthorized user is able to re-
move the WM message without noticeable distortions of the CM. The quality of
CM refers to the perceptual similarity between the original and the watermarked
versions of the CM. A great problem is posed on the selection of a WM quality
criterion that can predict the test results with human observers or listeners. As
it is well known, Watson's DCT-based visual model [1] can be applied to a vi-
sual CM, but it is indeed quite complex to be used in theoretical investigations.