ROBUSTNESS OF ASYMMETRIC WATERMARKING TECHNIQUE Teddy FURON THOMSON multimedia, Security Team, 1, av. Belle Fontaine, 35510 Cesson S´ evign´ e, France Pierre DUHAMEL Ecole Nationale Sup´ erieure des T´ el´ ecommunications de Paris, Laboratoire Traitement Signaux et Images, 46 rue Barrault, 75013 Paris, France ABSTRACT Asymmetric schemes belong to second generation of wa- termarking. Whereas their need and advantage are well understood, many doubts have been raised about their ro- bustness. According to a method presented in [1], a very robust symmetric technique is derived into an asymmetric scheme. Tests show that it is as robust as the symmetric version. Yet, asymmetric schemes undergo malicious at- tacks that confuse the detection process. Tests reveal that the quality loss due to these malicious attacks is too impor- tant for the signal to be used after the attack. 1. INTRODUCTION To build a copy protection system for consumer electronic devices, we are looking for a technique, which could embed in an original content a signal commonly called watermark. Compliant devices such as players or recorders are able to detect the presence of this watermark. In this particular case, its presence means that the content is protected and thus it is illegal to copy it. This embedded watermark must not be perceptible. To assess the security of watermarking, we made a threat analysis of these techniques. Some achieve good re- sults in non-perceptibility and robustness, and all of them are symmetric schemes. Symmetric means that the detec- tion process make use of the parameters used by the em- bedding process. The knowledge of these parameters allow pirates to forge illegal contents by modifying or removing watermark. This set of parameters is called the secrete key and must be stored safely. This is not possible in consumer electronics. Tamper proof device is too expensive. This is the reason why asymmetric watermarking sche- mes inspired from the cryptography domain have been re- cently studied ([2], [3] and [1]). They should be as robust as symmetric techniques with a detector needing a set of parameters called the public key different from the embed- ding’s secret key. knowing the public key, it should be nei- ther possible to deduce the private key nor possible to re- move the watermark . In this paper, we choose a symmetric technique achiev- ing very good results in robustness. According to our me- thod, we render it asymmetric. The first issue is to test the derived technique against common image transformations (for instance, JPEG, filtering, cropping...). The main result is that this derived technique is as robust as the symmetric one. The second issue is the vulnerability against mali- cious attacks. These attacks are specific of the asymmetric method, but their visual impact depends on the watermark- ing technique. 2. ALGORITHMS We describe in this section the algorithms of the symmetric technique, its derivation into a public key scheme, and its human perceptual model. 2.1. The symmetric technique In this subsection, we give the technical details about the implementation of the symmetric technique invented by Alessia De Rosa and al.[4]. Its robustness is impressive, especially with the optimal version of the detector. From a cover content Co belonging to the “media space” the extraction function X(.) maps cover data into a vector in the “watermark space”: ro = X(Co). The “media space” is the spatial domain. X(.) orders in a vector ro a subset of the magnitude of N discrete Fourier transform coefficients of Co . These coefficients are extracted between the k-th and the (k + n)-th diagonal in the first quadrant and their symmetrical images in the second quadrant [4]. They are ordered in a pseudo random manner, so that we can assume the sequence {ro [m]} is a white stationary process. The role of the “mixing function” f (.) is to modify the extracted vector ro into a vector rw which is sufficiently similar to the watermark signal w: rw = f (ro ,w). In this paper, it modifies the amplitude of the DFT coefficients store in ro proportionally to their value: rw [m]= ro [m].(1 + γ.w[m]) ∀m ∈ [0..N − 1] where γ> 0 fixes the embedding depth. If w[m] < −1 γ , then rw [m] is clipped to 0. The application of the “inverse extraction” function Y (.) concludes the embedding process. It maps back from the “watermark space” to the “media space”: Cw = Y (rw ,Co). Here, Y (.) copies the DFT coefficients of Co and changes the amplitude of those used at the extrac- tion according to the watermarked vector rw . 2.2. The asymmetric version In [1], we described a method allowing to derive an asym- metric technique from classical spread spectrum ones. The