# Collusion Attack Resilient 3D Mesh Watermarking Based on Anti-Collusion Fingerprint Code
## 2 Backgrounds
### Related Work  
There are two categories of countermeasure techniques were previously researched to cope with collusion attacks. The first technique works by pre-warping at the signal-processing level, so that each copy of the multimedia content is varied in a slightly different way [5; 6]. The pre-warping process is effective to cope with collusion attack, because a simple averaging attack causes degradation of the quality of the protected contents. Colluders must then resort to more complex attacks that bring about the registration of the original contents prior to the attack itself [5]. However, some doubts exist about the real effectiveness of these techniques given that registering the pre-warping contents does not appear to be an impossible task [6]. Moreover, in the case that the method fails to protect against collusion attack, it cannot provide information useful for tracking the attackers.  
The second countermeasures are based on the averaging-resilient fingerprint, which theoretically guarantees robustness against several attackers [4; 7; 8; 9; 10]. In contrast to pre-warping-based methods, the anti-collusion based techniques work passively by providing explicit clues for tracking the attackers. [PERSON] et al. [4] first defined the collusion attack for digital data, and they analyzed the characteristics of a collusion-attack resilient code. Based on the combinatorial theory, [PERSON] et al. [7] proposed a code system for an anti-collusion fingerprint code. [PERSON] et al. [9] proposed a constructive algorithm for an anti-collusion fingerprint code, which is called group-divisible partially balanced incomplete block design (GD-PBIBD), based on group-divisible designs. [PERSON] has proposed a randomized fingerprinting code that is provably secure against collusion attack [17] which performs state-of-the-art performance. The papers listed in this paragraph only proposed a code system, so that they did not suggest any practical system or experimental results for multimedia data. For fingerprinting system based on the anti-collusion code, [PERSON] et al. [8] proposed an image fingerprinting system using balanced incomplete block design (BIBD). For video fingerprinting, [PERSON] et al. [18] introduced a practical fingerprint scheme that adopted the anti-collusion fingerprint, which was called group-divisible partially balanced incomplete block design (GD-PBIBD). [PERSON] et al. [19] proposed a collusion resilient optimized image watermarking scheme using genetic algorithms and multiband wavelets. [PERSON] [20] suggested a simplified maximum a posteriori detector for binary fingerprinting code.  
Recently, the demand for 3D mesh watermarking has increased due to the emergence of low-cost 3D printers and 3D model sharing platforms such as Thingiverse, Pinshape, and Sketchfab. In spite of various watermarking methods [1; 11; 12; 13; 21; 22], mesh watermarking techniques resilient to collusion attack were rarely considered [6; 14]. [PERSON] et al. [6] proposed anti-collusion watermarking for 3D meshes by pre-warping, which changes the vertices ordering and the associated faces. However, there is no algorithm that utilizes the averaging-resilient fingerprint code into 3D mesh watermarking. As we found in the previous literature, most of the watermarking schemes based on anti-collusion codes were intended to protect image and video data. To the best of our knowledge, anti-collusion code-based 3D mesh watermarking has not been reported yet.