  In this paper, for overcoming the drawbacks of the prior approaches, such as
low generality, high cost, and high overhead, we propose a Low-Cost
Anti-Copying (LCAC) 2D barcode by exploiting the difference between the noise
characteristics of legal and illegal channels. An embedding strategy is
proposed, and for a variant of it, we also make the corresponding analysis. For
accurately evaluating the performance of our approach, a theoretical model of
the noise in an illegal channel is established by using a generalized Gaussian
distribution. By comparing with the experimental results based on various
printers, scanners, and a mobile phone, it can be found that the sample
histogram and curve fitting of the theoretical model match well, so it can be
concluded that the theoretical model works well. For evaluating the security of
the proposed LCAC code, besides the direct-copying (DC) attack, the improved
version, which is the synthesized-copying (SC) attack, is also considered in
this paper. Based on the theoretical model, we build a prediction function to
optimize the parameters of our approach. The parameters optimization
incorporates the covertness requirement, the robustness requirement and a
tradeoff between the production cost and the cost of illegally-copying attacks
together. The experimental results show that the proposed LCAC code with two
printers and two scanners can detect the DC attack effectively and resist the
SC attack up to the access of 14 legal copies.
