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.
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