Existing copyright protection schemes for 3D models of oblique photography predominantly utilize digital watermarking technology, most of which suffer from shortcomings such as the potential false accusation of legitimate users and the inability to effectively trace unauthorized distributors. In response to these challenges, this article proposes a homomorphic encryption domain asymmetric fingerprinting scheme for 3D models of oblique photography. Initially, the fingerprints to be embedded are collaboratively generated by the transacting parties, with the publisher remaining unaware of the user's actual fingerprint. This approach ensures the effective implementation of the asymmetric nature of the fingerprinting scheme. Subsequently, potential geometric and non‐geometric attacks are considered prior to fingerprint embedding. Robustness is enhanced for the proposed solution through relative coordinate transformations and normalization procedures. Ultimately, the embedding and extraction of fingerprints are achieved through the application of an effective bit parity check method, in conjunction with the vertex‐paradigm projection length mapping mechanism and the Paillier homomorphic encryption system, minimizing embedding distortion while ensuring data security. Experimental results demonstrate that the proposed solution exhibits satisfying robustness against common manipulations, such as cropping, simplification, and geometric attacks. Additionally, the scheme effectively safeguards legitimate users from false accusations and accurately traces maliciously authorized users.

中文翻译：

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倾斜摄影3D模型的同态加密域非对称指纹识别方案

现有的倾斜摄影3D模型版权保护方案主要采用数字水印技术，但大多存在合法用户可能被诬告、无法有效追踪未经授权的发行者等缺点。针对这些挑战，本文提出了一种用于倾斜摄影3D模型的同态加密域非对称指纹识别方案。最初，要嵌入的指纹是由交易方协作生成的，发布者仍然不知道用户的实际指纹。这种方法确保了指纹方案的非对称性的有效实现。随后，在指纹嵌入之前考虑潜在的几何和非几何攻击。通过相对坐标变换和标准化程序增强了所提出的解决方案的鲁棒性。最终，通过应用有效的位奇偶校验方法，结合顶点范式投影长度映射机制和Paillier同态加密系统，实现指纹的嵌入和提取，在保证数据安全的同时最大限度地减少嵌入失真。实验结果表明，所提出的解决方案对裁剪、简化和几何攻击等常见操作表现出令人满意的鲁棒性。此外，该方案有效保障合法用户免受虚假指控，并准确追踪恶意授权用户。