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Histogram-based lossless data embedding (LDE) has been recognized as an effective and efficient way for copyright protection of multimedia. Recently, a LDE method using the statistical quantity histogram has achieved good performance, which utilizes the similarity of the arithmetic average of difference histogram (AADH) to reduce the diversity of images and ensure the stable performance of LDE. However, this method is strongly dependent on some assumptions, which limits its applications in practice. In addition, the capacities of the images with the flat AADH, e.g., texture images, are a little bit low. For this purpose, we develop a novel framework for LDE by incorporating the merits from the generalized statistical quantity histogram (GSQH) and the histogram-based embedding. Algorithmically, we design the GSQH driven LDE framework carefully so that it: (1) utilizes the similarity and sparsity of GSQH to construct an efficient embedding carrier, leading to a general and stable framework; (2) is widely adaptable for different kinds of images, due to the usage of the divide-and-conquer strategy; (3) is scalable for different capacity requirements and avoids the capacity problems caused by the flat histogram distribution; (4) is conditionally robust against JPEG compression under a suitable scale factor; and (5) is secure for copyright protection because of the safe storage and transmission of side information. Thorough experiments over three kinds of images demonstrate the effectiveness of the proposed framework.