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• An adaptive HEVC video steganography algorithm is designed, which can effectively resist the PU shift-based steganalysis. • The introduction of multivariate STC allows for smaller modifications with the same embedding capacity. • The superiority of this algorithm over the state-of-the-art video steganography algorithm is verified through extensive experiments. Calibration-based steganalysis methods are a fatal threat to current HEVC steganography algorithms. The current steganography algorithms based on prediction unit (PU) still lack resistance to this type of steganalysis. The reason is that the improvements in HEVC codec provide more potential steganographic space as well as introduce more detectable distortion. Therefore, a HEVC video steganography method that has resistance to PU shift-based steganalysis is proposed in this paper. First, the PU shift phenomenon that exists in PU-based steganography is introduced. Then the existing calibration-based steganalysis method is enhanced. According to the encoding rules of HEVC, the distortion cost function according to the difference of rate distortion cost (RD cost) during recompression is designed, which aims to obtain better resistance to calibration-based steganalysis. Experimental results demonstrate that the steganography algorithm designed in this paper provides excellent resistance ability for calibration-based steganalysis. [ABSTRACT FROM AUTHOR]