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Steganography has been proposed as a methodology for transmitting messages through innocuous covers to conceal their existence. This work proposes an asymmetric image steganographic method based on a chaotic dynamic system and the Euler theorem. The hidden message can be recovered using orbits different from the embedding orbits, and the original image is not required to extract the hidden message. Experimental results and discussions reveal that the proposed scheme possesses security, imperceptibility and survivability.