NDFT-based Image Steganographic Scheme with Discrimination of Tampers

A new and secure image steganographic scheme based on nonuniform discrete Fourier transform (NDFT) is proposed in this paper. First, the chaotic system is introduced to select embedding points randomly in NDFT domain suitable range, and NDFT is implemented on every non-overlapping block of eight consecutive pixels. Second, the secret messages are scrambled by chaotic systems, and embedded into frequency coefficients by quantization method. The stego-image is obtained by inverse NDFT (INDFT). Besides, in order to discriminate tampers, the low frequency wavelet coefficients of 7 most significant bits (MSBs) of the stego-image are converted into the binary sequence after nonuniform scalar quantization. Then the obtained binary sequence is scrambled by the chaotic systems, and embedded into the least significant bit (LSB) of the stego-image. Finally, the watermarked stego-image can be obtained by a new improved LSB steganographic method. The embedded secret messages can be extracted from the watermarked stego-image without the original cover image. Experimental results show the validity of the proposed scheme, and dual statistics attacks are also conducted to indicate the security.