Nonparametric Steganalysis of QIM Steganography Using Approximate Entropy

Abstract—This paper proposes an active steganalysis method for quantization index modulation (QIM)-based steganography. The proposed nonparametric steganalysis method uses irregularity (or randomness) in the test image to distinguish between the cover image and the stego image. We have shown that plain quantization (quantization without message embedding) induces regularity in the resulting quantized object, whereas message embedding using QIM increases irregularity in the resulting QIM-stego. Approxi-mate entropy, an algorithmic entropy measure, is used to quan-tify irregularity in the test image. The QIM-stego image is then analyzed to estimate secret message length. To this end, the QIM codebook is estimated from the QIM-stego image using first-order statistics of the image coefficients in the embedding domain. The estimated codebook is then used to estimate secret message. Simu-lation results show that the proposed scheme can successfully esti-mate the hidden message from the QIM-stego with very low de-coding error probability. For a given cover object the decoding error probability depends on embedding rate and decreases mono-tonically, approaching zero as the embedding rate approaches one. Index Terms—Algorithmic entropy, approximate entropy, complexity, dither modulation, embedding rate, entropy, mes-sage recovery, quantization index modulation, steganalysis, steganography. I