Steganography Techniques Based on Modulus Function and PVD Against PDH Analysis and FOBP

Steganography Techniques Based on Modulus Function and PVD Against PDH Analysis and FOBP

DOI: 10.4018/978-1-5225-7516-0.ch007


This chapter proposes two improved steganography techniques by addressing two problems in the existing literature. The first proposed technique is modulus function-based steganography and it addresses pixel difference histogram (PDH) analysis. The modulus function is used to calculate an evaluation function and based on the value of the evaluation function embedding decision is taken. There are two variants of this technique: (1) modulus 9 steganography and (2) modulus 16 steganography. In modulus 9 steganography, the embedding capacity in a pair of pixels is 3 bits, and in modulus 16 steganography the embedding capacity in a pair of pixels is 4 bits. Both the variants possess higher PSNR values. The experimental results prove that the PDH analysis cannot detect this technique. The second proposed technique is based on pixel value differencing with modified least significant bit (MLSB) substitution and it addresses fall off boundary problem (FOBP). This technique operates on 2×2 pixel blocks. In one of the pixels of a block data hiding is performed using MLSB substitution. Based on the new value of this pixel, three difference values with three neighboring pixels are calculated. Using these difference values, PVD approach is applied. Experimental results prove that the PDH analysis and RS analysis is unable to detect this proposed technique. The recorded values of bit rate and peak signal-to-noise ratio are also satisfactory.
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Least significant bit (LSB) substitution is one of the oldest data hiding approaches, wherein one or more LSBs of a pixel are substituted by secret data bits. This simplest technique is detected by RS analysis (Fridrich, Goljian, & Du, 2001). Wu & Tsai (2003) exposed the fact that the edge regions in an image can conceal more amount of data as compared to the smooth regions. Based on this principle they proposed pixel value differencing (PVD) steganography. The image is partitioned into 1×2 size non-overlapped pixel blocks. For a block the difference value between the two pixels is computed and changed to a new value by hiding data in it. The PVD technique with block size of 2×2 has been proposed to enhance the embedding capacity in (Chang, Chang, Huang, & Tu, 2008; Lee, Lee, Chen, Chang, Su & Chang, 2012). In blocks of size 2×2, edges in three directions are considered to increase the hiding capacity. Chang & Tseng (2004) considered the values of 2, 3, and 4 neighboring pixels, to find the correlation among the pixels of a block, and then calculated the pixel value differences. Based on these differences embedding decision is taken.

LSB substitution techniques offer higher embedding capacity, but PVD techniques offer higher imperceptibility. Thus, PVD and LSB substitution techniques have been combined to obtain higher hiding capacity and higher imperceptibility (Wu, Wu, Tsai & Hwang, 2005; Yang, Weng, Wang & Sun, 2010). Chen (2014) proposed a PVD steganography technique using two reference tables to randomize the data embedding. Khodaei & Faez (2012) proposed a combination of modified LSB (MLSB) substitution with PVD in 1×3 pixel blocks to achieve higher embedding capacity. This idea is extended to 2×2 pixel blocks in (Swain, 2016b). This extended technique possesses higher hiding capacity, but it suffers with fall off boundary problem (FOBP). Based on pixel value differences adaptive LSB substitution has been performed in (Liao, Wen & Zhang, 2011).

The traditional PVD steganography techniques follow a static range table. Due to this some zig-zag appearance (known as step effect) is introduced in pixel difference histograms of the stego-images (Chang, Su & Chang, 2012). This is referred as pixel difference histogram (PDH) analysis. The step effect can be avoided by applying two tricks, (i) using adaptive range table and (ii) utilizing edges in all possible directions. Luo, Huang & Huang (2010) also proposed an adaptive PVD steganography with three-pixel blocks, which does not suffer from step effects. Swain (2016a) proposed two adaptive PVD steganography techniques using vertical and horizontal edges, which does not suffer from step effects. In general, adaptive image steganography schemes possess lower embedding capacity. The edges can be predicted by some prediction functions and hiding capacity depends upon this prediction functions. If we hide in smooth regions distortion will be more. Based on the level of complexity of the edge regions, adaptive embedding can be applied (Chakraborty, Jalal & Bhatnagar, 2017). In this way capacity can be increased and chance of detection can be decreased.

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