On the use of the Stirling Transform in image steganography

Abstract

Stirling Transform (ST) is primarily used in combinatorial mathematics to convert a polynomial sequence of n non-negative integers into another integer sequence. The source sequence can also be re-generated from the target sequence based on the principle of inverse Stirling Transform (IST). This property is considered as an interesting study and has been exploited for steganography in digital images. In this paper, the cover image is decomposed into the pair (n = 2) of neighboring pixel components in row major order. Stirling Transform (ST) converts the pair of pixel components into the pair of transformed components corresponding to red, green and blue channels. The obtained transformed components are always non-negative, which fabricates varying sizes of the secret image based on the specified payload in the range of 0.5 to 3 bpB (bits per Byte). To address the security issue, the secret image is scrambled through a simple scrambling process prior to embedding. The pixel adjustment process ensures the non-occurrence of overflow/underflow during embedding. Inverse Stirling Transform (IST) re-computes the pair of pixel components from the embedded pair of transformed components. This process is repeated till the secret information is concealed and the stego-image is produced. At the recipient end, the reverse procedure is applied to extract the concealed information from the stego-image based on the following parameters: shared PIN, system time and the one time password (OTP). Message digest obtained through MD5 algorithm is used to verify the authenticity. Simulation results ensures that the proposed scheme outperforms Chang et al.’s [17], Xia et al.’s [18], 3-LSB [2] and hybrid GEMD [7] schemes in terms of image quality with respect to increasing payloads.