About DCT-Based Mod4 Method:

We can make an innocent image a communication channel by embedding a message within the image. The image will represent a hidden communication channel, where no one knows what it contains except the sender and the intended receiver. Many image-based steganographic methods have been invented in the spatial and DCT domains. In this project, we focus on the Mod4 algorithm as one of the well-known algorithms in the DCT domain.

The Mod4 algorithm was developed by Wong, Qi, and Tanaka [1]. Each 8x8 block of qDCT coefficients is divided into 16 contiguous GQCs, where each GQC is composed of 2x2 qDCT coefficients. The GQCs are tested to identify the valid GQCs (vGQC). The vGQC must meet two conditions considering the magnitudes of the coefficients and their number, where these conditions are donated by the values of Φ1, Φ2, τ1, and τ2 parameters.

The Modulo operation of 4 is used as a hash function. Applying The Modulo operation to a vGQC will produce 2 Bits. To embed 2 Bits in a vGQC, the sender needs to modify its coefficients accordingly, so when the receiver hashes the modified vGQC, the secret message of 2 Bits will be obtained. The modifications applied to the vGQC are restricted to the shortest route modification scheme SRM developed by Wong et al. [1]. The SRM is based on two principles; firstly, the modifications applied to the coefficients should be minimal; secondly, the modifications should be applied to the larger coefficient first.

What is the Magic Triangle ?:

In the field of information hiding, there is a visual requirements model called the Magic Triangle, proposed by Johnson et al. [2]. Each corner, in the Magic Triangle, represents a basic requirement; undetectability, robustness to attacks, and the insertion capacity. This visual model is convenient for presenting the balance between the three desirable requirements. It shows that these requirements cannot be made perfect at the same time; when we get closer to a corner, we move away from another corner. As a clarification, there is a trade-off between the insertion capacity and the robustness against attacks. It is not possible to have high insertion capacity and high robustness to signal modifications at the same time. In other words, the presence of large embedded data makes the carrier medium vulnerable to signal modification attacks.

Steganography pays much more attention to insertion capacity rather than robustness against attacks, while watermarking has a great interest in robustness against signal modifications since it aims to protect the ownership of a medium. On the other side, steganographic algorithms should not cause any perceptible distortion and have to be statistically invisible, so it should be very difficult to prove the presence of a hidden message. In the steganography, we aim to hide a large message using an undetectable way, but we cannot realize a perfect undetectability and a large capacity at the same time.

Comparing Mod4 with F5 from The perspective of the Magic Triangle:

The determination of the approximate locations of Mod4 and F5 algorithms is the result of a comparative study completed in chapter 4 of the Ms thesis of Al Chamaa [3]. The resulting Magic Triangle shows how Mod4 stands compared to F5. In other words, it shows how each algorithm satisfies each requirement compared to the other one.

In the following, we will show some comparative results taken from the MS thesis we mentioned above [3]. These results concern the insertion capacity, stego image quality, and statistical distribution:

The Insertion Capacity of Mod4 Compared to F5:

The following graph shows the bpc values for 60 jpeg images.

The Stego Image Quality of Mod4 Compared to F5 - (MSE, PSNR):

The following table presents the average values for 60 jpeg images.

The Resulting Histogram of Mod4 Compared to F5:

The following graph shows the resulting histograms. The inserted message corresponds to the maximum capacity provided by Mod4.

References:

[1]:   "A DCT-based Mod4 Steganographic Method"  by Wong et al., 2007.
[2]:   "Information Hiding: Steganography and Watermarking Attacks and Countermeasures". by Johnson et al., 2001.
[3]:   "Cryptography and Steganography in Digital Images" by Al Chamaa, 2009.