Information Hiding
and its Applications
Steganography and Watermarking
A detailed look at Steganography
   ◦ Text Steganography
   ◦ Hypertext Steganography
   ◦ Audio Steganography
   ◦ Image Steganography
   ◦ Steganography in Open System
Image Steganography Techniques
   ◦ Spatial Domain LSB Insertion
   ◦ Masking and Filtering
   ◦ DCT-based Steganography
   ◦ Wavelet-based Steganography
How to Detect Steganography
   ◦ Blind Detection
   ◦ Analytical Detection

DCT-based Steganography

The Discrete Cosine Transformation (DCT) is used by the JPEG compression algorithm, therefore the DCT-based steganography methods apply only for jpeg image format. The DCT transformation is used by the JPEG algorithm to transform successive 8x8 pixels blocks of the image, into 64 DCT coefficients each. Each 8x8 pixels block of the image will be transformed into an 8x8 DCTs block by the use of the relation shown below. Each DCT coefficient F(u , v) of an 8x8 block of image pixels f(x , y) is given by:

where C(x) = 1/√2 when x equals 0 and C(x) = 1 otherwise. After calculating the coefficients, the following quantizing operation is performed:

where Q(u, v) is a 64-element quantization table. A simple code algorithm to hide a message inside a JPEG image could look like this:

Although a modification of a single DCT will affect all 64 image pixels, the LSB of the quantized DCT coefficient can be used to hide information. Lossless compressed images will be suspectible to visual alterations when the LSB are modified. This is not the case with the above described method, as it takes place in the frequency domain inside the image, instead of the spatial domain and therefore there will be no visible changes to the cover image.

References:
• Steganography and Steganalysis,  by J.R. Krenn,  January 2004.