Simulation-Based Exploration of SVD-Based Technique for Hidden Communication by Image Steganography Channel - Computer Network Security - page 353

1. Compute SVD of the block ~ . Let Delta(Red), be the vector of singular values
ordered in decreasing mode, X and Y be the singular vectors of the matrix ~ ,
i=1,2,…,r , and r is the rank of matrix ~ .
2. Compute the Euclidean norm of vector

V ~

λ

, i.e.

V ~

~

∑ =

r
i

λ

(

v λ

)

2

Norm ( )= .

1

3. Compute ~

V ~ )/ Delta]* .
4. Compute the value of the hidden bit b :
{If ~ is even then b = 1 else b = 0 }

λ

= [Norm (

5. End of extraction procedure for a single block of the segmented digital image con-
taining hidden message.
Several secret keys can be used for restriction of the access to the embedded mes-
sage. They are sizes of block used for image segmentation, code of pseudorandom
seeding of the message bits, initial shift of the first position of image segmentation,
and quantization step sizes, Delta(Red), Delta(Green), Delta(Blue), have been used
for quantization of the vector

V ~

λ

module.

3 Transmission Channel Distortions and Simulation Attributes

Consider a steganography channel distorted by JPEG compression. It is well known
that such a distortion is non-additive and also non-Gaussian. For this reason, the ana-
lytical exploration of the distortion of the extracted message given the capacity rate
and JPEG compression quality, like it is done in [18] for additive white Gaussian
noise, is impossible. This is why it is explored empirically via simulation.
The simulation scheme of hidden communication including a message embedding,
distortion of transmitted image within communication channel, intentional distortion
and distorted message extraction is presented in Fig. 1. Both distortions, within com-
munication channel and intentional one are modeled as JPEG compressions.
The invisibility of embedded message is assured by the chosen value of the quanti-
zation step of the vector V module, Delta (see Section 2 ), which was assigned ac-
cording to the results of empirical optimization presented in [10]. The primary simula-
tion goal is to assess BER of the extracted message subjected to a combination of the
above distortions, JPEG- 1 and JPEG- 2, given a varying size of blocks of cover
image segmentation (this attribute also implicitly specifies the capacity rate of the
embedded message). The other goal of simulation is to define recommendations with
regard to the choice of the attributes of SVD-based data embedding procedure for a
given message size and given admissible upper threshold for BER.