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In

Compressed Images

(Advanced Database Systems- Spring 2004)

Anurag Sharma,Gautami Shirhatti & Manish Billa

Department of Computer Science, University of Central Florida ,Orlando

~ Motivation

Protection of Digital Media.

Privacy of Information transmitted across the

word wide web.

~ Goal

To make the transmitted information invisible by embedding the information in a cover media.

We try to enhance the security and the robustness of the information against attacks and Image processing techniques.

- Steganography is “Data Hiding”
- Steps in Steganography:
- The data to be transmitted is hidden in a “Cover Image”.
- The resulting image called the “Stego –Image” is transmitted.
- The receiver then applies the inverse process to retrieve the data.

- Hiding capacity of the technique.
- Quality of the stego-image resulting from the technique.
- Robustness of the stego-image against image processing techniques.

- Practical Solution:
- Steganography does not emphasize the robustness.
- The capacity( the amount of information) and the quality of information are considered at priori.

- Image Compression
- Steganography(Information hiding)
- Encryption
- Related Algorithms
- Block Truncation Coding
- PAN et al Hiding Scheme

Various Techniques

Method 1

- To modify the least significant bits which constitute the pixel.

Disadvantage

- It is not at all the robust against compression schemes.
- A slight modification of the pixel would result into significant changes to the message.
- Lossy Compression like JPEG

Approach 1

[To embed one data bit per pixel byte]

- Assumption:

Jpeg would not increase a byte value more than seven or decrease a byte value more than eight.

Outcome: Failed

JPEG produced enough errors so as to make the hidden data unrecognizable.

An Image Hiding Technique Using Block Truncation Coding

- The secret message embedded into a block truncation coding (BTC).
- The message is hidden in the bit planes of the BTC encoded block.
- The amount of information that is hidden in the block varies according to the nature of the block.

Advantages:

- Proposed scheme tries to improve the security of the Data.
- It encrypts the data before it is embedded so that compress the image using a BTC technique.

With the presence of data id too, decryption is not possible.

Robustness increased manifold.

The method hides one image in another image and works with 24 bit bitmap color images.

Block Truncation Coding

Proposed by Delp and Mitchell compress digital images.

Encoding Steps

- Each image is divided into a set of non-overlapping blocks of n×n pixels.
- Pixel values of each block are used to calculate a bit plane B and two quantization levels l and h.
- The triple (l, h, B) is used to represent the encoded block for storage or transmission.

Decoding Steps

- The received bit planes and quantization levels are used to reconstruct the image.

- AMBTC
- (Absolute Moment Block Truncation Coding)
- A binary bit plane B is calculated to record the grouping information of each pixel in each image block.
- The bit plane B is determined according to the mean value x .
- If the pixel value of the image block is greater than or equal to x , a bit value of 1 is set in the bit plane.

Example ( Encoding –AMBTC )

- Figure 1(a) shows the pixel values of an image block of 4×4 pixels.
- The bit plane of the encoded block from Figure 1(a) is shown in Figure 1(b), where x equals 131.
- Two quantization levels l and h of AMBTC are 129 and 133, respectively.
- The reconstructed block using the triple (l, h, B) is shown in Figure 1(c).

PAN et al Hiding Scheme

Proposed by Pan et al for two-color images .

Steps

- The two-color cover image is divided into blocks of size n×n.
- A secret key matrix S and a weight matrix W of size n×n – Embedding
- The secret key matrix S is a binary matrix – To protect the hiding information.
- The weight matrix W is an integer matrix - To compute the modification bits of the block when the secret message is embedding.
- The number of embedding bits r of each image block is determined by the size of image block

The embedding procedure

Step 1

Compute b ≡ sum((B(xor)S) .W) (mod 2r).

- (xor) - exclusive-or operator
- ‘.’ - product operator
- function sum(x) -

summation of the pixel values of image block x and b is the module result of the image block.

Step 2

Modify the bit plane B of the image block to satisfy the equation

d ≡ sum((B΄(xor)S) .W) (mod 2r)

B΄ - The modified image block’s bit plane

d - The integer value ofthe secret message.

Step 3

If there is other secret message to be embedded, go to Step 1

Message Recovery

Steps In Extraction

- The extracting procedure is similar to the embedding procedure.
- Each received stego-image block B΄ is employed to extract the hidden information according to the equation

d ≡ sum((B΄(xor)S) .W) (mod 2r).

3. d is the extracted hidden information and will be transformed to of binary r bits.

4. The secret message is recovered

Example (Embedding and extracting procedures -Pan et al’s)

Embedding

- Each image block embeds 3 bits of the secret message.
- A secret key matrix S and a weight matrix W are designed as in Figures 2(a) and 2(b), respectively.
- The calculated result of the equation

b ≡ sum((B΄(xor)S) .W) (mod 2r) is

1 (3+2+3+4+6+7 mod 8).

Steps

The extracting procedure extracts the hidden information according to the equation d ≡ sum((B΄(xor)S) .W) (mod 2r).

The module result d is the extracted secret message

The secret message is transformed to 3 bits data of the binary representation.

For the modified block of Figure 3(b), the extracting secret message is 3 (3+2+3+4+7 mod 8).

Additional Facts

- Pan et al’s scheme efficiently embeds the secret message into the two-color cover image with less modification.
- For two blocks of size 4×4 and 2×2, them maximum embedding size is.
- 4 bits and 2 bits, respectively.
- The hiding capacity is computed by the number of blocks times the number of embedding bits of each block.
- Thesmaller the block size, the more hiding capacity it will have.
- The modification bits are always restricted at most to 2 bits in each image block.

Improved Hiding Scheme

Goal

The goal of this scheme is to embed the secret message into the AMBTC-encoded blocks to avoid affecting of the image compression schemes.

Scheme-Overview

- The proposed hiding scheme consists of the Embedding and Extracting procedures.
- In the embedding procedure, the block activity of each BTC encoded block is exploited to decide the hiding capacity.
- The extracting procedure is similar to the embedding procedure, except that the extracting action is used instead of the embedding action.

Embedding procedure

Steps

- The cover image is first divided into a set of non-overlapped blocks of n×n pixels.
- The AMBTC scheme is employed to compress the cover image.
- Each AMBTC encoded block comes out to be a triple (l, h, B).
- The bit plane B of each encoded block is exploited to embed the secret message.
- Number of embedding bits r of each image block to be determined by the size of the image block.

To further extend the hiding capacity of the proposed scheme, a simple block classifier is introduced.

- The absolute distance between the two quantization levels l and h of each encoded block is exploited to determine the block activity.
- The current processing block tends to be a smooth block if a small absolute distance between l and h is calculated.
- If a large absolute distance between l and h is computed, the current processing block tends to be a non-smooth block.
- In the proposed scheme, the whole bit plane of each smooth block is used to hide the secret message

Types of Blocks

Smooth Block

The absolute distance between l and h is less than or equal to a threshold τ,

| l-h |≤τ

Non-Smooth Block:

The absolute distance between l and h is greater than threshold τ

| l-h |>=τ

Extracting procedure

Steps

- The extracting procedure is similar to the embedding procedure and imposed on the decoding procedure of BTC.
- BTC decoding procedure is performed, the secret message is extracted.
- The block activity is first determined according to the absolute distance between quantization levels.
- If a smooth block is distinguished, all the bits of the bit plane are extracted as a secret message.
- Otherwise, a non-smooth block is found and then Pan et al’s extracting procedure is performed.

The equation d ≡ sum((B΄(xor)S).W) (mod 2r) is calculated.

- The module result d is the extracted secret message.
- The extraction procedure calculates the module result using the equation d ≡ sum((B΄(xor)S).W) (mod 2r)
- The extracted secret message is the module result

3 (3+2+3+4+7 mod 8).

The Adaptive Hiding Capacity Determination Mechanism

Objective

The selection of the threshold is the key point to determine the tradeoff between

the quality of the stego-image and the hiding capacity of the cover image.

Steps

- The bit planes of the AMBTC-encoded smooth blocks are exploited to increase the hiding capacity.
- All the bits of the smooth block bit planes are used to embed the secret message.
- The hiding capacity of the smooth blocks is increased and less distortion is incurred.

The total hiding capacity consists of two parts: smooth blocks and non-smooth blocks.

Smooth blocks

The total number of bits of the secret message equals the product of thenumber of smooth blocks and the block size.

Non Smooth blocks

The maximum size of the secret message equals the product of the number of non-smooth blocks and the maximum number of bits that can be embedded in Pan etal’s scheme.

Advantages (Winning Edge)

- The proposed scheme introduces an adaptive hiding capacity determination mechanism.
- For a large size secret message, quality of the stego-image is preserved.
- The proposed scheme improves the hiding capacity using smooth blocks.
- Traditional image hiding schemes employ the non-smooth blocks to raise the hiding capacity .
- The proposed scheme introduces a different approach to improve the hiding capacity by using smooth blocks.

Analysis

- The minimum and maximum hiding capacities of the proposed scheme using different sizes of cover images are given in Table 2.
- Each cover image is first partitioned into a set of non-overlapped image blocks of 4×4.
- The total numbers of image blocks of the cover images can be calculated.
- The maximum number of bits to be embedded in each non-smooth block can be determined using the equation r ≤ _log24×4+1_.
- Non Smooth block - 4 Bits (Embedded)
- Smooth block - 6 Bits(Maximum)

- A 24 bit Bitmap image ‘dog.bmp’ was used to evaluate the performance of our compression and steganography algorithms.
- The stego-images are also shown adjacent to the corresponding compressed images, these stego-images hide 1.78 kB of text data.
- The following figures show the images when compressed using AMBTC taking block sizes as 2, 4, 8 and 16 respectively.

A 3 KB image yahoo.bmp used as secret data and was hid in the compressed stego-images.

secret message ‘yahoo.bmp’

block size = 16

Analysis of BTC compression using different image sizes and block sizes

- A simple image hiding scheme has been introduced.
- The affection of the image compression procedure can be avoided.
- The improved scheme obtains more benefits from the smooth cover image than the non-smooth cover image. This is different from the traditional hiding schemes.
- To further improve the security of the secret message in the cover image, we have used encryption to encrypt the secret message before it is embedded.
- The encrypted secret message enhances the security of the secret message but does not influence the proposed embedding and extracting procedures.

Reference

- Surmounting the effects of lossy compression on steganography. Danel L. Currie, III Cynthia E. Irvine. 1996uqing Song and Aidong Zhang.
- An Image hiding technique using block truncation coding. Piyu Tsai, Yu Chen Hu and Chin Chen Chang. July 2002.
- An Entropy Based Technique For Information Embedding In Images. Marc Van Droogenbroeck and Jerome Delvaux. May 2002.
- Y. K. Chan and C. C. Chang, “Concealing a Secret Image Using the Breadth First Traversal Linear Quadtree Structure,” IEEE Proceedings of the Third International Symposium on Cooperative Database Systems for Advanced Applications (CODAS 2001), pp. 194-199, 2001.

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