SHARBANI BHATTACHARYA

Watermarking Digital Image Using Fuzzy

Matrix Rules

SACTA 201419th April 2014ITS , Ghaziabad

WATERMARKING Watermarking is done in digital

images for authentication and to restrict its unauthorized usages.

There are two kinds of watermark

Visible Invisible

ENCRYPTED WATERMARKWatermarking are sometimes

invisible and can be extracted only by authenticated party i.e .

It is encrypted with public key –private key method.

ENCRYPTION There are various method of

encryption like DES, RSA, Deffie -Hellman and etc.

In this paper Encryption is done using Fuzzy Matrix.

FUZZY RULESThe Fuzzy rules are consisting of

rules defined on fuzzy set. Fuzzy set are acquired from

Crisp Set(say any algebraic set) using membership function.

This process is known as Fuzzification.

Converting fuzzy set to Crisp set is called Defuzzification.

FUZZY SETFuzzy set has members which can

take values 0 to 1. Thus, Fuzzy set A values like

A= {0.2/x1 , 0.3/x2 , 0.4/x3}.

MEMBERSHIP FUNCTION This means 0.2 is membership

value of x1 in set A 0.3 membership value for x2 0.4 membership value for x3 in

set A

FUZZY MATRIX COMPOSITIONS Max-Min Fuzzy Composition Max-Product Fuzzy Composition Min-Max Fuzzy Composition Min-Product Fuzzy Composition

PROPOSED FUZZY MATRIX RULES Max-Mod-Minus Fuzzy

Composition

Complimentary-Sum-Minus Fuzzy Composition

MAX-MOD-MINUS FUZZY COMPOSITION

Let A, B and C are fuzzy set with A(x1,x2), B(y1,y2) and C(z1,z2)

µA,B(x1,y1)=0.2 µA,B (x1,y2)=0.3 µA,B (x2,y1)=0.2 µA,B (x2,y2)=0.4 µB,C (y1,z1)=0.3 µB,C (y1,z2)=0.5 µB,C (y2,z1)=0.2 µB,C (y2,z2)=0.2

MAX-MOD-MINUS FUZZY COMPOSITION

µA,C (x1,z1)= max{|µA,B(x1,y1)-µB,C (y1,z1)|,

| µA,B (x1,y2) - µB,C (y2,z1) |}=0.1 µA,C (x1,z2)= max{|µA,B(x1,y1) -µB,C (y1,z2) |,|µA,B

(x1,y2) - µB,C (y2,z2)|}=0.3 µA,C (x2,z1)= max{|µA,B (x2,y1) , µB,C (y1,z1)|, |µA,B

(x2,y2) - µB,C (y2,z1)|}=0.2 µA,C (x2,z2)= max{|µA,B (x2,y1) ,µB,C (y1,z2)|, |µA,B

(x2,y2) - µB,C (y2,z2)|}=0.3

COMPLIMENT-SUM-MINUS FUZZY MATRIX RULE µA,B(x1,y1)=0.2 µA,B (x1,y2)=0.3 µA,B (x2,y1)=0.2 µA,B (x2,y2)=0.4 µB,C (y1,z1)=0.3 µB,C (y1,z2)=0.5 µB,C (y2,z1)=0.2 µB,C (y2,z2)=0.2

COMPLIMENT-SUM-MINUS FUZZY MATRIX RULE

µA,C (x1,z1)= |1-{|µA,B(x1,y1) -µB,C (y1,z1)|+ | µA,B (x1,y2) - µB,C (y2,z1) |}|

=0.8 µA,C (x1,z2)= |1-{|µA,B(x1,y1) -µB,C (y1,z2) |+|µA,B

(x1,y2) - µB,C (y2,z2)|}|=0.6 µA,C (x2,z1)= |1-{|µA,B (x2,y1) - µB,C (y1,z1)| +|µA,B

(x2,y2) - µB,C (y2,z1)|}|=0.7 µA,C (x2,z2)= |1-{|µA,B (x2,y1) -µB,C (y1,z2)|+ |µA,B

(x2,y2) - µB,C (y2,z2)|}|=0.5

ALGORITHM FOR ENCRYPTION Step 1:Choose one Fuzzy matrix

appropriate for encryption according to the file size. It is public key.

Step2: Select one fuzzy matrix from database.

Step3: Find the Fuzzy Compliment-Sum-Minus Matrix.

Step3: Generate random number using Fuzzy

Step4: Retrieve the encrypted text/files.

DECRYPTION ALGORITHM Decryption algorithm is used decrypt the

encrypted file. The following algorithm is used-

Step1: Collect the encrypted four parts from four different embedded region of image and combine to for one file.

Step2:Use Private key Fuzzy matrix key for decryption.

Step3: Break the file into same four parts with appropriate values of fraction of Fuzzy Matrix elements.

Step4: Retrieve the original file.

EMBEDDING THE WATERMARKIN COVERT IMAGE Encrypted file is divided into four parts

and b11, b12, b21 and b22. The four encrypted files are embedded

in digital image as watermark using appropriate fuzzy rule.

Max-Mod-Minus Fuzzy matrices and Complimentary-Sum-Minus Fuzzy matrices rules are chosen according to suitability.

STEPS FOR EMBEDDING WATERMARK The two fuzzy matrices obtained as

public key and private key are first used for encrypting watermark.

For embedding the various compositions of fuzzy matrices are used.

The encrypted four parts of file are inserted at four places of digital image using the most suitable fuzzy matrix composition obtained using same keys.

3(a) 3(b) 3(c) 3(d)

Figure 3

(a)Original Image peppers.tif

(b)Watermarked using Fuzzy Max-Mod-Minus matrix

(c) Fuzzy Min-Max Matrices

(d) Fuzzy Compliment-Sum-Minus Matrix using the two fuzzy matrices

4(a) 4(b)

Figure 4(a) Original image lena.gif

4(b) Watermarked using Fuzzy Max-Mod-Minus matrix lena.gif

5(a) 5(b)

5(a) Original Image Mypic.jpg (b) Watermarked using Fuzzy Max-Mod-Minus Matrix

CONCLUSION The digital images are watermarked

with encrypted files in order to have invisible watermark.

The watermark are encrypted and decrypted to see the image is authentic or it is tried to tamper.

The above method is robust as the keys used as public keys does not lead to any clue for private keys.

CONCLUSION It can restrain attacks like compression,

geometric filters and noise filters. The watermark is robust against

changes in file format. This embedding method can be used for

all file formats.

Thank you