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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
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.