Sharbani bhattacharya sacta 2014

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Information about Sharbani bhattacharya sacta 2014

Published on January 29, 2016

Author: b_sharbani


1. Watermarking Digital Image Using Fuzzy Matrix Rules SACTA 2014 19th April 2014 ITS , Ghaziabad

2. Watermarking is done in digital images for authentication and to restrict its unauthorized usages. There are two kinds of watermark Visible Invisible

3. Watermarking are sometimes invisible and can be extracted only by authenticated party i.e . It is encrypted with public key –private key method.

4. There are various method of encryption like DES, RSA, Deffie - Hellman and etc. In this paper Encryption is done using Fuzzy Matrix.

5. The 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.

6. Fuzzy 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}.

7. 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

8. Max-Min Fuzzy Composition Max-Product Fuzzy Composition Min-Max Fuzzy Composition Min-Product Fuzzy Composition

9.  Max-Mod-Minus Fuzzy Composition Complimentary-Sum-Minus Fuzzy Composition

10. 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

11.  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

12.  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

13.  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

14.  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.

15. 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.

16.  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.

17.  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.

18. 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

19. 4(a) 4(b) Figure 4(a) Original image lena.gif 4(b) Watermarked using Fuzzy Max-Mod-Minus matrix lena.gif

20. 5(a) 5(b) 5(a) Original Image Mypic.jpg (b) Watermarked using Fuzzy Max-Mod-Minus Matrix

21.  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.

22.  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.

23. Thank you

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