This document discusses using fuzzy matrix rules for watermarking digital images. It describes how watermarking can be used for authentication and restricting unauthorized usage of images. There are two types of watermarks: visible and invisible. The document then explains how encryption is done using fuzzy matrices. Fuzzy rules are defined on fuzzy sets, which are derived from crisp sets using membership functions. The fuzzy sets assign membership values between 0 and 1 to elements. Various fuzzy compositions are used for encryption and embedding encrypted files in images at different locations to create an invisible watermark. Decryption extracts the encrypted files from the watermarked image. The method provides robust watermarking that is resistant to attacks like compression or noise filtering.

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

15.  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.

17. 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.

18.  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.

19.  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.

20. 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

21. 4(a) 4(b)
Figure 4(a) Original image lena.gif
4(b) Watermarked using Fuzzy Max-Mod-Minus matrix lena.gif

22. 5(a) 5(b)
5(a) Original Image Mypic.jpg
(b) Watermarked using Fuzzy Max-Mod-Minus Matrix

23.  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.

24.  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.

25. Thank you