1. 1. PROJECT PRESENTED BY CHETANA BHANUSHALI BE-3 / 05 PRANAV SHETTY BE-3 / 69 CHINTAN TANNA BE-3 / 71
2. 2. INTRODUCTION Its a symmetric algorithm used to encrypt/decrypt an image Two primary steps:- 1. Shuffling of image using Rubiks cube principle 2. Ciphering of image using chaotic cipher
3. 3. WHY DO WE NEED IMAGE ENCRYPTION? To safely and securely transfer images for the following users 1. Military 2. Healthcare 3. Mapping and position 4.Picture messages on phones 5. Privacy 6. Government documents
4. 4. Chaos and noise are the two most natural and irregular behaviours Greatest advantage of a chaotic system is that the chaotic system is deterministic Exact knowledge of initial conditions and system parameters enables one to recover a message Robustness and effectiveness is due to highly sensitive nature of initial values and parameters. WHY USE CHAOTIC MAPS
5. 5. WHY USE TENT MAP Tent map is a very popular one dimensional chaotic map. Small key space of just two values Extremely sensitive even to changes at the 10-15 bit. Equation of tent map is as given below F(t)= r (1 - | 1 - 2x | )
6. 6. ENCRYPTION 0.6234371269561046 0.7518558163881806 0.4954515198042242 0.9892321669740052 0.021499352352634157 0.042926199771751404 0.0857076341938524 0.17112622589855478 0.34167534159265917 0.6440168761405893 0.7107657216608624 0.6821984090367663 0.6345314201893496 0.7297046445833093 0.5396791602688351 0.9190892823792112 0.16154856998937464 0.32255232969168957 0.039775596331519135 0.07941705248428722 0.15856627698864093 0.31659780124694287 0.5774931360340702 0.8435888556110641 0.31229480406860155 0.6235364176207965 0.7516575699090251 0.4958473441913356 0.9900224808605345 0.019921389853155023 0.632127900446191 0.7345035783817747 0.5300974767117909 A BASIC SEQUENCE OF VALUES GENERATED BY THE TENTS MAP EQUATION
7. 7. ENCRYPTION STEP 1 :- Assume all the constants , i.e. , values of b1, b2, a, r, x where, b1:- modulo operator for row b2:- modulo operator for column a:- number of iterations r & x:- starting values values ORIGINAL IMAGE
8. 8. ENCRYPTION STEP 2 :- (a)Sum=Sum of pixel values in row 1 (b)M = Sum%b1 (c)S = M%2 (d)if S=0 then circular right shift (e)if S=1 circular left shift
9. 9. ENCRYPTION After all row operations the image we get a shuffled image and then we proceed to column operations.
10. 10. ENCRYPTION STEP 3 :- (a)Sum = Sum of pixel values in column 1 (b)M = Sum%b2 (c)S = M%2 (d)if S=0 then circular up shift (e)if S=1 circular down shift.
11. 11. ENCRYPTION After all the column operations we get the following image.
12. 12. ENCRYPTION Original image Image after 1st iteration This process will be repeated for a number of iterations.
13. 13. Original image Image after shuffling ENCRYPTION
14. 14. ENCRYPTION STEP 4:- Compute cipher matrices each for row and column. We use the tent map which is represented by the by the equation given below. F(t)= r (1 - | 1 - 2x | ) We then use the above equation to generate chaotic stream of values.
15. 15. ENCRYPTION STEP 4:- We then use a multi-level discretization method on the generated chaotic sequence Old/ Traditional multilevel discretization method:- X= 0 if VALUE < 0.5 1 if VALUE > = 0.5 Proposed two-bit discretization method:- X=00 if VALUE- [0,0.25] 01 if VALUE- [0.25,0.5] 10 if VALUE- [0.5,0.75] 11 if VALUE- [0.75,1.0]
16. 16. ENCRYPTION WHY DO WE USE THIS MULTILEVEL DISCRETIZATION METHOD? Because it helps maintain statistical properties of the elements Generates a continuous stream of values
17. 17. STEP 4:- a. Enter the bit stream values acquired after the multilevel discretization method into two separate matrices b. Both matrices are of the same size as the image c. We then X-OR the shuffled image with these two matrices and get our final ciphered image. ENCRYPTION
18. 18. Original Image Row cipher matrice Image after row operation Image after row operation Column cipher matrice ENCRYPTION Final ciphered image
19. 19. encryption Enter the values of the shared keys Row operations Compute the cipher matrices Ciphered image Carry out x-or operation between shuffled image and cipher matrices Column operations
20. 20. Original image Image after shuffling Image after shuffling and ciphering ENCRYPTION
21. 21. Recieved image Row cipher matrice Image after row operation Image after row operation Column cipher matrice DECRYPTION Image after diciphering
22. 22. DECRYPTION STEP 2 :- (a)Sum=sum of pixel values in column 1 (b)M=Sum%b2 (c)S=M%2 (d)if S=0 then circular down shift (e)if S=1 circular up shift.
23. 23. DECRYPTION STEP 3 :- (a)Sum = Sum of pixel values in row 1 (b)M = Sum%b1 (c)S = M%2 (d)if S=0 then circular left shift (e)if S=1 then circular right shift
24. 24. DECRYPTION After all row operations the image we get the following image. Image after row operations Image after column operations
25. 25. DECRYPTION Decrypted imageDiciphered image
26. 26. DECRYPTION Enter the values of the shared key Column operations Compute the cipher matrices Deciphered image Carry out x-or operation between shuffled image and cipher matrices Row operations
27. 27. Encrypted Image Image after deciphering Decrypted image DECRYPTION
28. 28. Advantages of above encryption algorithm: Can resist exhaustive cryptanalytic attacks. Key space size is large (1088) Sensitive to even small change in values. Disadvantages of above encryption algorithm: Very high execution time. Image size has to be small. Real time applications are limited
29. 29. CONCLUSION We have achieved our aim of developing a secure algorithm that is robust and preserves the privacy of the client. Despite its limited real-time applications due to the large execution time, encryption of images is with limited number of pixels is done with maximum efficiency. Will find use in various fields such as military, multimedia messaging etc. for sending of images with limited pixel size Solution to the lengthy execution time once found, it will find widespread real-time use.
30. 30. REFERENCES [2] A.-V. Diaconu, Multiple bitstreams generation using chaotic sequences, The Annals of Duarea De Jos University of GalatiFascicle III, vol. 35, no. 1, pp. 3742, 2012. [1] A.-V. Diaconu and K. Loukhaoukha, An Improved Secure Image Encryption Algorithm Based on Rubiks Cube Principle and Digital Chaotic Cipher,2013 WEBSITES http://www.netbeans.org