Discrete fractional wavelet transform and its application to multiple encryption

Information Sciences

Volumn 223, Issue , 2013, Pages 297-316

  Bhatnagar, Gaurav ^a   Wu, Q M Jonathan ^a   Raman, Balasubramanian ^b  

^a UNIVERSITY OF WINDSOR   (Canada)

^b INDIAN INSTITUTE OF TECHNOLOGY ROORKEE   (India)

Author keywords

Encryption; Fractional Fourier transform; Fractional Wavelet transform; Multiple encryption; Wavelet transform

Indexed keywords

CHAOTIC MAP; ENCRYPTION SCHEMES; FRACTIONAL FOURIER TRANSFORMS; FRACTIONAL WAVELET TRANSFORMS; MULTIPLE IMAGE; NUMERICAL TECHNIQUES; SECURITY ANALYSIS; SIGNAL AND IMAGE PROCESSING; SYSTEM OF LINEAR EQUATIONS; TIME-FREQUENCY PLANES; TRANSIENT SIGNAL;

BIOMETRICS; CHAOTIC SYSTEMS; CRYPTOGRAPHY; IMAGE COMPRESSION; IMAGING SYSTEMS; SIGNAL PROCESSING;

WAVELET TRANSFORMS;

EID: 84870252217     PISSN: 00200255     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ins.2012.09.053     Document Type: Article

References (42)

1. J.B. Allen, and L.R. Rabinar A unified approach to short-time fourier analysis and synthesis Proceedings of IEEE 65 1977 1558 1564
2. L.B. Almeida The fractional Fourier transform and time-frequency representations IEEE Transaction on Signal Processing 42 1994 3084 3091
3. G.E. Andrews, R. Askey, and R. Roy Special Functions 1999 Cambridge University Press Cambridge
4. S. Behnia, A. Akhshani, S. Ahadpour, H. Mahmodi, and A. Akhavan A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps Physics Letters A 366 2007 391 396
5. A. Bultheel, H. Martinez, A Shattered Survey of Fractional Fourier Transform, Technical Report on Numerical Analysis and Applied Mathematics, vol. 337, Department of Computer Science, K.U. Leuven, TW, 2003, pp. 1-52 < http://nalag.cs.kuleuven.be/papers/ade/frft/manuscript.pdf >.
6. G. Bhatnagar, and B. Raman Encryption based robust watermarking in fractional wavelet domain M. Grgic, K. Delac, M. Ghanbari, Recent Advances in Multimedia Signal Processing and Communication vol. 231 2009 Springer Verlag 375 416
7. G. Bhatnagar, Q.M.J. Wu, and B. Raman A novel image encryption framework based on markov map and singular value decomposition Proceedings of International Conference on Image Analysis and Recognition 2 2011 286 296
8. G. Bhatnagar, Q.M.J. Wu, and B. Raman Image and video encryption based on dual space filling curves The Computer Journal 55 6 2012 667 685
9. G. Bhatnagar, and Q.M.J. Wu Selective image encryption based on pixels of interest and singular value decomposition Digital Signal Processing 22 4 2012 648 663
10. H.D. Bie Fourier transform and related integral transforms in superspace Journal of Mathematical Analysis and Applications 345 1 2008 147 164
11. T. Blu, M. Unser, The fractional spline wavelets transform: definition end implementation, in: Proceedings of IEEE International Conference on Acoustics, Speech, and Signal Processing, 2000, pp. 512-515.
12. R.N. Bracewell The Fourier Transform and Its Applications 1986 McGraw-Hill
13. C.B. Burckhardt Use of a random phase mask for the recording of Fourier transform holograms of data masks Applied Optics 9 1970 695 700
14. L. Chen, and D. Zhao Optical image encryption based on fractional wavelet transforms Optics Communications 254 4-6 2005 361 367 (Pubitemid 41345190)
15. C.K. Chui Wavelets: A Tutorial in Theory and Applications 1992 Academic Press
16. I. Daubechies The wavelet transform time frequency localization and signal analysis IEEE Transactions on Information Theory 36 1990 961 1005 (Pubitemid 20738359)
17. I. Daubechies Ten Lectures Notes on Wavelet 1992 SIAM Philadelphia p. 61
18. B. Furht, D. Socek, Multimedia Security, Encryption Techniques, IEC Comprehensive Report on Information Security, International Engineering Consortium, Chicago, IL, 2003.
19. H. Gao, Y. Zhang, S. Liang, and D. Li A new chaotic algorithm for image encryption Chaos, Solitons and Fractals 29 2006 393 399 (Pubitemid 43152206)
20. T. Gaoa, and Z. Chen A new image encryption algorithm based on hyper-chaos Physics Letters A 372 2008 394 400
21. M.Z. He, L.Z. Cai, Q. Liu, X.C. Wang, and X.F. Meng Multiple image encryption and watermarking by random phase matching Optics Communications 247 2005 29 37 (Pubitemid 40266292)
22. M.A. Jafarizadeh, S. Behnia, S. Khorram, and H. Nagshara Hierarchy of chaotic maps with an invariant measure Journal of Statistical Physics 104 2001 1013 1028
23. A. Kerckhoffs La cryptographie militaire Journal des sciences militaires IX 1883 5 83
24. 2 and applications to differential equations Journal of Mathematical Analysis and Applications 136 2 1988 404 418
25. S. Lian MultiMedia Content Encryption, Techniques and Applications 2008 CRC Press Boca Raton, FL
26. S.G. Mallat A theory for multiresolution signal decomposition: the wavelet representation IEEE Transactions on Pattern Analysis and Machine Intelligence 11 1989 674 693
27. R.J. Marks, I.A. Gravagne, and J.M. Davis A generalized Fourier transform and convolution on time scales Journal of Mathematical Analysis and Applications 340 2 2008 901 919
28. A.C. McBride, and F.H. Kerr On namias fractional Fourier transforms IMA Journal of Applied Mathematics 39 1987 159 175
29. D. Mendlovic, Z. Zalevsky, D. Mas, J. Garca, and C. Ferreira Fractional wavelet transform Applied Optics 36 1997 4801 4806 (Pubitemid 127615615)
30. X.F. Menga, L.Z. Caia, Y.R. Wanga, X.L. Yanga, X.F. Xua, G.Y. Donga, and X.X. Shena Digital image synthesis and multiple-image encryption based on parameter multiplexing and phase-shifting interferometry Optics and Lasers in Engineering 47 2009 96 102
31. V. Namias The fractional order Fourier transform and its application to quantum mechanics Journal of the Institute of Mathematics and its Applications 25 1980 241 265
32. H.M. Ozaktas, M.A. Kutay, and Z. Zalevsky The Fractional Fourier Transform with Applications in Optics and Signal Processing 2000 John Wiley & Sons
33. M. Pollicott, and M. Yuri Dynamical Systems and Ergodic Theory 1998 London Mathematical Society Student Text Series Cambridge
34. M.R. Portnoff Time-frequency representation of digital signals and systems based on short-time fourier analysis IEEE Transactions on ASSP 28 1980 55 69
35. G. Situ Position multiplexing for multiple-image encryption Journal of Optics A: Pure and Applied Optice 8 2006 391 397 (Pubitemid 43800782)
36. C.E. Shannon Communication theory of secrecy system Bell System Technical Journal 28 1949 656 715
37. A.G. Smirnov On localization properties of Fourier transforms of hyperfunctions Journal of Mathematical Analysis and Applications 351 1 2009 57 69
38. I.N. Sneddon Fourier Transforms 1995 Dover New York
39. H.G. Stark Continuous wavelet transform and continuous multiscale analysis Journal of Mathematical Analysis and Applications 169 1 1992 179 196
40. X. Tong, and M. Cui Image encryption scheme based on 3D baker with dynamical compound chaotic sequence cipher generator Signal Processing 89 2009 480 491
41. X. You, L. Du, Y. Cheung, and Q. Chen A blind watermarking scheme using new nontensor product wavelet filter banks IEEE Transactions on Image Processing 19 2 2010 3271 3284
42. H. Zhou, and X.T. Ling Generating chaotic secure sequences with desired statistical properties and high security International Journal of Bifurcation and Chaos 1 1997 205 213