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Steganography wavelet


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  • 2. STEGANOGRAPHYSteganography is the art and science of writing hiddenmessages in such a way that no one, apart from thesender and intended recipient, suspects the existence ofthe message.The word ‘steganography’ is of Greek origin and means‘concealed writing’ from the Greek words ‘stegan-xgraf-ein’.Definition:
  • 3. STEGANOGRAPHYHistory:EXAMPLE NOTED BY HERODOTUS :A man called Harpagus wanted to send a message to Cyrus, but allroads were guarded – he used a here to conceal the message in itsstomach.A trusted servant dressed as a huntsman carried the here and byword of mouth asked the recipient to cut the sewed animal.
  • 4. STEGANOGRAPHYHistory:EXAMPLE NOTED BY HERODOTUS :Histiaios, being himself detained, wished to inform Aristagoras thathe should revolt. Therefore he shaved the hair of a faithful servant andtattooed his head.once his hair had grown back, the slave traveled to Mileots wherehe had his head re-shaved and thus message was retrieved.
  • 5. In 1499 Johannes Trithemius, from Würzburg, wrote 3books “Steganographia”.In 1518 Trithemius printed 6 books, 540 pages, oncryptography and steganography. Books title:Polygraphiae.In 1665 Gaspari Schotti published the book“Steganographica”, 400pages. (New presentation ofTrithemius.)HISTORY
  • 6. Ancient Chinese wrote messages on fine silk, which was thencrunched into a tiny ball and covered in wax. The messenger thenswallowed the ball of wax.During Second World War a technique was developed to shrinkphotographically a page of text into a dot less than one millimeterin diameter, and then hide this microdot in an apparentlyinnocuous letter. (The first microdot has been spotted by FBI in1941.)HISTORY
  • 7. MODERN DIGITAL SCIENTIFIC STUDY1983 : Simmons stated the ‘prisoners problem’
  • 8. 8Steganography and WatermarkingGENERAL STEGANOGRAPHIC MODELA general model of a steganography system has alreadyemerged.Model of steganographic systems
  • 10. TEXT
  • 11. WEB based TEXT
  • 13. IMAGE
  • 15. AUDIO
  • 17. VIDEO
  • 18. STEGANOGRAPHY1.To have secure secret communication where strong cryptography is impossible.2. In some cases, for example in military applications, even the knowledge thattwo parties communicate can be of large importance. (Covert Channel)3. The health care, and especially medical imaging systems, may very muchbenefit from information hiding techniques.4. Automatic monitoring and tracking of copy-write material on WEB. (Forexample, a robot searches the Web for marked material and thereby identifiespotential illegal issues.)5. Fingerprinting applications (in order to distinguish distributed data)Uses:
  • 19. Wavelets are functions that “wave” above and below the x-axis, have1. Varying frequency,2. Limited duration,3 An average value of zero.WAVELETWavelet
  • 20. What are Wavelets? (cont’d)• There are many different wavelets:MorletHaar Daubechies
  • 21. • Simultaneous localization in time and scale- The location of the wavelet allows to explicitly representthe location of events in time.- The shape of the wavelet allows to represent differentdetail or resolution.Properties of Wavelets
  • 22. Properties of Wavelets (cont’d)• Sparsity: for functions typically found inpractice, many of the coefficients in a waveletrepresentation are either zero or very small.• Linear-time complexity: many wavelettransformations can be accomplished in O(N)time.
  • 23. Properties of Wavelets (cont’d)• Adaptability: wavelets can be adapted torepresent a wide variety of functions (e.g.,functions with discontinuities, functionsdefined on bounded domains etc.).– Well suited to problems involving images, open orclosed curves, and surfaces of just about anyvariety.– Can represent functions with discontinuities orcorners more efficiently (i.e., some have sharpcorners themselves).
  • 24. Wavelet Transforms• Continuous Wavelet Transform (CWT)• Discrete Wavelet Transform (DWT)
  • 25. CWT: Main Steps1. Take a wavelet and compare it to a section at the startof the original signal.2. Calculate a number, C, that represents how closelycorrelated the wavelet is with this section of thesignal. The higher C is, the more the similarity.
  • 26. CWT: Main Steps (cont’d)3. Shift the wavelet to the right and repeat steps 1 and 2 untilyouve covered the whole signal.
  • 27. CWT: Main Steps (cont’d)4. Scale the wavelet and repeat steps 1 through 3.5. Repeat steps 1 through 4 for all scales.
  • 28. DWT• ImageDecomposition– Scale 2– 4 subbands:• Each coeff. a 2*2area in scale 1 image• Low Frequency:• High frequencies:HL1LH1 HH1HH2LH2HL2LL24/0  2/4/  
  • 29. DWT• Image Decomposition– Parent– Children– Descendants:corresponding coeff. atfiner scales– Ancestors: correspondingcoeff. at coarser scalesHL1LH1 HH1HH2LH2HL2HL3LL3LH3 HH3
  • 30. • Image Decomposition– Feature 1:• Energy distribution similar toother Transform: Concentrated inlow frequencies– Feature 2:• Spatial self-similarity acrosssubbandsHL1LH1 HH1HH2LH2HL2HL3LL3LH3 HH3The zigzag scanning order of the subbands for encoding the significancemap.DWT
  • 31. Filterbank Structure: Decomposition
  • 32. Filterbank Structure: Reconstruction•
  • 33. Example - Haar basis (revisited)low-pass,down-samplinghigh-pass,down-sampling(9+7)/2 (3+5)/2 (9-7)/2 (3-5)/2[9 7 3 5]
  • 34. Example - Haar basis (revisited)high-pass,down-samplinglow-pass,down-sampling(8+4)/2 (8-4)/2[9 7 3 5]
  • 35. Illustrating1D Haar wavelet decompositionx x x x x x … x x…re-arrange:re-arrange:detailaverage
  • 36. Examples of lowpass/highpassanalysis filtersDaubechiesHaarh0h1h0h1
  • 37. d0 d1 d2 d3 0 0 0 0g0 g1 g2 g3 0 0 0 00 0 d0 d1 d2 d3 0 00 0 g0 g1 g2 g3 0 00 0 0 0 d0 d1 d2 d30 0 0 0 g0 g1 g2 g30 0 0 0 0 0 d0 d1 d2 d30 0 0 0 0 0 g0 g1 g2 g3Daubechies D4 forward transform matrix for 8 elementg0= d3 g1= -d2g2= d1 g0= -d0
  • 38. A note in the “Ripples in Mathematics”
  • 39. Wavelet Decomposition:ExampleLENA D4 construction
  • 40. Applications• Noise filtering• Image compression– Fingerprint compression• Image fusion• Recognition• Image matching and retrieval
  • 41. 1. Ranjan Parekh, “Principles of Multimedia” ,Chapter Image,Graphics , TataMcGraw-Hill2. Giuseppe Mastronardi, Marcello Castellano, FrancescomariaMarino, “Steganography Effects in Various Formats of Images. APreliminary Study,”3. Debnath Bhattacharyya, Poulami Das, Samir kumarBandyopadhyay and Tai-hoon Kim, “Text Steganography: A NovelApproach,”4. Barry J. Blake “Secret Language’’, pp. 72 - 113, 2010.5. Bryan Clair, "Steganography: How to Send a Secret Message“, Gary C. Kessler,"Steganography: Hiding Data Within Data" ,