statistics and steganalysis
play

Statistics and Steganalysis CSM25 Secure Information Hiding Dr Hans - PowerPoint PPT Presentation

Aug 25, 2023 •452 likes •1.51k views

Statistics and Steganalysis CSM25 Secure Information Hiding Dr Hans Georg Schaathun University of Surrey Spring 2009 Week 2 Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 Week 2 1 / 54 Learning Outcomes After this

  1. Visual Steganalysis The Histogram Outline Visual Steganalysis 1 The LSB plane The Histogram Limitations Statistics 2 Statistical models Pairs of Values I visual approach Error types Postlogue 3 Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 17 / 54

  2. Visual Steganalysis The Histogram A typical image Image histogram made by imhist in Matlab Gives number of pixels per colour-value Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 18 / 54

  3. Visual Steganalysis The Histogram And a stego-image Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 19 / 54

  4. Visual Steganalysis The Histogram And a stego-image Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 19 / 54

  5. Visual Steganalysis The Histogram What happened? Histogram of stego-image: More ragged Every other bar sticks out. Why? 50.8% 1-s in the binary message. Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 20 / 54

  6. Visual Steganalysis The Histogram What happened? Histogram of stego-image: More ragged Every other bar sticks out. Why? 50.8% 1-s in the binary message. Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 20 / 54

  7. Visual Steganalysis The Histogram What happened? Histogram of stego-image: More ragged Every other bar sticks out. Why? 50.8% 1-s in the binary message. Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 20 / 54

  8. Visual Steganalysis The Histogram What happened? Histogram of stego-image: More ragged Every other bar sticks out. Why? 50.8% 1-s in the binary message. Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 20 / 54

  9. Visual Steganalysis The Histogram What happened? Histogram of stego-image: More ragged Every other bar sticks out. Why? 50.8% 1-s in the binary message. Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 20 / 54

  10. Visual Steganalysis The Histogram What is characteristic? Pairs of values Consider colour 2 i ( i = 0 , 1 , . . . , 127) What happens under LSB embedding? 2 i → 2 i , 2 i + 1 Never 2 i → 2 i − 1. Likewise 2 i + 1 → 2 i , 2 i + 1 ( 2 i , 2 i + 1 ) is a Pair of Values A pixel in ( 2 i , 2 i + 1 ) before embedding ... is a pixel in ( 2 i , 2 i + 1 ) after embedding Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 21 / 54

  11. Visual Steganalysis The Histogram What is characteristic? Pairs of values Consider colour 2 i ( i = 0 , 1 , . . . , 127) What happens under LSB embedding? 2 i → 2 i , 2 i + 1 Never 2 i → 2 i − 1. Likewise 2 i + 1 → 2 i , 2 i + 1 ( 2 i , 2 i + 1 ) is a Pair of Values A pixel in ( 2 i , 2 i + 1 ) before embedding ... is a pixel in ( 2 i , 2 i + 1 ) after embedding Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 21 / 54

  12. Visual Steganalysis The Histogram What is characteristic? Pairs of values Consider colour 2 i ( i = 0 , 1 , . . . , 127) What happens under LSB embedding? 2 i → 2 i , 2 i + 1 Never 2 i → 2 i − 1. Likewise 2 i + 1 → 2 i , 2 i + 1 ( 2 i , 2 i + 1 ) is a Pair of Values A pixel in ( 2 i , 2 i + 1 ) before embedding ... is a pixel in ( 2 i , 2 i + 1 ) after embedding Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 21 / 54

  13. Visual Steganalysis Limitations Outline Visual Steganalysis 1 The LSB plane The Histogram Limitations Statistics 2 Statistical models Pairs of Values I visual approach Error types Postlogue 3 Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 22 / 54

  14. Visual Steganalysis Limitations Visual methods Advantages and Limitations Human perception is very flexible can exploit the unexpected you don’t have to know what you look for Manual work the process cannot be automated or computerised How do you check a million images? Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 23 / 54

  15. Statistics Outline Visual Steganalysis 1 Statistics 2 Statistical models Pairs of Values I visual approach Error types Postlogue 3 Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 24 / 54

  16. Statistics Statistical models Outline Visual Steganalysis 1 The LSB plane The Histogram Limitations Statistics 2 Statistical models Pairs of Values I visual approach Error types Postlogue 3 Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 25 / 54

  17. Statistics Statistical models The remit of statistics Statistics can estimate ‘normal’ behaviour and compare behaviours Advantages Automated decisions Extract detail Exact, quantifiable features Aggregate measures Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 26 / 54

  18. Statistics Statistical models The remit of statistics Statistics can estimate ‘normal’ behaviour and compare behaviours Advantages Automated decisions Extract detail Exact, quantifiable features Aggregate measures Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 26 / 54

  19. Statistics Statistical models The fundamental question Wendy the Warden intercepts an image. Depends on a model for natural images Statistical models and probability distributions With a perfect model, cipher with ciphertexts distributed as natural images If Wendy has a better model than Alice and Bob, then she can do effective steganalysis In reality, we do not know what a natural image looks like Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 27 / 54

  20. Statistics Statistical models The fundamental question Wendy the Warden intercepts an image. Is the image a stegogramme? Depends on a model for natural images Statistical models and probability distributions With a perfect model, cipher with ciphertexts distributed as natural images If Wendy has a better model than Alice and Bob, then she can do effective steganalysis In reality, we do not know what a natural image looks like Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 27 / 54

  21. Statistics Statistical models The fundamental question Wendy the Warden intercepts an image. Is it a probable, natural image? Is it a probable stegogramme? Depends on a model for natural images Statistical models and probability distributions With a perfect model, cipher with ciphertexts distributed as natural images If Wendy has a better model than Alice and Bob, then she can do effective steganalysis In reality, we do not know what a natural image looks like Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 27 / 54

  22. Statistics Statistical models The fundamental question Wendy the Warden intercepts an image. Is it a probable, natural image? Is it a probable stegogramme? Depends on a model for natural images Statistical models and probability distributions With a perfect model, cipher with ciphertexts distributed as natural images If Wendy has a better model than Alice and Bob, then she can do effective steganalysis In reality, we do not know what a natural image looks like Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 27 / 54

  23. Statistics Statistical models The fundamental question Wendy the Warden intercepts an image. Is it a probable, natural image? Is it a probable stegogramme? Depends on a model for natural images Statistical models and probability distributions With a perfect model, cipher with ciphertexts distributed as natural images If Wendy has a better model than Alice and Bob, then she can do effective steganalysis In reality, we do not know what a natural image looks like Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 27 / 54

  24. Statistics Statistical models The fundamental question Wendy the Warden intercepts an image. Is it a probable, natural image? Is it a probable stegogramme? Depends on a model for natural images Statistical models and probability distributions With a perfect model, cipher with ciphertexts distributed as natural images If Wendy has a better model than Alice and Bob, then she can do effective steganalysis In reality, we do not know what a natural image looks like Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 27 / 54

  25. Statistics Statistical models The fundamental question Wendy the Warden intercepts an image. Is it a probable, natural image? Is it a probable stegogramme? Depends on a model for natural images Statistical models and probability distributions With a perfect model, cipher with ciphertexts distributed as natural images If Wendy has a better model than Alice and Bob, then she can do effective steganalysis In reality, we do not know what a natural image looks like Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 27 / 54

  26. Statistics Pairs of Values Outline Visual Steganalysis 1 The LSB plane The Histogram Limitations Statistics 2 Statistical models Pairs of Values I visual approach Error types Postlogue 3 Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 28 / 54

  27. Statistics Pairs of Values Pairs of Values The statistic Image X . Random variable Y k = # { ( x , y ) | X xy = k } The Y k -s is the Histogramme. Recall that ( 2 l , 2 l + 1 ) is a pair of values. First 7 pixel bits determined by image colour. i.e. which pair Last bit (LSB) determined by message i.e. which half of the pair Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 29 / 54

  28. Statistics Pairs of Values Pairs of Values Expected behaviour Sum Y 2 l + Y 2 l + 1 unaffected by embedding. For a random message steganogram, Expect 50-50 2 l and 2 l + 1 i.e. E ( Y 2 l ) = E ( Y 2 l + 1 ) = 1 2 ( Y 2 l + Y 2 l + 1 ) For a natural image, what can we expect? In a given image, we can observe Y 2 l . Is the observation probable? Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 30 / 54

  29. Statistics Pairs of Values Pairs of Values Expected behaviour Sum Y 2 l + Y 2 l + 1 unaffected by embedding. For a random message steganogram, Expect 50-50 2 l and 2 l + 1 i.e. E ( Y 2 l ) = E ( Y 2 l + 1 ) = 1 2 ( Y 2 l + Y 2 l + 1 ) For a natural image, what can we expect? In a given image, we can observe Y 2 l . Is the observation probable? Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 30 / 54

  30. Statistics Pairs of Values Pairs of Values Expected behaviour Sum Y 2 l + Y 2 l + 1 unaffected by embedding. For a random message steganogram, Expect 50-50 2 l and 2 l + 1 i.e. E ( Y 2 l ) = E ( Y 2 l + 1 ) = 1 2 ( Y 2 l + Y 2 l + 1 ) For a natural image, what can we expect? In a given image, we can observe Y 2 l . Is the observation probable? Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 30 / 54

  31. Statistics Pairs of Values Pairs of Values Expected behaviour Sum Y 2 l + Y 2 l + 1 unaffected by embedding. For a random message steganogram, Expect 50-50 2 l and 2 l + 1 i.e. E ( Y 2 l ) = E ( Y 2 l + 1 ) = 1 2 ( Y 2 l + Y 2 l + 1 ) For a natural image, what can we expect? In a given image, we can observe Y 2 l . Is the observation probable? Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 30 / 54

  32. Statistics Pairs of Values Hypothesis testing The principle We have two possible hypotheses H 0 The image is a steganogram with random message 1 Known distribution: E ( Y 2 l ) = E ( Y 2 l + 1 ) = 1 2 ( Y 2 l + Y 2 l + 1 ) H 1 The image is a natural image 2 Unknown distribution Statistics allows us to answer is the observed Y 2 l -s likely under H 0 ? We cannot ask a similar question under H 1 . Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 31 / 54

  33. Statistics Pairs of Values Hypothesis testing The principle We have two possible hypotheses H 0 The image is a steganogram with random message 1 Known distribution: E ( Y 2 l ) = E ( Y 2 l + 1 ) = 1 2 ( Y 2 l + Y 2 l + 1 ) H 1 The image is a natural image 2 Unknown distribution Statistics allows us to answer is the observed Y 2 l -s likely under H 0 ? We cannot ask a similar question under H 1 . Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 31 / 54

  34. Statistics Pairs of Values Hypothesis testing The principle We have two possible hypotheses H 0 The image is a steganogram with random message 1 Known distribution: E ( Y 2 l ) = E ( Y 2 l + 1 ) = 1 2 ( Y 2 l + Y 2 l + 1 ) H 1 The image is a natural image 2 Unknown distribution Statistics allows us to answer is the observed Y 2 l -s likely under H 0 ? We cannot ask a similar question under H 1 . Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 31 / 54

  35. Statistics Pairs of Values The χ 2 test Statistical hypothesis tests exist for many purposes The χ 2 test can compare different distributions i.e. the H 0 distribution and the observed distribution aggregate several numbers i.e. Y 2 l for every l Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 32 / 54

  36. Statistics Pairs of Values The χ 2 statistic Several random variable F 0 , F 1 , . . . , F m Known expectations E ( F 0 ) , E ( F 1 ) , . . . , E ( F m ) m ( F o − E ( F o )) 2 � S = E ( F o ) i = 0 Definition 127 127 ( Y 2 l − 1 2 ( Y 2 l + Y 2 l + 1 )) 2 1 2 ( Y 2 l − Y 2 l + 1 ) 2 � � S PoV = = 1 Y 2 l + Y 2 l + 1 2 ( Y 2 l + Y 2 l + 1 ) l = 0 l ∈ 0 χ 2 distributed with m degrees of freedom Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 33 / 54

  37. Statistics Pairs of Values Making Conclusions If the observed S is likely under χ 2 distribution, the assumed distribution (and thus H 0 ) is plausible If the observed S is unlikely under χ 2 distribution, H 0 is implausible Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 34 / 54

  38. Statistics Pairs of Values Making Conclusions If the observed S is likely under χ 2 distribution, the assumed distribution (and thus H 0 ) is plausible If the observed S is unlikely under χ 2 distribution, H 0 is implausible Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 34 / 54

  39. Statistics Pairs of Values The χ 2 PDF Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 35 / 54

  40. Statistics Pairs of Values The Pairs-of-Values χ 2 Distribution χ 2 PDF 127 degrees of freedom Red: 2% prob. +Green: 5% +Blue: 10% Cumulative Density Function (CDF) Area under the curve Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 36 / 54

  41. Statistics Pairs of Values The Pairs-of-Values χ 2 Distribution χ 2 PDF 127 degrees of freedom Red: 2% prob. +Green: 5% +Blue: 10% Cumulative Density Function (CDF) Area under the curve Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 36 / 54

  42. Statistics Pairs of Values The Pairs-of-Values χ 2 Distribution χ 2 PDF 127 degrees of freedom Red: 2% prob. +Green: 5% +Blue: 10% Cumulative Density Function (CDF) Area under the curve Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 36 / 54

  43. Statistics Pairs of Values The p -value Let S be a stochastic χ 2 distributed variable Let s be the observed χ 2 statistic Define p -value: p = P ( S < s ) I.e. low p -value ⇒ s is unusually small Improbable if the image is a stegogramme. Conclusion: probably natural image Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 37 / 54

  44. Statistics Pairs of Values p -value illustrated We read the statistic ( χ 2 ) on the x -axis The p -value is the area under the PDF to the right Compute it with chi2cdf Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 38 / 54

  45. Statistics Pairs of Values Corrections You may have to exclude pixel values which do not occur have at least four pixels of each pair of values used This keeps the χ 2 distribution a good approximation This reduces the degrees of freedom Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 39 / 54

  46. Statistics Pairs of Values χ 2 in Matlab Defined in the Statistics toolbox Simplified functions available on website: chi2pdf (the PDF) chi2cdf(s,v) – P ( S ≤ s ) when S ∼ χ 2 ( v ) chi2inv(p,v) – s such that P ( S ≤ s ) = p Note that the p -value is P ( S ≥ s ) = 1 − P ( S ≤ s ) use chi2cdf to calculate it Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 40 / 54

  47. Statistics Pairs of Values χ 2 in Matlab Defined in the Statistics toolbox Simplified functions available on website: chi2pdf (the PDF) chi2cdf(s,v) – P ( S ≤ s ) when S ∼ χ 2 ( v ) chi2inv(p,v) – s such that P ( S ≤ s ) = p Note that the p -value is P ( S ≥ s ) = 1 − P ( S ≤ s ) use chi2cdf to calculate it Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 40 / 54

  48. Statistics I visual approach Outline Visual Steganalysis 1 The LSB plane The Histogram Limitations Statistics 2 Statistical models Pairs of Values I visual approach Error types Postlogue 3 Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 41 / 54

  49. Statistics I visual approach Part-image The χ 2 statistic is effective when the image is full of hidden information What happens if only a small part is used? Basic LSB embedding uses the first N pixels We calculate the χ 2 and p values for every N The result can be plotted use plot or fplot in Matlab Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 42 / 54

  50. Statistics I visual approach Plots No message χ 2 statistic p -value Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 43 / 54

  51. Statistics I visual approach Plots 30% of capacity χ 2 statistic p -value Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 44 / 54

  52. Statistics I visual approach Plots 60% of capacity χ 2 statistic p -value Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 45 / 54

  53. Statistics I visual approach Plots 100% of capacity χ 2 statistic p -value Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 46 / 54

  54. Statistics Error types Outline Visual Steganalysis 1 The LSB plane The Histogram Limitations Statistics 2 Statistical models Pairs of Values I visual approach Error types Postlogue 3 Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 47 / 54

  55. Statistics Error types Classification errors Steganalysis is a binary classification problem identify an unknown object (image) as either suspicious innocent Two error types False positive an innocent image wrongly accused False negative a «guilty» image not identified Which type is most severe? Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 48 / 54

  56. Statistics Error types Classification errors Steganalysis is a binary classification problem identify an unknown object (image) as either suspicious innocent Two error types False positive an innocent image wrongly accused False negative a «guilty» image not identified Which type is most severe? Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 48 / 54

  57. Statistics Error types Hypothesis testing and errors Hypothesis testing is a recurring theme in statistics. Typical null hypotheses Treatment A makes patients recover no more quickly than no treatment. The climate in South-East Britain is as warm/cold today as it was a 100 years ago. The image sent by Alice is a natural (innocent) image. When the hypothesis has been phrased, experiments can tell us whether it is plausible or not. Wrongly accepting the null hypothesis is the least serious error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 49 / 54

  58. Statistics Error types Hypothesis testing and errors Hypothesis testing is a recurring theme in statistics. Typical null hypotheses Treatment A makes patients recover no more quickly than no treatment. The climate in South-East Britain is as warm/cold today as it was a 100 years ago. The image sent by Alice is a natural (innocent) image. When the hypothesis has been phrased, experiments can tell us whether it is plausible or not. Wrongly accepting the null hypothesis is the least serious error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 49 / 54

  59. Statistics Error types Hypothesis testing and errors Hypothesis testing is a recurring theme in statistics. Typical null hypotheses Treatment A makes patients recover no more quickly than no treatment. The climate in South-East Britain is as warm/cold today as it was a 100 years ago. The image sent by Alice is a natural (innocent) image. When the hypothesis has been phrased, experiments can tell us whether it is plausible or not. Wrongly accepting the null hypothesis is the least serious error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 49 / 54

  60. Statistics Error types Hypothesis testing and errors Hypothesis testing is a recurring theme in statistics. Typical null hypotheses Treatment A makes patients recover no more quickly than no treatment. The climate in South-East Britain is as warm/cold today as it was a 100 years ago. The image sent by Alice is a natural (innocent) image. When the hypothesis has been phrased, experiments can tell us whether it is plausible or not. Wrongly accepting the null hypothesis is the least serious error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 49 / 54

  61. Statistics Error types Hypothesis testing and errors Hypothesis testing is a recurring theme in statistics. Typical null hypotheses Treatment A makes patients recover no more quickly than no treatment. The climate in South-East Britain is as warm/cold today as it was a 100 years ago. The image sent by Alice is a natural (innocent) image. When the hypothesis has been phrased, experiments can tell us whether it is plausible or not. Wrongly accepting the null hypothesis is the least serious error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 49 / 54

  62. Statistics Error types Hypothesis testing and errors Hypothesis testing is a recurring theme in statistics. Typical null hypotheses Treatment A makes patients recover no more quickly than no treatment. The climate in South-East Britain is as warm/cold today as it was a 100 years ago. The image sent by Alice is a natural (innocent) image. When the hypothesis has been phrased, experiments can tell us whether it is plausible or not. Wrongly accepting the null hypothesis is the least serious error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 49 / 54

  63. Statistics Error types Hypothesis testing and errors Hypothesis testing is a recurring theme in statistics. Typical null hypotheses Treatment A makes patients recover no more quickly than no treatment. The climate in South-East Britain is as warm/cold today as it was a 100 years ago. The image sent by Alice is a natural (innocent) image. When the hypothesis has been phrased, experiments can tell us whether it is plausible or not. Wrongly accepting the null hypothesis is the least serious error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 49 / 54

  64. Statistics Error types Hypothesis testing and errors Hypothesis testing is a recurring theme in statistics. Typical null hypotheses Treatment A makes patients recover no more quickly than no treatment. The climate in South-East Britain is as warm/cold today as it was a 100 years ago. The image sent by Alice is a natural (innocent) image. When the hypothesis has been phrased, experiments can tell us whether it is plausible or not. Wrongly accepting the null hypothesis is the least serious error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 49 / 54

  65. Statistics Error types Asymmetry of hypothesis testing Treatment A makes patients recover more quickly than no treatment. One error is more serious than another. Type I: Accepting the hypothesis when it is wrong Patients get ineffective (or unhealthy) medicine. Type II: Rejecting the hypothesis when it is right More research will be made to optimise the treatment. H 0 retained H 0 rejected H 0 true No error Error Type I H 0 false Error Type II No error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 50 / 54

  66. Statistics Error types Asymmetry of hypothesis testing Treatment A makes patients recover more quickly than no treatment. One error is more serious than another. Type I: Accepting the hypothesis when it is wrong Patients get ineffective (or unhealthy) medicine. Type II: Rejecting the hypothesis when it is right More research will be made to optimise the treatment. H 0 retained H 0 rejected H 0 true No error Error Type I H 0 false Error Type II No error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 50 / 54

  67. Statistics Error types Asymmetry of hypothesis testing Treatment A makes patients recover more quickly than no treatment. One error is more serious than another. Type I: Accepting the hypothesis when it is wrong Patients get ineffective (or unhealthy) medicine. Type II: Rejecting the hypothesis when it is right More research will be made to optimise the treatment. H 0 retained H 0 rejected H 0 true No error Error Type I H 0 false Error Type II No error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 50 / 54

  68. Statistics Error types Asymmetry of hypothesis testing Treatment A makes patients recover more quickly than no treatment. One error is more serious than another. Type I: Accepting the hypothesis when it is wrong Patients get ineffective (or unhealthy) medicine. Type II: Rejecting the hypothesis when it is right More research will be made to optimise the treatment. H 0 retained H 0 rejected H 0 true No error Error Type I H 0 false Error Type II No error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 50 / 54

  69. Statistics Error types Asymmetry of hypothesis testing Treatment A makes patients recover more quickly than no treatment. One error is more serious than another. Type I: Accepting the hypothesis when it is wrong Patients get ineffective (or unhealthy) medicine. Type II: Rejecting the hypothesis when it is right More research will be made to optimise the treatment. H 0 retained H 0 rejected H 0 true No error Error Type I H 0 false Error Type II No error Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2009 – Week 2 50 / 54

Recommend

Statistics and Steganalysis CSM25 Secure Information Hiding Dr Hans Georg Schaathun University

Statistics and Steganalysis CSM25 Secure Information Hiding Dr Hans Georg Schaathun University

Statistics and Steganalysis CSM25 Secure Information Hiding Dr Hans Georg Schaathun University of Surrey Spring 2007 Dr Hans Georg Schaathun Statistics and Steganalysis Spring 2007 1 / 52 Learning Outcomes After this sessions, everyone

1.78k views • 150 slides
Steganography and Steganalysis in digital age Tom Pevn Agent Technology Center, CTU 3rd

Steganography and Steganalysis in digital age Tom Pevn Agent Technology Center, CTU 3rd

Steganography and Steganalysis in digital age Tom Pevn Agent Technology Center, CTU 3rd December 2009 T. Pevn | Steganography and Steganalysis 1/30 Outline 1 Introduction What is steganography and steganalysis Definition of security

310 views • 30 slides
Steganalysis by Ensemble Classifiers with Boosting by Regression, and Post-Selection of Features

Steganalysis by Ensemble Classifiers with Boosting by Regression, and Post-Selection of Features

Steganalysis by Ensemble Classifiers - Marc Chaumont - ICIP2012 Steganalysis by Ensemble Classifiers with Boosting by Regression, and Post-Selection of Features Marc Chaumont, Sarra Kouider LIRMM, Montpellier, France October 2, 2012 IEEE

376 views • 26 slides
A Two-Factor Error Model for Quantitative Steganalysis Security, Steganography and Watermarking

A Two-Factor Error Model for Quantitative Steganalysis Security, Steganography and Watermarking

A TWO-FACTOR ERROR MODEL FOR QUANTITATIVE STEGANALYSIS A Two-Factor Error Model for Quantitative Steganalysis Security, Steganography and Watermarking of Multimedia Contents SPIE 2006 San Jos California USA Rainer Bhme

574 views • 29 slides
Modern Steganalysis Can Detect YASS Jan Kodovsk, Tom Pevn, Jessica Fridrich January 18,

Modern Steganalysis Can Detect YASS Jan Kodovsk, Tom Pevn, Jessica Fridrich January 18,

Modern Steganalysis Can Detect YASS Jan Kodovsk, Tom Pevn, Jessica Fridrich January 18, 2010 / SPIE Modern Steganalysis Can Detect YASS 1 / 13 YASS Curriculum Vitae Birth Location: University of California, Santa Barbara Birth

668 views • 19 slides
Pooled steganalysis in JPEG: how to deal with the spreading strategy? Ahmad ZAKARIA 1 , 2 , Marc

Pooled steganalysis in JPEG: how to deal with the spreading strategy? Ahmad ZAKARIA 1 , 2 , Marc

Pooled steganalysis in JPEG: how to deal with the spreading strategy? Pooled steganalysis in JPEG: how to deal with the spreading strategy? Ahmad ZAKARIA 1 , 2 , Marc CHAUMONT 1 , 4 , G erard SUBSOL 1 , 3 LIRMM 1 , Univ Montpellier 2 , CNRS 3 ,

483 views • 26 slides
Steganalysis in high dimensions: Fusing classifiers built on random subspaces Jan Kodovsk,

Steganalysis in high dimensions: Fusing classifiers built on random subspaces Jan Kodovsk,

Steganalysis in high dimensions: Fusing classifiers built on random subspaces Jan Kodovsk, Jessica Fridrich January 25, 2011 / SPIE Steganalysis in high dimensions:, Fusing classifiers built on random subspaces 1 / 14 Motivation Modern

536 views • 19 slides
A General Framework for the Structural Steganalysis of LSB Replacement Andrew Ker

A General Framework for the Structural Steganalysis of LSB Replacement Andrew Ker

A General Framework for the Structural Steganalysis of LSB Replacement Andrew Ker adk@comlab.ox.ac.uk Royal Society University Research Fellow Oxford University Computing Laboratory 7 th Information Hiding Workshop 8 June 2005 A General

663 views • 42 slides
Towards dependable steganalysis Tom Pevn a , c , Andrew D. Ker b a Cisco systems, Inc.,

Towards dependable steganalysis Tom Pevn a , c , Andrew D. Ker b a Cisco systems, Inc.,

Towards dependable steganalysis Tom Pevn a , c , Andrew D. Ker b a Cisco systems, Inc., Cognitive Research Team in Prague, CZ b Department of Computer Science, University of Oxford, UK c Department of Computers, CVUT in Prague, CZ 10th

796 views • 26 slides
Image Forensics and Steganalysis (Hans) Georg Schaathun Department of Computing University of

Image Forensics and Steganalysis (Hans) Georg Schaathun Department of Computing University of

Image Forensics and Steganalysis (Hans) Georg Schaathun Department of Computing University of Surrey 26 June 2009 (Hans) Georg Schaathun Image Forensics and Steganalysis 26 June 2009 1 / 47 Outline Examples 1 Tampering Different

1.15k views • 86 slides
Optimizing Pixel Predictors for Steganalysis Vojtch Holub and Jessica Fridrich Dept. of

Optimizing Pixel Predictors for Steganalysis Vojtch Holub and Jessica Fridrich Dept. of

Optimizing Pixel Predictors for Steganalysis Vojtch Holub and Jessica Fridrich Dept. of Electrical and Computer Engineering SUNY Binghamton, New York IS&amp;T / SPIE 2012, San Francisco, CA Steganography The art of secret communication

252 views • 21 slides
Batch Steganography and Pooled Steganalysis Andrew Ker adk@comlab.ox.ac.uk Royal Society

Batch Steganography and Pooled Steganalysis Andrew Ker adk@comlab.ox.ac.uk Royal Society

Batch Steganography and Pooled Steganalysis Andrew Ker adk@comlab.ox.ac.uk Royal Society University Research Fellow Oxford University Computing Laboratory 8 th Information Hiding Workshop 11 July 2006 The Prisoners Problem

820 views • 16 slides
The Challenges of Rich Features in Universal Steganalysis Tom Pevn a and Andrew D. Ker b a

The Challenges of Rich Features in Universal Steganalysis Tom Pevn a and Andrew D. Ker b a

The Challenges of Rich Features in Universal Steganalysis Tom Pevn a and Andrew D. Ker b a Agent Technology Center, Czech Technical University in Prague, Czech Republic. a Department of Computer Science, Oxford University, England. 7th

465 views • 20 slides
Quantitative Evaluation of Pairs and RS Steganalysis Andrew Ker Oxford University Computing

Quantitative Evaluation of Pairs and RS Steganalysis Andrew Ker Oxford University Computing

Quantitative Evaluation of Pairs and RS Steganalysis Andrew Ker Oxford University Computing Laboratory adk@comlab.ox.ac.uk Royal Society University Research Fellow / Junior Research Fellow at University College, Oxford SPIE EI04 19

455 views • 18 slides
On Completeness of Feature Spaces in Blind Steganalysis Jan Kodovsk y Jessica Fridrich

On Completeness of Feature Spaces in Blind Steganalysis Jan Kodovsk y Jessica Fridrich

Introduction Feature Correction Method (FCM) Experimental results On Completeness of Feature Spaces in Blind Steganalysis Jan Kodovsk y Jessica Fridrich September 23 / MM&amp;SEC 2008 Kodovsk y, Fridrich On Completeness of Feature

575 views • 19 slides
Statistics for Social Sciences I: Introduction to Statistics Introduction to Statistics

Statistics for Social Sciences I: Introduction to Statistics Introduction to Statistics

Undergraduate Degree Programme in International Studies Statistics for Social Sciences I: Introduction to Statistics Introduction to Statistics Motivation: uses of statistics Surveys Economic predictions Poverty indices Decision making

534 views • 24 slides
Statistics 3-1 Definitions Statistics is a branch of Mathematics

Statistics 3-1 Definitions Statistics is a branch of Mathematics

Statistics 3-1 Definitions Statistics is a branch of Mathematics that deals collecting, analyzing, summarizing, and presenting data to help in the decision-making process. Statistics is applied in all

452 views • 17 slides
Who we are? OECD STATISTICS ESTONIA AUSTRALIAN BUREAU OF STATISTICS STATISTICS NEW ZEALAND

Who we are? OECD STATISTICS ESTONIA AUSTRALIAN BUREAU OF STATISTICS STATISTICS NEW ZEALAND

UPDATE ON THE ACTIVITIES OF THE OECD&quot;S STATISTICAL INFORMATION SYSTEM COLLABORATION COMMUNITY MSIS2013 By Jonathan Challener Who we are? OECD STATISTICS ESTONIA AUSTRALIAN BUREAU OF STATISTICS STATISTICS NEW ZEALAND EUROPEAN COMMISSION

415 views • 18 slides
Statistics Liberia Office of National Statistics The compilation of External Trade

Statistics Liberia Office of National Statistics The compilation of External Trade

UNITED NATIONS DEPARTMENT OF ECONOMIC AND SOCIAL AFFAIRS STATISTICS DIVISION Workshop on compilation of international merchandise trade statistics, Abuja, Nigeria, 30 aot - 2 septembre 2005 Country Presentation Statistics Liberia Office

68 views • 4 slides
The Statistics Network The Statistics Network Statistics network Compute servers Desktop PCs

The Statistics Network The Statistics Network Statistics network Compute servers Desktop PCs

Where are my files? The Statistics Network The Statistics Network Statistics network Compute servers Desktop PCs fs0x: /homes Susan Hutchinson (Oxford) Computing in Statistics October 2018 1/1 Where are my files? Your local desktop

598 views • 16 slides
1 Practical Information 2 Introduction to Statistics Per Bruun Brockhoff 3 Descriptive Statistics:

1 Practical Information 2 Introduction to Statistics Per Bruun Brockhoff 3 Descriptive Statistics:

Agenda Course 02402 Introduction to Statistics Lecture 1: Introduction to Statistics 1 Practical Information 2 Introduction to Statistics Per Bruun Brockhoff 3 Descriptive Statistics: Summary Statistics DTU Informatics Building 305 - room 110

194 views • 5 slides
Quality Assurance in Official Statistics Directorate of Economics &amp; Statistics, Planning

Quality Assurance in Official Statistics Directorate of Economics &amp; Statistics, Planning

Quality Assurance in Official Statistics Directorate of Economics &amp; Statistics, Planning Department, Govt. of Maharashtra 1 Official Statistics Background Official Statistics is Statistics derived by the Government agencies from

348 views • 11 slides
Statistics Sierra Leone Statistics Sierra Leone PRESENTATION : Compilation process of Sierra

Statistics Sierra Leone Statistics Sierra Leone PRESENTATION : Compilation process of Sierra

UNITED NATIONS DEPARTMENT OF ECONOMIC AND SOCIAL AFFAIRS STATISTICS DIVISION Workshop on compilation of international merchandise trade statistics, Abuja, Nigeria, 30 aot - 2 septembre 2005 Country Presentation Statistics Sierra Leone

468 views • 12 slides
Statistics Ghana The Ghana Statistical Service (GSS) 1 PRACTICES IN INTERNATIONAL

Statistics Ghana The Ghana Statistical Service (GSS) 1 PRACTICES IN INTERNATIONAL

UNITED NATIONS DEPARTMENT OF ECONOMIC AND SOCIAL AFFAIRS STATISTICS DIVISION Workshop on compilation of international merchandise trade statistics, Abuja, Nigeria, 30 aot - 2 septembre 2005 Country Presentation Statistics Ghana The

437 views • 4 slides

More recommend