The DCT domain and JPEG

Transcription

1 The DCT domain and JPEG CSM25 Secure Information Hiding Dr Hans Georg Schaathun University of Surrey Spring 2009 Week 3 Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 1 / 47

2 Learning Objectives Be able to work with and JPEG images and other representations in the transform domain. Understand what happens during JPEG compression, and its potential consequence to watermarking and steganography. Be able to apply simple LSB embedding in the JPEG domain. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 2 / 47

3 Outline Overview 1 Overview 2 Image Representation 3 Compression 4 Steganography in JPEG 5 Matlab Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 3 / 47

4 Overview The elements of JPEG Operates on luminence and chrominance (YCbCr) (not on RGB) Grayscale images have luminence component only. Downsampling Works in the DCT domain (not the spatial domain) Quantisation Entropy coding (lossless compression) Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 4 / 47

5 Overview JPEG is not a file format JPEG is a compression system The system employs three different compression techniques JPEG is not a file format. Files with extension.jpeg are often JFIF or EXIF. JFIF is traditionally the most common file format for JPEG. EXIF is made for digital cameras and contain extra meta information. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 5 / 47

6 Overview Reading Core Reading Digital Image Processing Using MATLAB. Chapter 6: colour images Representation Processing Conversion Chapter 8.5: JPEG compression Chapter 4: Frequency domain processing Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 6 / 47

7 Outline Image Representation 1 Overview 2 Image Representation Alternatives to RGB The blockwise DCT domain 3 Compression 4 Steganography in JPEG 5 Matlab Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 7 / 47

8 Image Representation Alternatives to RGB The RGB colour representations RGB : A colour is a vector (R, G, B) R is amount of red light. G is amount of green light. B is amount of blue light. Each pixel can be either A colour vector (R, G, B); or a reference to an array of colour vectors (the palette) Each coefficient can be [0, 1]; floating point (double in matlab) {0, 1,..., 255}; 8-bit integer (uint8 in matlab) {0, 1,..., }; 16-bit integer (uint16 in matlab) Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 8 / 47

9 Alternatives to RGB Image Representation Alternatives to RGB NTSC : (Y, I, Q) where R, G, B [0, 1]. YCbCr : (Y, Cb, Cr) Y R I = G Q B Y R Cb = G Cr B where R, G, B [0, 1] and Y, Cb, Cr [0, 255]. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 9 / 47

10 Image Representation The blockwise DCT domain Block-wise Each colour-channel (Y,Cb,Cr) considered separately M N matrix divided into 8 8 blocks Each block is handled separately Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 10 / 47

11 The DCT transform Image Representation The blockwise DCT domain Several different DCT transform. We use the following. T f (u, v) = M 1 N 1 x=0 y=0 α(u)α(v) f (x, y) cos MN (2x + 1)uπ 2M cos (2y + 1)vπ 2N where α(a) = M = N = 8, { 1, if a = 0, 2, otherwise. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 11 / 47

12 The DCT transform Image Representation The blockwise DCT domain The inverse is similar f (x, y) = M 1 N 1 u=0 v=0 α(u)α(v) T f (u, v) cos MN (2x + 1)uπ 2M cos (2y + 1)vπ 2N where α(a) = M = N = 8, { 1, if a = 0, 2, otherwise. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 12 / 47

13 Image Representation The blockwise DCT domain Matlab Matlab functions dct2 (2D DCT transform) idct2 (Inverse) blkproc ( X, [M N], FUN ) For instance blkproc ( X, [8 ) Use help system for details Do not use imread for JPEG images converts images to the spatial domain. you don t even know the compression parameters... Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 13 / 47

14 Image Representation The blockwise DCT domain Transform image Linear combination of patterns (see right) DC (upper left) gives average colour intensity Low frequency: coarse structure High frequency: fine details Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 14 / 47

15 Outline Compression 1 Overview 2 Image Representation 3 Compression Downsampling Quantisation Source Coding 4 Steganography in JPEG 5 Matlab Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 15 / 47

16 Compression Downsampling What is sampling? Fact The human eye is more sensitive to changes in luminance than in chrominance. To sample is to collect measurements. Each pixel is a sample (measuring the colour of the image). Lower resolution means fewer samples. Reducing resolution = downsampling Basic M N image: N M samples per component (Y, Cb, Cr). Y is more useful than Cb and Cr. Therefore we can downsample Cb and Cr M/2 N/2 is common for Cb and Cr Still use M M for Y Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 16 / 47

17 Compression Downsampling What is sampling? Fact The human eye is more sensitive to changes in luminance than in chrominance. To sample is to collect measurements. Each pixel is a sample (measuring the colour of the image). Lower resolution means fewer samples. Reducing resolution = downsampling Basic M N image: N M samples per component (Y, Cb, Cr). Y is more useful than Cb and Cr. Therefore we can downsample Cb and Cr M/2 N/2 is common for Cb and Cr Still use M M for Y Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 16 / 47

18 Compression Downsampling What is sampling? Fact The human eye is more sensitive to changes in luminance than in chrominance. To sample is to collect measurements. Each pixel is a sample (measuring the colour of the image). Lower resolution means fewer samples. Reducing resolution = downsampling Basic M N image: N M samples per component (Y, Cb, Cr). Y is more useful than Cb and Cr. Therefore we can downsample Cb and Cr M/2 N/2 is common for Cb and Cr Still use M M for Y Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 16 / 47

19 Compression Downsampling What is sampling? Fact The human eye is more sensitive to changes in luminance than in chrominance. To sample is to collect measurements. Each pixel is a sample (measuring the colour of the image). Lower resolution means fewer samples. Reducing resolution = downsampling Basic M N image: N M samples per component (Y, Cb, Cr). Y is more useful than Cb and Cr. Therefore we can downsample Cb and Cr M/2 N/2 is common for Cb and Cr Still use M M for Y Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 16 / 47

20 Compression Downsampling What is sampling? Fact The human eye is more sensitive to changes in luminance than in chrominance. To sample is to collect measurements. Each pixel is a sample (measuring the colour of the image). Lower resolution means fewer samples. Reducing resolution = downsampling Basic M N image: N M samples per component (Y, Cb, Cr). Y is more useful than Cb and Cr. Therefore we can downsample Cb and Cr M/2 N/2 is common for Cb and Cr Still use M M for Y Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 16 / 47

21 Compression Downsampling What is sampling? Fact The human eye is more sensitive to changes in luminance than in chrominance. To sample is to collect measurements. Each pixel is a sample (measuring the colour of the image). Lower resolution means fewer samples. Reducing resolution = downsampling Basic M N image: N M samples per component (Y, Cb, Cr). Y is more useful than Cb and Cr. Therefore we can downsample Cb and Cr M/2 N/2 is common for Cb and Cr Still use M M for Y Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 16 / 47

22 Compression Downsampling What is sampling? Fact The human eye is more sensitive to changes in luminance than in chrominance. To sample is to collect measurements. Each pixel is a sample (measuring the colour of the image). Lower resolution means fewer samples. Reducing resolution = downsampling Basic M N image: N M samples per component (Y, Cb, Cr). Y is more useful than Cb and Cr. Therefore we can downsample Cb and Cr M/2 N/2 is common for Cb and Cr Still use M M for Y Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 16 / 47

23 Compression Downsampling What is sampling? Fact The human eye is more sensitive to changes in luminance than in chrominance. To sample is to collect measurements. Each pixel is a sample (measuring the colour of the image). Lower resolution means fewer samples. Reducing resolution = downsampling Basic M N image: N M samples per component (Y, Cb, Cr). Y is more useful than Cb and Cr. Therefore we can downsample Cb and Cr M/2 N/2 is common for Cb and Cr Still use M M for Y Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 16 / 47

24 Compression Downsampling What is sampling? Fact The human eye is more sensitive to changes in luminance than in chrominance. To sample is to collect measurements. Each pixel is a sample (measuring the colour of the image). Lower resolution means fewer samples. Reducing resolution = downsampling Basic M N image: N M samples per component (Y, Cb, Cr). Y is more useful than Cb and Cr. Therefore we can downsample Cb and Cr M/2 N/2 is common for Cb and Cr Still use M M for Y Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 16 / 47

25 Compression Downsampling What is sampling? Fact The human eye is more sensitive to changes in luminance than in chrominance. To sample is to collect measurements. Each pixel is a sample (measuring the colour of the image). Lower resolution means fewer samples. Reducing resolution = downsampling Basic M N image: N M samples per component (Y, Cb, Cr). Y is more useful than Cb and Cr. Therefore we can downsample Cb and Cr M/2 N/2 is common for Cb and Cr Still use M M for Y Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 16 / 47

26 Compression Downsampling What do we save? Original: M N pixels 3 components. Compressed: 2 M 2 N 2 + M N = 11 2 M N Ratio We just saved 50% Compressed Original = MN 3MN = 1 2. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 17 / 47

27 Compression Downsampling What do we save? Original: M N pixels 3 components. Compressed: 2 M 2 N 2 + M N = 11 2 M N Ratio We just saved 50% Compressed Original = MN 3MN = 1 2. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 17 / 47

28 Compression Downsampling What do we save? Original: M N pixels 3 components. Compressed: 2 M 2 N 2 + M N = 11 2 M N Ratio We just saved 50% Compressed Original = MN 3MN = 1 2. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 17 / 47

29 Compression Downsampling What do we save? Original: M N pixels 3 components. Compressed: 2 M 2 N 2 + M N = 11 2 M N Ratio We just saved 50% Compressed Original = MN 3MN = 1 2. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 17 / 47

30 Compression Downsampling Chrominance versus Luminence Fact The human eye is more sensitive to changes in luminance than in chrominance. Watermarking tend to embed in Y (luminence) Embedding in Cb and Cr would more easily be destroyed by JPEG Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 18 / 47

31 Compression Downsampling Chrominance versus Luminence Fact The human eye is more sensitive to changes in luminance than in chrominance. Watermarking tend to embed in Y (luminence) Embedding in Cb and Cr would more easily be destroyed by JPEG Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 18 / 47

32 Compression Downsampling Chrominance versus Luminence Fact The human eye is more sensitive to changes in luminance than in chrominance. Watermarking tend to embed in Y (luminence) Embedding in Cb and Cr would more easily be destroyed by JPEG Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 18 / 47

33 Compression Downsampling Downsampling in JPEG 1 Translation to YCbCr. 2 Downsampling 3 DCT transform Each downsampled component matrix Y, Cb, Cr is Divided into 8 8 blocks DCT transformed blockwise An 8 8 block in Cb can be associated with 1,2 or 4 Y blocks depending on downsampling. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 19 / 47

34 What is quantisation? Rounding in general Compression Quantisation Rounding numbers is quantisation. Measuring gives continuous numbers Whether you measure pixel luminence, or the length of your garage. No matter how close to points are, there is a point in between. However, our precision is limited. We give lengths to the nearest unit. Luminence is categorised into 256 intervals (8bit integers). Computer memory is finite, 256 different possibilites for a byte Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 20 / 47

35 Compression Quantisation Quantisation in JPEG Quantisation in the DCT domain Each coefficient is divided by the quantisation constant. The result is rounded to nearest integer. Different quantisation constants for each coefficient in the block. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 21 / 47

36 Compression Quantisation Example Quantisation in JPEG DCT matrix Quantisation matrix / Quantised DCT matrix Example from Wikipedia. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 22 / 47

37 Entropy Coding Compression Source Coding Recall Observe 0 is extremely common ±1 is common Two-digit numbers are very rare This is typical Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 23 / 47

38 Entropy Coding Compression Source Coding In order to compress the data Use few bits (short codewords) for frequent symbols Many bits (long codewords) only for rare symbols Usually, JPEG uses a simple Huffman code. it can use other codes (saving space, but computionally costly) For instance, a single short codeword to say the rest of the block is zero Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 24 / 47

39 Outline Steganography in JPEG 1 Overview 2 Image Representation 3 Compression 4 Steganography in JPEG Into the compressed domain JSteg and OutGuess Matlab Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 25 / 47

40 Steganography in JPEG Before or after compression Into the compressed domain pixmap message LSB embedding JPEG compression stegoimage pixmap JPEG compression message LSB embedding stegoimage Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 26 / 47

41 Steganography in JPEG Into the compressed domain Fragility of LSB LSB embedding is criticised for being fragile JPEG removes insignificant information... such as the LSB JPEG compression after embedding (probably) ruins the message When is this a problem? Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 27 / 47

42 Steganography in JPEG When fragility is a problem Into the compressed domain It is a problem in robust watermarking JPEG compression is common-place most applications need robustness If the purpose is steganography, and Alice and Bob are allowed to exchange pixmaps, then it is not a problem. Obviously, if your steganogram is supposed to be JPEG... Do not do LSB in the pixmap. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 28 / 47

43 Steganography in JPEG When fragility is a problem Into the compressed domain It is a problem in robust watermarking JPEG compression is common-place most applications need robustness If the purpose is steganography, and Alice and Bob are allowed to exchange pixmaps, then it is not a problem. Obviously, if your steganogram is supposed to be JPEG... Do not do LSB in the pixmap. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 28 / 47

44 Steganography in JPEG When fragility is a problem Into the compressed domain It is a problem in robust watermarking JPEG compression is common-place most applications need robustness If the purpose is steganography, and Alice and Bob are allowed to exchange pixmaps, then it is not a problem. Obviously, if your steganogram is supposed to be JPEG... Do not do LSB in the pixmap. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 28 / 47

45 Steganography in JPEG Into the compressed domain Double compression Common bug in existing software Read an arbitrary image file JPEG is decompressed on reading... pixmap Embedding works on JPEG image is compressed to produce JPEG signal quality factor (QF) either default or supplied by user A JPEG steganogram has now been compressed twice different QF produces an artifact Is there any reason for de- and recompressing? Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 29 / 47

46 Important lessons Steganography in JPEG Into the compressed domain 1 Do not make unnecessary image conversions. 2 Many techniques apply to any format LSB applies to JPEG signals... but it is called Jsteg 3 Use a technique which fits the target (stego-) format i.e. the format you are allowed to use on the channel. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 30 / 47

47 Steganography in JPEG Into the compressed domain Main development The past at a glance Core Reading Hide and Seek: An Introduction to Steganography by Niels Provos and Peter Honeyman, in IEEE Security & Privacy JSteg was published 2 JSteg was broken 3 OutGuess was published 4 OutGuess was broken 5 F5 was published 6 F5 was broken Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 31 / 47

48 Steganography in JPEG Into the compressed domain Main development The past at a glance Core Reading Hide and Seek: An Introduction to Steganography by Niels Provos and Peter Honeyman, in IEEE Security & Privacy JSteg was published 2 JSteg was broken 3 OutGuess was published 4 OutGuess was broken 5 F5 was published 6 F5 was broken Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 31 / 47

49 Steganography in JPEG Into the compressed domain Main development The past at a glance Core Reading Hide and Seek: An Introduction to Steganography by Niels Provos and Peter Honeyman, in IEEE Security & Privacy JSteg was published 2 JSteg was broken 3 OutGuess was published 4 OutGuess was broken 5 F5 was published 6 F5 was broken Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 31 / 47

50 Steganography in JPEG Into the compressed domain Main development The past at a glance Core Reading Hide and Seek: An Introduction to Steganography by Niels Provos and Peter Honeyman, in IEEE Security & Privacy JSteg was published 2 JSteg was broken 3 OutGuess was published 4 OutGuess was broken 5 F5 was published 6 F5 was broken Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 31 / 47

51 Steganography in JPEG Into the compressed domain Main development The past at a glance Core Reading Hide and Seek: An Introduction to Steganography by Niels Provos and Peter Honeyman, in IEEE Security & Privacy JSteg was published 2 JSteg was broken 3 OutGuess was published 4 OutGuess was broken 5 F5 was published 6 F5 was broken Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 31 / 47

52 Steganography in JPEG Into the compressed domain Main development The past at a glance Core Reading Hide and Seek: An Introduction to Steganography by Niels Provos and Peter Honeyman, in IEEE Security & Privacy JSteg was published 2 JSteg was broken 3 OutGuess was published 4 OutGuess was broken 5 F5 was published 6 F5 was broken Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 31 / 47

53 Steganography in JPEG JSteg and OutGuess 0.1 The JSteg algorithm JSteg denotes a software package. Approach: simple LSB in the DCT domain. No different from LSB in the spatial domain χ 2 analysis applies Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 32 / 47

54 Steganography in JPEG JSteg and OutGuess 0.1 Pseudocode The JSteg algorithm Input: Image I, Message m Output: Image J for each bit b of m c := next DCT coefficient from I while c = 0 or c = 1, c := next DCT coefficient from I end while c := c c mod 2 + b replace coefficient in I by c end for May ignore high and/or low frequency coefficients Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 33 / 47

55 Bitflips in JSteg Steganography in JPEG JSteg and OutGuess 0.1 Cover Stego Typical JPEG. Typical JSteg. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 34 / 47

56 Pros and Cons Steganography in JPEG JSteg and OutGuess 0.1 Why is JSteg important? First publicly available solution. Simple solution What are the disadvantages? Similar to LSB in Spatial domain. Histogramme analysis applies χ 2 /pairs of values applies Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 35 / 47

57 Pros and Cons Steganography in JPEG JSteg and OutGuess 0.1 Why is JSteg important? First publicly available solution. Simple solution What are the disadvantages? Similar to LSB in Spatial domain. Histogramme analysis applies χ 2 /pairs of values applies Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 35 / 47

58 Pros and Cons Steganography in JPEG JSteg and OutGuess 0.1 Why is JSteg important? First publicly available solution. Simple solution What are the disadvantages? Similar to LSB in Spatial domain. Histogramme analysis applies χ 2 /pairs of values applies Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 35 / 47

59 Pros and Cons Steganography in JPEG JSteg and OutGuess 0.1 Why is JSteg important? First publicly available solution. Simple solution What are the disadvantages? Similar to LSB in Spatial domain. Histogramme analysis applies χ 2 /pairs of values applies Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 35 / 47

60 Pros and Cons Steganography in JPEG JSteg and OutGuess 0.1 Why is JSteg important? First publicly available solution. Simple solution What are the disadvantages? Similar to LSB in Spatial domain. Histogramme analysis applies χ 2 /pairs of values applies Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 35 / 47

61 Pros and Cons Steganography in JPEG JSteg and OutGuess 0.1 Why is JSteg important? First publicly available solution. Simple solution What are the disadvantages? Similar to LSB in Spatial domain. Histogramme analysis applies χ 2 /pairs of values applies Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 35 / 47

62 Pros and Cons Steganography in JPEG JSteg and OutGuess 0.1 Why is JSteg important? First publicly available solution. Simple solution What are the disadvantages? Similar to LSB in Spatial domain. Histogramme analysis applies χ 2 /pairs of values applies Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 35 / 47

63 Steganography in JPEG JSteg and OutGuess 0.1 Outguess 0.1 How can we improve JSteg? How did we improve LSB in the Spatial Domain? Solution Choose random coefficients from the entire image. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 36 / 47

64 Steganography in JPEG JSteg and OutGuess 0.1 Outguess 0.1 How can we improve JSteg? How did we improve LSB in the Spatial Domain? Solution Choose random coefficients from the entire image. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 36 / 47

65 Steganography in JPEG JSteg and OutGuess 0.1 Outguess 0.1 How can we improve JSteg? How did we improve LSB in the Spatial Domain? Solution Choose random coefficients from the entire image. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 36 / 47

66 Steganography in JPEG JSteg and OutGuess 0.1 Pseudocode Outguess 0.1 Input: Image I, Message m, Key k Output: Image J Seed PRNG with k for each bit b of m c := pseudo-random DCT coefficient from I while c = 0 or c = 1, c := pseudo-random DCT coefficient from I end while c := c c mod 2 + b replace coefficient in I by c end for May ignore high and/or low frequency coefficients Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 37 / 47

67 Histogramme analysis Steganalysis Steganography in JPEG JSteg and OutGuess Pairs of values Generalised χ 2 works 2 Symmetry Embedding exchange and 2 1. The DCT histogramme is expected to be symmetric Outguess/JSteg destroy the symmetry. Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 38 / 47

68 Outline Matlab 1 Overview 2 Image Representation 3 Compression 4 Steganography in JPEG 5 Matlab The JPEG toolbox Randomness Masking Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 39 / 47

69 JPEG Toolbox Reading a JPEG image Matlab The JPEG toolbox» im = jpeg_read ( Kerckhoffs.jpg ) im = image_width: 180 image_height: 247 image_components: 3 image_color_space: 2 jpeg_components: 3 jpeg_color_space: 3 comments: {} coef_arrays: {[248x184 double] [128x96 double] [128x96 quant_tables: {[8x8 double] [8x8 double]} ac_huff_tables: [1x2 struct] dc_huff_tables: [1x2 struct] optimize_coding: 0 comp_info: [1x3 struct] progressive_mode: 0» Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 40 / 47

70 JPEG Toolbox JPEG data Matlab The JPEG toolbox» Xy = im.coef_arrays{im.comp_info(1).component_id} ;» whos Xy Name Size Bytes Class Attributes Xy 248x double» Q = im.quant_tables{im.comp_info(1).quant_tbl_no} Q =» Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 41 / 47

71 Matlab The JPEG toolbox w/o the toolbox Load/Save workspace jpeg_read and jpeg_write are compiled functions, Available on web page for Intel/Linux and Intel/Windows Compilation required for other systems. If you have trouble with the toolbox, it is possible to load/save files as Matlab workspaces.» load image.mat» whos Name Size Bytes Class Attributes im 1x struct There is one mat-file for each image on the web page Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 42 / 47

72 Other toolbox functions Matlab The JPEG toolbox If you want to write your own (de)compressor, the following functions are useful. bdct, ibdct, quantize, dequantize Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 43 / 47

73 Matlab Randomness Pseudo-random number generators A pseudo-random number generator (PRNG) finite state machine starting state given by user input the seed each transition outputs a number observing a sequence of number, it is computationally infeasible to predict the next number looks random It is deterministic if sender and receiver share the seed (a key) they can generate the same sequence Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 44 / 47

74 Random locations Matlab Randomness Many ways to do it but some makes it hard to avoid using the same pixel twice A simple approach 1 randomly permute the pixels 2 embed in the first pixels in the permuted sequence 3 reverse the permutation If the sender and receiver use the same PRNG seed, they get the same pseudo-random permutation Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 45 / 47

75 Matlab functions Matlab Randomness Many functions using a PRNG rand, randperm, randn And one dedicated for performing random permutations new = randintrlv ( old, seed ) the seed is given directly when the permutation is used reverse: old = randdeintrlv ( new, seed ) new/old should be a 1D vector serialise the image into a vector (im(:)) before randintrlv reshape ( vector, [ N, M ] ) to recover the 2D image after randdeintrlv Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 46 / 47

76 Matlab Masking Masking Boolean matrix as index Matlab allows Boolean (logical) matrices as indices Say A is an n m matrix B = logical(ones(n,m)) B(1,1) = 0 A(B) will be all elements of A except (1, 1) repmat(b,m,n) replicates B to form a larger matrix m times the heigh n times the width How do you extract the AC coefficients in a JPEG image? Make an 8 8 mask of ones Set the DC entry to 0, e.g. (1, 1) Replicate the mask using repmat Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 47 / 47

77 Matlab Masking Masking Boolean matrix as index Matlab allows Boolean (logical) matrices as indices Say A is an n m matrix B = logical(ones(n,m)) B(1,1) = 0 A(B) will be all elements of A except (1, 1) repmat(b,m,n) replicates B to form a larger matrix m times the heigh n times the width How do you extract the AC coefficients in a JPEG image? Make an 8 8 mask of ones Set the DC entry to 0, e.g. (1, 1) Replicate the mask using repmat Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 47 / 47

78 Matlab Masking Masking Boolean matrix as index Matlab allows Boolean (logical) matrices as indices Say A is an n m matrix B = logical(ones(n,m)) B(1,1) = 0 A(B) will be all elements of A except (1, 1) repmat(b,m,n) replicates B to form a larger matrix m times the heigh n times the width How do you extract the AC coefficients in a JPEG image? Make an 8 8 mask of ones Set the DC entry to 0, e.g. (1, 1) Replicate the mask using repmat Dr Hans Georg Schaathun The DCT domain and JPEG Spring 2009 Week 3 47 / 47