Learning outcomes. Palettes and GIF. The colour palette. Using the colour palette The GIF file. CSM25 Secure Information Hiding

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1 Learning outcomes Palettes and GIF CSM25 Secure Information Hiding Dr Hans Georg Schaathun University of Surrey Learn how images are represented using a palette Get an overview of hiding techniques in GIF et c. Understand how grayscale steganography can be adapted for palette images Spring 2007 Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30 The image format The image format The colour palette Using the colour palette The GIF file 0 The palette is a table of colours Typically 256 for images Sometimes 8 or 16 for screen view Each colour has an index The palette can be stored as array of (say) 256 entries each entry: RGB colour... using 3 8 bits The GIF file format uses the colour palette... in the spatial domain Like the grayscale image, GIF is a matrix, I entry (x, y) defines the colour of pixel (x, y) however I x,y is the index of a colour in the palette A GIF file has to store both A palette The pixel matrix (pixmap) Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30

2 The image format The palette in Matlab Which is best? GIF? JPEG? true colour? Loading a palette image GIF saves space compared to true colour Perfect representation of selected colours Perfect for drawings and computer graphics where only selected colours are used JPEG is better for photos Colours are truer can blur, losing contrast and detail Remember to store the palette [pixmap,palette] = imread ( picture.gif ) imshow ( pixmap, palette ) otherwise, treated as a weird grayscale image You can work on palette and pixmap separately >> [X,P] = imread ( krinslogo.gif ) ; >> whos X P Name Size Bytes Class Attributes P 256x double X 120x uint8 Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30 The palette in Matlab Exercise Preliminaries A simple idea Suppose a GIF file uses a 8-bit palette. How much space does this GIF file save compared to a 24-bit true-colour image? Consider a image and a image. Give the answer as a percentage. How do you generate a random binary message (bit string) in matlab? Look up in the help system and find the necessary commands to generate a random N binary (logical) matrix. Data hiding is possible in the palette leaving the pixmap unaltered How? Any ideas? Two basic ideas changing colours changing order Main disadvantage: low capacity Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30

3 Changing colours Changing order Minor changes to palette colours as if they were pixels in true colour only difference: there are only (say) 256 entries For instance, LSB Capacity bits (= 768 bits) Define a canonical colour order i.e. obtained by a deterministic sorting algorithm always same order, regardless of input order Assign colour indices according to canonical order For each message, assign a permutation P on {1, 2, 3,..., N} (N is palette size) Shuffle the palette using the permutation of the message Decoder can find canonical order (deterministic) and hence deduce P which maps to the message. N! = N possible messages Approx bits for an 8-bit palette Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Large-scale data hiding First attempt: LSB pixmap is main part of palette image file to hide a lot of data, the pixmap must be used the palette is small can cover a correspondingly small amount of data We still have a pixmap as before Logical to attempt LSB in the colour indices in selected pixels What happens? Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30

4 Exercise LSB test What it looks like Take any GIF image from the web. Some test GIF images can be found on the module web pages. Make stego-images by embedding random binary messages of length 10%, 30%, 50% and 75% of capacity in the least significant bit. View the images. What does it look like? Extract the message again. Do you get the same message back? Hint: Reuse functions from previous exercises. Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30 So, what do we do? Three possible solutions Green areas, are not too bad Visible, but still green Brown is terrible It is suddenly green Why is this? Neighbour colour in the palette, can be Similar or far away Somehow, we have to change to a similar colour Colour reduction Colour sorting Beyond sorting Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30

5 Reduce the palette An ancient solution Sorting Another obvious one Reduce colour depth by 50% 256 colours 128 colours Duplicate each colour (or use a slight variation of it) Such that colour i and colour i + 1 are identical (or almost) Now LSB embedding is hardly perceptible visually How do you steganalyse it? Sort the palette before embedding Consecutive colours similar Unsort before shipping Sorted palette may be suspect The original order should look innocent Many different sort orders Sort by luminence Travelling salesman (EzStego) Let (r i, b i, g i ) be RGB of colour i Minimise P 255 i=0 [(r i r i+1 ) 2 + (b i b i+1 ) 2 + (g i g i+1 ) 2 ] Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Abandon sorting according to Jessica Fridrich Sort order and colour difference Input: Image I, Palette C = {c 1, c 2,..., c L }, Message m Output: Image J for each bit b of m choose a pixel I x,y if I x,y mod 2 b, then find c i C such that c i mod 2 = b and c i I x,y 2 is minimised I x,y := c i end if end for What is the distance c 1 c 2 2 between colours? Euclidean: R 1 R G 1 G B 1 B 2 2 Ignore chrominence: Y 1 Y 2 No obvious choice. Same problem for sorting and abandon sorting Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30

6 General principles Reading General approaches in the spatial domain Visual steganalysis Statistical steganalysis... similar to other representations in the spatial domain Structural steganalysis Consider the file format Does it look normal? Core Reading David Wayner: Disappearing Cryptography Chapter 17 Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Structural steganalysis General, Spatial Approaches Structural steganalysis considers file format et c. Palette structure can be significant Duplicate colours? Unusual palette order? General structural artifacts (not limited to palette images) Resolution requirements; palette size; et c. Bad or limited software can create artifacts Most attacks on spatial, grayscale images apply χ 2 /pairs of values pairs analysis RS analysis Statistics may vary parameters may need tuning reasoning is the same Let s explore it in excersises. Dr Hans Georg Schaathun Palettes and GIF Spring / 30 Dr Hans Georg Schaathun Palettes and GIF Spring / 30

7 Exercise Steganalysis Take the stego-images created in the previous message, and plot the χ 2 statistic as a function of N. What do you observe? Remark Extra, challenging exercises on the exercise sheet on the web page. Dr Hans Georg Schaathun Palettes and GIF Spring / 30