steganographic techniques - wellesley cscs.wellesley.edu/~crypto/lectures/tr10.pdf · 1 cs349...

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CS349 Cryptography

Department of Computer ScienceWellesley College

Steganographic techniques

A brief survey

Stego Techniques 2-2

Steganographic taxonomies

o Stenanographic systems can be grouped by thetype of covers used (graphics, sound, text,executables) or by the techniques used tomodify the covers

o substitution,o transform domain techniques,o spread spectrum techniques,o statistical method,o distortion techniqueso cover generation methods

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Stego Techniques 2-3

Using grammar for mimicry*It's time for another gamebetween the Whappers and theBlogs in scenic downtownBlovonia . I've just got to saythat the Blog fans have come tosupport their team and rant andrave . Play Ball ! Top of theinning. Yup. What a game so fartoday . The pitcher spits. FrankGavi adjusts the cup and entersthe batter's box . Yeah. It's arattler . He swings for thestands, but no contact . Here'sthe pitch It's a bouncingknuckleball . . .

*http://www.wayner.org/texts/mimic/

Stego Techniques 2-4

Computer graphicso A digitized photograph is

represented by a matrixof numbers that stand forthe intensity of lightemanating from aparticular place at aparticular time.

o The array of charged-coupled devices thatconvert photons to bitsare not perfect.

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Stego Techniques 2-5

Soundo Digitized sounds are lists

of numbers representingpressure hitting amicrophone at a sequenceof time slices.

o Like digitized graphics,these numbers areimprecise and there is lotsof room to hideinformation in the noise.

Stego Techniques 2-6

Hidden volumeso At top scale, a Kodak

photo-CD images is 3072by 2048 pixels.

o Eight bits are used toencode each of theamount of red, blue, andgreen (or the amount cyan,magenta, and yellow).

o Borrowing the LSB ofeach color of each pixelyields about 1.8megabytes of storage.

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Stego Techniques 2-7

Where to hideo The least significant bits seem close to random, but often

contain hidden patterns.o Destroying these subtle statistical correlations may well

give the show away.

Peter Wayner’s deskDisappearing Cryptography.

Least significant bits of same

Stego Techniques 2-8

Another problemo Compressions artists often beat stenanographers to the

punch.o JPEG can often get by with one or two bits per pixel and

save a factor of ten in file size.

Peter Wayner’s desk again Most significant bits of same

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Stego Techniques 2-9

Hiding in a GIF fileo GIF compression

maintains a table of up to256 colors that bestrepresent the image.

o The color of each pixel isdescribed by indexing intothis color table.

o Changing the leastsignificant bit maysignificantly change theimage.

Stego Techniques 2-10

A possible solutiono Hide and Seek 4.1

converts the color tablefrom 256 colors to 128,then duplicates each ofthese colors so thatadjacent entries in thecolor table are duplicatesof each other.

o Unfortunately, thistechnique leaves a largered flag for anyonescanning GIFs for hiddeninformation.

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Stego Techniques 2-11

Another solutiono EzStego sorts the color

palette so that the colorsflow smoothly into eachother.

o The hope is that changingthe least significant bitdoesn’t drastically changethe color.

Stego Techniques 2-12

The Traveling Salesperson Problemo Ordering colors in one

dimension is easy.Ordering a threedimensional color space isnot.

o EzStego treats the colorsas cities in RGB space andand tries to find theshortest path through allof the stops.

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Stego Techniques 2-13

A heuristic for TSPBegin with a list of two

cities, {c1 c2}. Set C = c1.1. Find city, d, that is

farthest from C.2. Scan the list to find i

such thatd(d, ci) + d(d, ci+1) isminimized.

3. Insert d between i and i+1and set C = d.

Stego Techniques 2-14

EzStego covers its tracks

1. Sort the palette so closest colors fall next toeach other.

2. Encode the encrypted message by twiddling theleast significant bit.

3. Unsort the palette by renumbering all of thecolors with their original values.

4. Ship the image.5. Receiver resorts palette using same algorithm

and extracts bits by using the sorted palette.

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Stego Techniques 2-15

GIFShuffleo A palette containing N colors can be permuted in N!

different ways. Each permutation may encode log2(N!) bitsof information.

Original palette Sorted palette Permuted palette

Stego Techniques 2-16

Transform domain techniques

o LSB modification techniques are highlyvulnerable to even small cover modifications.

o Transform domain methods hide messages insignificant areas of the cover image making themmore robust modification than LSB methods.

o JPEGs are perfect candidates for hidinginformation using such methods.

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Stego Techniques 2-17

Fourier serieso Fourier series are expansions of periodic functions f(x) in

terms of an infinite sum of sines and cosines of the form

o Successive partial sums produce increasingly accurateapproximations to the f(x).

Stego Techniques 2-18

Cosines sufficeo Cosine functions similar to those shown below are used to

model sound waves in MP3 music compression.

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Stego Techniques 2-19

Gimme a Wo The Wellesley W was

recreated using the fourcosine functions shown onthe previous slide:1.0 cos(x) + 0.5 cos(2x) -0.8 cos (3x) + 0.3 cos(4x).

o MP3 compression usesDiscrete cosinetransforms to find cosinecoefficients givensequences of soundsamples.

Stego Techniques 2-20

A two-dimensional discrete analogueo The discrete cosine transform of a two-dimensional N x N

array, s, of real numbers is given by

o The inverse cosine transform is given by

where C(u) equals 2-1/2 if u is 0 and 1 otherwise.

S(u, v) =2N

C(u)C(v) s(x, y)cos(pu(2x +1)2Ny = 0

N -1

Âx =0

N-1

 )cos(p (2y +1)2N

)

s(x,y) =2N

C(u)C(v) S(u, v)cos(pu(2x +1)2Nv =0

N -1

Âu= 0

N -1

 )cos(p (2y +1)2N

)

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Stego Techniques 2-21

JPEG compression

Convert image into YCbCr colorspace and break up each colorplane into 8x8 blocks.

All blocks are DCT transformed.

Divide DCT coefficientsby predefined quantizationvalues to modulate influenceof spectral components on image.

Compress the quantizedDCT coefficients usingentropy coder.

Stego Techniques 2-22

Quantization factorso DCT coefficients corresponding to highest frequency

cosines are likely to be dominated by noise.o Values in the quantization table are calculated to reduce the

influence of these “noisy” coefficients.

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Stego Techniques 2-23

Encoding in the frequency domain1. Select two DCT coefficients,

Bi (u1, v1) and Bi(u2, v2) whosecorresponding cosinesfunctions are in the mid-frequency with equalquantization coeffs.

2. Split the cover into 8x8pixel blocks; each blockencodes one bit.

3. Select a pseudorandom blockbi to encode the ith messagebit.

4. Block encodes a 1 if Bi (u1, v1)> Bi(u2, v2) , otherwise a 0.