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Steganographic techniques - Wellesley CScs. crypto/lectures/tr10.pdf · PDF file1 CS349 Cryptography Department of Computer Science Wellesley College Steganographic techniques A brief

Apr 26, 2018

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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 Wayners 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 Wayners 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 bitdoesnt 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

    x =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

    u= 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.