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F5 Steganographic Algorithm Karthik

Apr 03, 2018

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    Professor: Dr. YUN QING SHIPresentation by: KARTHIK RAGHAVENDRA

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    STEGANOGRAPHY OVERVIEW

    JPEG FILE INTERCHANGE FORMAT

    JSTEG ALGORITHM

    F3 ALGORITHM

    F4 ALGORITHM

    F5 ALGORITHM AND ITS ADVANTAGES

    OVER OTHER ALGORITHMS F5 ALGORITHM DEMO

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    SteganographyEncryptionalgorithm

    Steganography is the art and science of writing hidden messages in a carrier medium insuch a way that no one, apart from the sender and intended recipient, suspects theexistence of the message, a form of security through obscurity.

    Many different carrier file formats can be used, but Digital Images are the mostpopular because of their frequency on the internet.

    SECRETMESSAGE

    No visible changes inimage steganogram

    Must resist Visual andStatistical Attacks

    High Capacity for SecretMessage

    IMAGE

    STEGANOGRAM

    CARRIERCARRIER

    SECRETMESSAGE

    SteganographyDecryptionalgorithm

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    JPEG compressor cuts the uncompressedimage into parts of 8 x 8 pixels.

    Discrete Cosine Transformation transfersthe 8 x 8 brightness values into 8 x 8frequency coefficients

    Quantization suitably rounds frequencycoefficients to integers in range -2048..2047. (Lossy step)

    Histogram in Fig 2 shows discretedistribution of coefficients frequency ofoccurrence.

    Quantization followed by Huffmancoding which ensures redundancy freecoding of quantized coefficients.

    Distribution in Fig 2 shows 2characteristic properties: Coefficients frequency of occurrence

    decreases with increasing absolute value.

    Difference between 2 bars of histogram inmiddle is larger than on margin.

    Fig 1: Flow of information in the JPEG compressor

    Fig 2: Histogram of JPEG coefficients after quantization

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    Fig 3a: Histogram of JPEG coefficients after quantization Fig 3b: JSTEG equalises pairs of coefficients

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    After quantization, JSTEG replaces the least significant bits of the frequency coefficients by the secret message.The embedding mechanism skips all coefficients with the values 0 or 1 as observed in Figure 3b.

    Resistant against visual attacks and offers a good capacity of about 12.8% of the staganograms size, but thesecret message can be easily detected by statistical attacks.

    Fig 4 shows the statistical attack on JSTEG steganogram (with 50% of the capacity used, i.e. 7680 bytes). Thediagram presents the probability of embedding: as a function of an increasing sample: Initially, the samplecomprises the first 1% of the JPEG coefficients, then the first 2%, 3%, . . . The probability is 1.00 up to 54% and0.45 at 56%; A sample of 59% and more contains enough unchanged coefficients to let thep-value drop to 0.00.

    Fig 4: Probability of embedding in a JSTEG steganogram

    (50 % of capacity used)

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    Fig 5a: Histogram of JPEG coefficients after quantization Fig 5b: F3 produces a superior number of even coefficients

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    Does not overwrite bits like JSTEG, instead it decrements the coefficients absolute values in case their LSBdoes not match except coefficients with the value zero, where we cannot decrement the absolute value.Hence zero coefficient is not used in this method. The LSB of nonzero coefficients match the secret messageafter embedding, but the LSB is not overwritten as overwritten bits can be detected by statistical methods (Chi-Square method).

    Some embedded bits fall victim to shrinkage. Shrinkage occurs every time F3 decrements the absolute value of1 and -1 producing a 0. The receiver cannot distinguish a 0 coefficient that is stegonagraphically unused from a0 produced by shrinkage. It skips all zero coefficients. Hence repetitive embedding is necessary.

    Figure 5b shows the histogram of frequence of occurance versus JPE G coefficients for after applying F3algorithm. The histogram shows more even coefficients than odd coefficients. This is due to repeatedembedding after shrinkage. Shrinkage occurs only if we embed a 0 bit. The repetition of these 0 bits shifts theratio of steganographic values in favour of the steganographic zeros. This is undesirable and can be detectedby statistical means.

    F3 WEAKNESSES:

    Due to exclusive shrinkage of steganographic zeros. F3 embeds more zeros than ones, and producesstatistically detectable peculiarities in the in the histogram.

    The histogram of Figure 2 contains more odd than even coefficients (except 0). Therefore, an unchanged carriermedia contain more steganographic ones than zeros.

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    Fig 6a: Histogram of JPEG coefficients after quantization Fig 6b: Histogram of JPEG coefficients with F4 interpretation ofSteganographic values

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    F4 eliminates the 2 weakness mentioned in F3 algorithm by mapping negativecoefficients to the inverted steganographic value: even negative coefficientsrepresent a steganographic one, odd negative a zero; even positive represents azero, odd positive and even negative a one, as shown in Figure 6b.

    In Figure 6b, each 2 bars of the same height represent coefficients with inversesteganographic value (steganographic zeros are black, steganographic ones white).

    F4 WEAKNESSES: Embeds secret message data continuously resulting in changes to concentrate on

    the start of the file, and unused rest resides on the end. This phenomenon is calledContinuous embedding.

    For a very short secret message comprising of 217 byes (1736 bits), F4 changes 1157places. This is shows that the number of bits changed is significantly more which isnot a good feature for attack proof steganographic algorithm. A new mechanism isrequired to decrease the number of bit changes.

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    Overall algorithm is same as F4 algorithm.

    F5 is enhanced version of F4 algorithm with

    respect to 2 main features stated below whichhelp in preventing statistical attacks andimproving embedding efficiency:

    PERMUTATIVE STRADDLING

    MATRIX ENCODING

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    CONTINUOUS EMBEDDING PROBLEM:In most of the cases, an embedded message does not require full capacity. Hence a part of the file

    remains unused. Figure 7 shows this concept of continuous embedding used by algorithm like F4.

    Figure 7 shows that the changes (x) concentrate on the start of the file, and unused rest resides on

    the end. To prevent attacks, the embedding function should use the carrier medium as regularly as

    possible. The embedding density must be same everywhere.

    Fig 7: Continuous Embedding concentrates changes (x)

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    PERMUTATIVE STRADDLING: To prevent the Continuous Embedding problem discussed before, F5 algorithm uses a

    technique called Permutative Straddling for scattering the secret message over the wholecarrier medium as shown in Figure 8 (Treat each pixel as JPEG coefficient).

    The straddling mechanism used in F5 shuffles all coefficients using a permutation first. Then,F5 embeds into the permuted sequence. The shrinkage does not change the number of

    coefficients (only their values) . The permutation depends on key derived from a password.

    F5 delivers the steganographically changed coefficients in its original sequence to the Huffmancoder.

    With correct key, ,receiver will be able to repeat the permutation.

    Fig 8: Permutative Straddling scatters the changes (x)

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    MATRIX ENCODING BY RON CRANDALL: New and efficient technique to improve embedding efficiency by reducing

    number of changes when embedding secret message.

    EXAMPLE:

    Message with 1736bits

    1157 bits changed 459 bits changed

    F4 F5

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    MATRIX ENCODING IMPLEMENTATION: Suppose we want to embed 2 bits x1,x2 in three modifiable bit places a1,a2 ,a3

    changing one place at most. We have following 4 cases:

    In all 4 cases, we do not change more than one bit.

    General case: If we have a code word a with n modifiable bit places for k secretmessage bits x, Matrix encoding technique embeds k secret message bits bychanging one of n= 2^k-1 places.

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    PRESERVING CHARACTERSITIC PROPERTIES:

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    F5 IMPLEMENTATION:

    Password driven Permutation.Pseudo one time pad for uniformly distributed message.Matrix Encoding with minimal embedding rate.Core embedding operation like F4.

    Fig: Block Diagram of F5 Implementation

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    F5 Implementation Steps:

    Start JPEG compression. Stop after the quantisation of coefficients.

    Initialise a cryptographically strong random number generator with thekey derived from the password.

    Instantiate a permutation (two parameters: random generator andnumber of coefficients).

    Determine the parameter k from the capacity of the carrier medium, andthe length of the secret message.

    Calculate the code word length n = 2^k 1.

    Embed the secret message with (1, n, k) matrix encoding (Hash based

    embedding). Implement inverse permutation.

    Continue JPEG compression (Huffman coding etc.)

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    F5 has high embedding capacity (>13%) butcan be pushed even further.

    F5 has high embedding efficiency.

    Resistance against both visual and statisticalattacks.

    Uses a common image format and carrier

    medium (JPEG).

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    F5A Steganographic Algorithm High Capacity Despite BetterSteganalysis Andreas Westfeld

    Ron Crandall: Some Notes on Steganography. Posted on Steganography

    Mailing List, 1998. http://os.inf.tu-dresden.de/westfeld/crandall.pdf

    Derek Upham: Jsteg, 1997, e. g.

    http://www.tiac.net/users/korejwa/jsteg.htm

    Andreas Westfeld: The Steganographic Algorithm F5, 1999.

    http://wwwrn.inf.tu-dresden.de/westfeld/f5.html

    www.Wikipedia.org

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