Data Hiding (3 of 3)

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Data Hiding (3 of 3)
Curtsey of Professor Min Wu Electrical
Computer EngineeringUniv. of Maryland, College
Park
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Watermark-Based Authentication
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Document Authentication

• Embed pre-determined pattern or content features
  beforehand
• Verify hidden datas integrity to decide on
  authenticity

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Image/Video Authentication via Watermarking

• Motivation
• Picture never lies? Easy to edit digital media
  Photoshop
• Important to detect tampering evidence in
  litigation, insurance government archive
• Original true image cannot be used to convince
  judge
• Basic idea for detecting tampering
• Recall authentication problem in crypto
• Embed some data in the image and certain
  relationship/property gets changed upon tampering
• Rely on
• fragility of embedding scheme, and/or
• embedding content features of original true image
• Two issues to address
• how to embed data?
• what data to embed?

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Useful Crypto Tools/Building-Blocks

• Cryptoly strong hash or digest function H( )
• One-way compression function
• M-bit input to N-bit output often with fixed N
  and M gtgt N
• Often used to produce a short ID for identifying
  the input
• Properties to be satisfied
• 1) Given a message m, H(m) can be calculated
  very quickly
• 2) Given a digest y, it is computationally
  infeasible to find a message m s.t. H(m) y
  (i.e., H is one-way)
• 3) It is computationally infeasible to find
  messages m1 m2 s.t. H(m1) H(m2) (i.e.
  H is strongly collision-free)
• Keyed Hash
• H( k, m ) Hash( concatenated string derived
  from k m )
• Commonly used crypto hash
• 160-bit SHA (Secure Hash Algorithm) by NIST
• 128-bit MD4 and MD5 by Rivest

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Data Integrity Verification (data authentication)

• Authentication is always relative
• with respect to a reference
• How to establish and use a reference
• Method-1 Give a genuine copy to a trusted
  3rd party
• Method-2 Append check bits
• Want hard to find a different meaningful msg.
  with same check bitsgt use cryptoly strong
  hash
• Want tamper-proof if hash func. is public
• Encrypt concatenated version of message and hash
• Keyed Hash (Message Authentication Code) no
  extra encryption needed
• Digital signature algorithm (using public-key
  crypto)
• Signed MsgHash i.e., encrypt by private key
  s.t. others cant forge

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Extension to Grayscale/Color Images

• Semi-fragile watermarking
• Want to distinguish content-preserving changes
  (e.g. moderate compression) vs. content tampering
• Achieve controlled robustness often via
  quantization
• How to embed
• One approach enforce pre-quantized DCT
  coefficients using a look-up table
• What to embed
• A visually meaningful pattern and/or a
  pre-selected one
• facilitate quick visual check and locate
  alteration
• Content features to avoid malicious
  counterfeiting attack
• limited precision (e.g., most significant bits)

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Watermark-based Authentication

• Embed patterns and content features using a
  lookup-table
• High embedding capacity/security via shuffling
• locate alteration
• differentiate content vs. non-content change
  (compression)

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Issues Beyond Embedding Mechanism
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Issues and Challenges

• Tradeoff among conflicting requirements
• Imperceptibility
• Robustness security
• Capacity
• Key elements of data hiding
• Perceptual model
• Embedding one bit
• Multiple bits
• Uneven embedding capacity
• Robustness and security
• What data to embed

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Techniques For Multi-bit Embedding

• Amplitude modulation
• Use M different amplitude of watermark to
  represent log2M bits
• ?i ? - J, -(M-3)J/(M-1), , (M-3)J/(M-1), J
  where J is JND
• accurate detection require clear distinction in
  received amplitudes
• use modulo-M operation for enforcement embedding
• Orthogonal and Biorthogonal
• Embed one of M orth. patterns representing log2M
  or log2(2M) bits
• TDMA-type (temporal or spatial or both)
• Embed each bit in different non-overlapped region
  or frame
• Unevenness in embedding capacity due to
  non-stationarity
• CDMA-type(Coded Modulation)
• Use plus vs. minus a pattern to embed one bit
• detector need to know the mutually orthogonal
  patterns

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Comparison (brief)

• TDMA vs. CDMA
• Equivalent in terms of watermark energy
  allocation
• Need to handle uneven embedding capacity for TDMA
• Need to set up and store orthogonal vectors for
  CDMA
• Orthogonal vs. TDMA/CDMA
• Orthogonal modulation has higher energy
  efficiency
• To explore further, See Section V and the
  reference therein of
• M. Wu, B. Liu "Data Hiding in Image and Video
  Part-I -- Fundamental Issues and Solutions'',
  submitted to IEEE Trans. on Image Proc., Jan. 2002

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Comparison (1)

• Applicable Media Types
• not always easy to find many CDMA orthogonal
  directions (e.g., binary image)
• Amplitude is applicable to most features
• TDMA can be applied temporally and spatially
• TDMA vs. CDMA
• Equivalent in terms of watermark energy
  allocation
• Need to handle uneven embedding capacity for TDMA
• Variable Embedding Rate (need to embed some side
  info.)
• Constant Embedding Rate (shuffling helps increase
  embed.rate)
• Need to set up and store orthogonal vectors for
  CDMA

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Comparison (2)

• TDMA / CDMA vs. Orthogonal Modulation
• Constant minimum separation for orthogonal
  modulation as of embedded bits B increases but
  total wmk energy ? unchanged
• Orthogonal modulation require book-keeping more
  orthogonal vectors and more computation in
  classic detection
• Combining the two to improve embedding rate with
  small increase in computation and storage

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Comparison (3)

• Amplitude Modulation vs. Other Techniques
• Amplitude modulation can embed multiple bits on a
  single feature/direction
• Without the need of many orthogonal vectors
• Minimum separation for same avg. wmk energy ?
  and embedding bits B
• O( 2 -B ?1/2 ) for amplitude modulation
• O( B -1/2 ?1/2 ) for TDMA/CDMA
• O( ?1/2 ) for orthogonal modulation
• Modulation techniques for communications
  Proakis
• Bandwidth-efficient techniques vs.
  Energy-efficient techniques
• Non-trivial amplitude modulation is not good when
  signal energy is limited (very low SNR), esp. for
  blind detection

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What Data to Embed? Recall Important to
determine what data to embed in authentication
applications
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Tracing Traitors

• Robustly embed digital fingerprint
• Insert ID or fingerprint to identify each
  customer
• Prevent improper redistribution of multimedia
  content
• Collusion A cost-effective attack
• Users with same content but different
  fingerprints come together to produce a new copy
  with diminished or attenuated fingerprints
• Anti-collusion fingerprinting
• Trace traitors and colluders to actively deter
  collusion/redistribution
• Rely on joint fingerprint encoding embedding

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Embedded Fingerprinting for Multimedia
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Collusion Scenarios

• Result of collusion Fingerprint energy decreases
• Jointly design encoding and embedding of
  fingerprints

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16-bit ACC Example for Detecting 3 Colluders
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Anti-Collusion Fingerprint Codes

• Simplified assumption
• Assume fingerprint codes follow logic-AND op in
  colluded images
• K-resilient AND ACC code
• A binary code Cc1, c2, , cn such that the
  logical AND of any subset of K or fewer
  codevectors is non-zero and distinct from the
  logical AND of any other subset of K or fewer
  codevectors
• Example (1110), (1101), (1011), (0111)
• ACC code via combinatorial design
• Balanced Incomplete Block Design (BIBD)

Simple Example ACC code via (7,3,1) BIBD for
handling up to 2 colluders among 7 users
To explore further, see Trappe-Wu-Liu paper
(2001).
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Anti-Collusion Fingerprint Codes (contd)

• (v,k,l)-BIBD code is an (k-1)-resilient ACC
• Defined as a pair (X,A)
• X is a set of v points
• A is a collection of blocks of X, each with k
  points
• Every pair of distinct points is in exactly l
  blocks
• blocks
• Example (7,3,1) BIBD code
• X1,2,3,4,5,6,7
• A123, 145, 167, 246, 257, 347, 356
• Code length for n1000 users
• This code O( n0.5 ) dozens bits
• Prior art by Boneh-Shaw O( (log n)4) thousands
  bits

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Efficient Collusion Detection for Orth. Mod.
Amount of correlations needed ? Considerable
reductions in computation!

• EffDet(y,S)
• Break S into S0 and S1
• if then
• if Sj 1 then Output Sj,
• else EffDet(y,Sj)