Docstoc

Collusion-resistant fingerprinting for multimedia

Document Sample
Collusion-resistant fingerprinting for multimedia Powered By Docstoc
					Collusion-resistant
fingerprinting for
    multimedia
  Wade Trappe, Min Wu,
      K.J. Ray Liu
   Anti-collusion codes
• Anti-collusion codes (ACC) are
  designed to be resistant to averaging,
  and able to exactly identify groups of
  colluders.
                 ACC (1)
•    We shall describe codes using the binary
     symbols {0,1} to {-1,1} via f ( x)  2 x  1
    for use in CDMA-based watermarking.
                                         f ( x)  2 x  1




•    We assume that when a sequence of
     watermarks is averaged, the effect it has is
     that the resulting binary is the logical AND of
                        j
     the codewords c
•    For example ,when the codes (1110) and (1101)
     are combined, the result is (1100).
                ACC (2)
• Definition 1.
  A binary code C  {c ,  , c } such that the
                      1         n

  logical AND of any subset of k or fewer
  codevectors in non-zero and distinct from the
  logical AND of any other subset of k or fewer
  codevectors is a k-resilient anti-collusion code,
  or an ACC code.
• For example, when n=4,C={1110,1101,1011,0111}.
  It is easy to see when k  n 1 of these
  vectors are combined under AND, that this
  combination is unique .
        ACC -BIBD (1)
• Definition 2:
  A (v, k ,  ) balanced incomplete block
                                       
  design (BIBD) is a pair (  , ) ,where  is a
  collection of k-element subsets (blocks) of a
  v-element set ,such that each pair of
              
  elements of occur together in exactly 
  blocks.
            ACC –BIBD (2)
• A (v, k ,  ) -(BIBD) has b   (v  v) /(k  k ) blocks.
                                    2        2

  Corresponding to a block design is the v  b
  incidence matrix M  (mij ) defined by

      1 if the ith element belongs to the jth block
mij  
      0                                  otherwise
• If we assign the codewords as the bit-
  complement of the column vectors of M then we
  have a (k-1)-resilient ACC.
        ACC –BIBD (3)
• Theorem 1.
  Let (  , ) be a (v,k,1)-BIBD, and M the
  corresponding incidence matrix. If the
  codevectors are assigned as the bit
  complement of the columns of M ,then
  the resulting scheme is a (k-1)-collusion
  resistant code.
       ACC – BIBD (4)
• We now present an example. The
  following is the bit-complement of the
  incidence matrix for a (7,3,1)-BIBD:
         0   0   0   1   1   1   1
                                  
         0   1   1   0   0   1   1
         1   0   1   0   1   0   1
                                  
     M  0   1   1   1   1   0   0
         1   1   0   0   1   1   0
                                  
         1   0   1   1   0   1   0
                                  
         1   1   0   1   0   0   1
          ACC – BIBD (5)
• This code requires 7 bits for 7 users and provides
  2-resiliency since any two column vectors share a
  unique pair of 1 bits.
• Each column vector c of M is mapped to {1}
  by f ( x)  2 x  1 .
                                         
                                           v
• The CDMA watermark is then w                f (c j )s j
                                           j1
• When two watermarks are averaged, the locations
  where the corresponding ACC codes agree and
  have a value of 1 identify the colluding users.
          ACC –BIBD (6)
• For example, let
   w1   s1  s2  s3  s4  s5  s6  s7
   w 2   s1  s2  s3  s4  s5  s6  s7
  be the watermarks for the first two
 columns of the above (7,3,1) code, then
 (w  w ) / 2 has coefficient vector
    1    2

 (-1,0,0,0,1,0,1).
     Restriction of BIBD
• In general, (v, k ,  )  BIBDs do not necessarily exist
  for an arbitrary choice of v, and k.
• The condition that b must be an integer restricts
  some possibilities for v, and k, and for a given
  triple there may not exist a (v, k ,  )  BIBD    .
• The Bose construction builds Steiner triple systems
  when v  1 (mod 6) ,and the Skolem construction
  builds Steniner triple systems when v  3 (mod 6) .
  Additionally,( p d , p,1)  BIBD can be constructed
  when p is of prime power.
         Subgroup-based
          constructions
• In many application, a group of users will be
  suspected of likely colluding, but not with others.
  This could be due to geographical of social
  variables, or based upon a pervious precedent.
• Suppose the code matrix C is constructed as a
  block diagonal matrix C  diag (C1 , C2 ,  , C s ) ,
  where the matrices C j on the diagonal
  correspond to matrices for smaller codes.
          Simulation (1)
• In order to demonstrate the capabilities of using
  an ACC code with CDMA watermarking to
  fingerprint users and detect colluders, we used an
  additive spread spectrum watermarking scheme,
  where the perceptually weighted watermark was
  added to block DCT coefficients.
• The detection of the watermark is performed
  without the knowledge of the host image via the Z
  detection statistic.
• We used the 512*512 lenna as the host image for
  the fingerprints.
          Simulation(2)
• We assigned the code vectors as the column vectors
  of the bit complement of the incidence matrix for a
  (15,3,1) –BIBD that was constructed using the Bose
  method with a symmetric idempotent quasigroup
  structure on Z 5 given by the binary
  operation x  y  (3x  3 y)(mod5)        .
• Two example code vectors that were assigned to
  user 1 and 6 are
       User 1 : (-1,-1,-1, 1, 1,1,1,1,1,1, 1,1,1,1,1)
       User 6 : (-1,1, 1, -1, 1,1,1,1,1,1,-1,1,1,1,1)
      Average:(-1, 0, 0, 0, 1,1,1,1,1,1, 0,1,1,1,1)
         Simulation (3)
• An example of the behavior of the Z
  statistic when two users collude is
  depicted in figure 1, where we depict the
  values of the Z statistic for the 15
  different spreading sequences used when
  user 1 and user6 average their differently
  marked images and then compress using
  JPEG with quality factor 50%.
        Simulation (4)
• We present a histogram containing the
  Z statistics form roughly 200 pairs of
  users in figure 2 when the watermarked
  images are compressed using JPEG with
  a quality factor of 50%.

				
DOCUMENT INFO
Shared By:
Categories:
Tags:
Stats:
views:63
posted:3/30/2012
language:
pages:18