Abstract:
A product and process for extracting hidden data from a stego-image that has been subjected to scaling attacks are disclosed. The hidden data extraction method of the present invention retains the one-to-one mapping of the stego-image blocks to the corresponding blocks in the scaled image. When the stego-image is scaled down, the block size for extracting the hidden data is reduced proportionally. When the stego-image is scaled up, the block size for extracting the hidden data is increased proportionally. The total overall number of blocks of pixels to be examined is kept constant between the scaled image and the stego-image. The hidden data extraction method can be combined with any existing block-DCT based data hiding method to provide an overall method for dealing with scaling attacks. Both the extraction method and the combined method can be implemented in software and stored within a machine-readable medium.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS  
       [0001]     This application claims the benefit of U.S. provisional patent application No. 60/600,578 filed Aug. 11, 2004, the disclosure of which is incorporated herein by reference in its entirety. 
     
    
     GOVERNMENT INTERESTS  
       [0002]     This invention was made with Government support under Agreement F30602-03-2-0044 awarded by the Air Force. The Government has certain rights in this invention. 
     
    
     FIELD OF THE INVENTION  
       [0003]     The present invention relates to digital imaging and, more particularly, to a method for extracting hidden data embedded in a larger collection of digital data, e.g., a digital image.  
       BACKGROUND OF THE INVENTION  
       [0004]     With the growth of multimedia systems in distributed environments, issues such as copy control, illegal distribution, copyright protection, covert communications, etc., have become important. Digital data hiding schemes have been proposed in recent years as a viable way of addressing some of these security concerns. Digital data hiding is one aspect of the larger field of steganography, which is concerned with the hiding of one media type within another, such as text, voice, or another image into an image or video. The potential customers having the greatest interest in steganography, particularly digital data hiding, include the entertainment industry, where digital data hiding would be used for copyright protection and electronic fingerprinting, and defense agencies, where digital data hiding would be used for covert communications and authentication of documents.  
         [0005]     In conventional watermarking of paper documents, an ink-based image is embedded in the larger document. When authenticating the document, holding the document up to a light source reveals the faint traces of the watermark, which may or may not be visible under normal lighting conditions. For the entertainment or defense industries, it becomes increasingly important not to allow digital hidden data (e.g., a digital watermark) to be easily visible in a stego-image (a digital image with hidden data). Thus, one important property of a good digital data hiding technique is to keep the distortion of a host image (the original image) to a minimum. The digital hidden data must also be relatively immune to both intentional and unintentional attacks by those for whom the hidden data was not intended, such as counterfeiters and computer hackers. Some examples of attacks include digital-to-analog conversion, analog-to-digital conversion, requantization, dithering, rotation, scaling, and cropping. One of these types of attacks, scaling, is particularly insidious because of its ability to cause minimal perceptible differences between the original and the attacked overall image yet cause severe loss of the hidden data.  
         [0006]     Scaling attacks generally refer to the reduction or expansion in the size of a stego-image, and come in two categories as is known in the art:  
         [0007]     Category 1—The scaled image is the same size as the stego-image. This means a down-scaling operation is followed by an up-scaling operation or vice versa.  
         [0008]     Category 2—The scaled image is not the same size as the stego-image (either up-scaled or down-scaled).  
         [0009]     Probably the most common category of data hiding techniques used against both Category 1 and Category 2 attacks are based on the discrete cosine transform (DCT), as is known in the art. The 2D-DCT (2-dimensional DCT) data hiding technique used most often, and virtually a standard, is that described in J. R. Hernandez et al., “DCT-Domain Watermarking Techniques for Still Images: Detector Performance Analysis and a New Structure,” IEEE Transactions on Image Processing, January 2000, Vol. 9, pp. 55-68 (the generic data hiding and hidden data extraction methods). In this scheme, 8×8 pixel blocks of the host image are first transformed using the 2D-DCT, and the mid-frequency regions of the 2D-DCT coefficient blocks are the locations where the hidden data is embedded. By using the mid-frequency regions for data hiding, the hidden data causes fewer distortions to the stego-image as compared to the low frequency regions, where most of the host image information is stored, while at the same time the hidden data would not be removed by compression schemes such as JPEG, where the high frequency regions of the 2D-DCT coefficients are thrown away.  
         [0010]     At the encoder end, the real values of the hidden data representing the grey scale or color pixel amplitudes (in the range of 0-255) are converted to binary form. If the current bit from the hidden data is a ‘1’, the ‘1’ bit is replaced by a real-valued pseudo-random noise (PN) sequence. A second PN sequence represents the ‘0’ bit. The two PN&#39;s are chosen to have minimal correlation with each other. The two PN&#39;s are known on both the encoding end and extracting end of the communications channel over which the stego-image is sent. The use of one PN representing an ‘0’ and another representing a ‘1’ minimizes the risk of misjudging a received ‘1’ bit for an ‘0’ bit and vice versa when the communication channel is noisy.  
         [0011]     The mid-band 2D-DCT coefficients, represented as real-valued data, are modulated with one of the PN sequences according to the following equations: 
 
 I   w ( u, v )= I ( u, v )×(1 +k   s   ×W   b ( u, v ,)),  u, v ε F   M  
 
 I   w ( u,v )= I ( u,v ),  u,v εF   M  
 
 W b  is either the PN sequence for ‘0’, W 0 , or the PN sequence for ‘1’, W 1 ; F M  is the set of the coefficients of the 2D-DCT matrix block corresponding to mid-band frequencies; I(u, v) is an 8×8 2D-DCT block; k s  is a gain factor used to specify the strength of the hidden data, and is adjusted according to the size of the particular 2D-DCT coefficient used (e.g., larger values of k s  can be used for coefficients of higher magnitude and vice versa); and I W (u,v) represents the corresponding 2D-DCT block with hidden data. After all blocks of the host image have been processed, each block of the stego-image in the frequency domain is then inverse transformed to give the stego-image I W *(x,y), where x is the distance from the upper left-hand corner of the image along the x-axis, and y is the distance from the upper left-hand corner of the image along the y-axis. 
 
         [0012]     In the generic hidden data extraction method, to extract the hidden data at the other end of the communications channel, the received stego-image (which may or may not have been attacked) is broken down into 8×8 blocks, and a 2D-DCT transformation is performed. Then the correlation between the mid-band 2D-DCT coefficients, I W  and both the PN&#39;s, W b , are calculated, where W b  is normalized to zero mean. If the correlation between the mid-band 2D-DCT coefficients and one of the PN sequences is higher than the other, then H i , the i th  reconstructed hidden data bit, is chosen according to the relation: 
 
 H   i =1, corr( I   w   , W   1 )&gt;corr( I   w   , W   0 ) 
 
H i =0, otherwise 
 
 where corr( ) is the discrete correlation function. One way the discrete correlation function is implemented, as is known in the art, is to use a Matlab™ function corr2(a, b). Given the argument C=corr2(a, b), Matlab™ takes in two sequences a and b and returns a real value C which is the correlation coefficient of a and b. This value is less than or equal to +1, with +1 being 100% correlation. 
 
         [0013]     The formula and example below illustrate how the coefficient is calculated for a specific sequence. 
 
 C =sum[sum( a′.*b ′)]/sqrt[sum{sum( a′.*a ′))*sum{sum( b′.*b ′))]Formula: 
 
         [0014]     Where, a′=a—mean(a) 
        b′=b—mean(b)     x.*y is the inner product of the vectors x and y        
 
         [0017]     The usage of this formula can be illustrated with the following steps: 
 
a=[1, 0, 0, 0, 1, 1, 1, 0]
 
b=[0, 0, 1, 0, 1, 1, 1, 1]
 
         [0018]     Step 1: 
 
mean( a )=(1+0+0+0+1+1+1+0)/8=0.5 
 
mean( b )=(0+0+1+0+1+1+1+1)/8=0.625 
 
         [0019]     Step 2: 
 
 a′=a -mean( a )=[0.5, −0.5, −0.5, −0.5, 0.5, 0.5, 0.5, −0.5]
 
 b′=b -mean( b )=[−0.625, −0.625, 0.375, −0.625, 0.375, 0.375, 0.375, 0.375]
 
         [0020]     Step 3: 
 
 ′.*b =[−0.3125, 0.3125, −0.1875, 0.3125, 0.1875, 0.1875, 0.1875, −0.1875]
 
 a′.*a =0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25, 0.25]
 
 b′.*b =[0.39062, 0.39062, 0.14062, 0.39062, 0.14062, 0.14062, 0.14062, 0.14062]
 
         [0021]     Step 4: 
 
sum[sum( a′.*b ′)]=0.5 
 
sum[sum( a′.*a ′)]=2.0 
 
sum[sum( b′.*b ′)]=1.875 
 
         [0022]     Step 5: 
 
sum[sum( a′.*a ′)]*sum[sum( b′.*b ′)]=(2.0*1.875)=3.75 
 
         [0023]     Step 6: 
 
Sqrt(sum[sum( a′.*a ′)]*sum[sum( b′.*b ′)])=(2.0*1.875)=1.936492 
 
         [0024]     Step 7: 
 
sum[sum( a′.*b ′)]/sqrt[sum{sum( a′.*a ′)}*sum{sum( b′.*b ′)}]=0.5/1.93649=0.2582 
 
         [0025]     The main problem with the generic extraction method is that it performs poorly against Category 2 attacks. Down-scaling the stego-image by a mere 4% or up-scaling it by a factor of 5% causes the generic extraction method to lose 50% of the hidden data. This is equivalent to just assuming all extracted bits are ‘1’, and thus the extracted hidden data is unrecognizable.  
         [0026]     The main cause of the loss of hidden data is that when the stego-image is scaled (i.e., resized), there will be fewer or greater 8×8 bocks of pixels to be examined in the attacked image compared to the un-scaled stego-image. If the scaled stego-image is partitioned into 8×8 blocks, then the spatial information in each block of the scaled stego-image is not the same as that in the corresponding block of the un-scaled stego-image. If the image size is reduced, then each 8×8 pixel block in the scaled image contains more hidden data information than the corresponding block of the un-scaled stego-image. As such, scaling destroys the one-to-one mapping between the blocks of the attacked image and the corresponding blocks in the un-scaled stego-image.  
       SUMMARY OF THE INVENTION  
       [0027]     The present invention overcomes the disadvantages and shortcomings of the prior art discussed above by providing an enhanced method of extracting hidden data from a digital image, which includes the steps of receiving the digital image; determining a first number of blocks used to hide data in an original version of the digital image; computing an optimum block size for extracting the hidden data from the digital image based upon the first number of blocks; computing optimal locations in blocks of the digital image for extracting the hidden data therefrom; and extracting the hidden data from the optimal locations using the optimal block size. The method of the present invention can be applied to extract hidden data from both attacked and unattacked stego-images. In the case of an attacked stego-image, the method computes an optimum block size based on both the current size and the original size of the stego-image such that the number of blocks used for extracting the hidden data from the attacked stego-image remains the same as the number of blocks used to hide the hidden data in the original version of the stego-image.  
         [0028]     The hidden data extraction method can be combined with any existing block-DCT based data hiding method to provide an overall method for dealing with scaling attacks. Further, the method of the present invention can be implemented in software and stored within a machine-readable medium or down-loaded over the Internet via a computer data signal embodied in a carrier wave. Moreover, the method of the present invention could be incorporated into a larger system for sending and receiving images having hidden data.  
         [0029]     Further features and advantages of the invention will appear more clearly on a reading of the following detailed description of the exemplary embodiments of the invention, which are being provided by way of example only with reference to the accompanying drawings. 
     
    
     BRIEF DESCRIPTION OF THE DRAWINGS  
       [0030]     For a more complete understanding of the present invention, reference is made to the following detailed description of the exemplary embodiments considered in conjunction with the accompanying drawings, in which:  
         [0031]      FIG. 1A  is a view of data to be hidden in a digital image;  
         [0032]      FIG. 1B  is a view of a host image in which the data shown in  FIG. 1A  can be hidden to produce a stego-image;  
         [0033]      FIG. 1C  is a view of the stego-image produced by hiding the data shown in  FIG. 1A  into the host image shown in  FIG. 1B ;  
         [0034]      FIG. 1D  is a diagram of a down-scaled version of the stego-image of  FIG. 1C  in which the image is divided in accordance with the present invention into an appropriate number of blocks for extracting hidden data;  
         [0035]      FIG. 1E  is a block diagram showing the coefficients of the discrete cosine transformation along with the middle frequency coefficients used by the present invention to hide data in blocks of the stego-image of  FIG. 1D ;  
         [0036]      FIG. 1F  shows the extracted hidden data derived from  FIG. 1D  after processing by the method of the present invention;  
         [0037]      FIG. 2  is a flow chart showing the overall method of the present invention;  
         [0038]      FIG. 3  is a flow chart showing the method of  FIG. 2  in greater detail, wherein an optimal block size is computed based on the image dimensions;  
         [0039]      FIG. 4  is a flow chart showing the method of  FIG. 2  in greater detail, wherein appropriate 2D-DCT mid-band locations are chosen and δ rows and β columns are eliminated;  
         [0040]      FIG. 5  is a flow chart showing the method of  FIG. 2  in greater detail, wherein hidden data bits are extracted;  
         [0041]      FIG. 6  is a block diagram of an apparatus capable of employing the method of  FIG. 2 ;  
         [0042]      FIG. 7  is flow chart of another embodiment of the present invention wherein the extraction method is incorporated into a system for sending and receiving data across a communications channel;  
         [0043]      FIG. 8  is a graph of bit error rates (BER) versus scaling factors, comparing the performance of the hidden data extraction method of the present invention to the generic method for a Category-1 Down-Scaling attack;  
         [0044]      FIG. 9  is a graph of bit error rates (BER) versus scaling factors, comparing the performance of the hidden data extraction method of the present invention to the generic method for a Category-1 Up-Scaling attack;  
         [0045]      FIG. 10  is a graph of bit error rates (BER) versus scaling factors, comparing the performance of the hidden data extraction method of the present invention to the generic method for a Category-2 Down-Scaling attack; and  
         [0046]      FIG. 11  shows graphs of bit error rates (BER) versus scaling factors, comparing the performance of the hidden data extraction method of the present invention to the generic method for a Category-2 Up-Scaling attack. 
     
    
     DETAILED DESCRIPTION OF THE INVENTION  
       [0047]     Referring now to  FIGS. 1A-1F , there is shown visually how the enhanced hidden data extraction method (i.e., the hidden data extraction method of the first embodiment) of the present invention acts upon a scaled-down stego-image. In  FIG. 1A , a digital representation of exemplary data to be hidden  2  is depicted, with the letters in the name “TOM” in uppercase letters. The letters of “TOM” are composed of digital grey-scale real numbers or pixels of dark areas  4  surrounded by light areas  6 . Generally these pixels range in value from 0-255 encoded in binary representation in a computer. If the image  2  were in color, then the letters  4  and the background  6  would be represented by three sets of numbers for each pixel. The discussion of the foregoing enhanced extraction method of the present invention will consider the simpler case of a grey scale image, although the enhanced extraction method works equally well on a color image in which the same method is applied to three sets of blocks of numbers instead of one.  
         [0048]     Now referring to  FIGS. 1B and 1C ,  FIG. 1B  is the original host image  9 , while  FIG. 1C  is the stego-image  10  with data hidden according to the generic method (i.e., the prior art method). The stego-image  10  shows a person  12  surrounded by a background  14 . The hidden data itself does not remain intact in the image  10 , but is spread out or “hidden” over the entire stego-image  10 , resulting in a small amount of distortion or stray pixels of dark areas or light areas  16 . The stego-image  10  has pixel dimensions of M 0 ×N 0 , which represents the original size of the stego-image  10 .  
         [0049]      FIG. 1D  shows an attacked version  10 ′ of the stego-image  10  shown in  FIG. 1C , wherein the image  10 ′ has been the subject of a scaling attack. When run through the enhanced extraction method of the present invention, the attacked stego-image  10 ′, in this case reduced in size to M W  pixels by N W  pixels, is divided into n x ×n y  blocks  18  where n x  is the number of columns and n y  is the number of rows in the attacked image. Each of the blocks  18  represents a matrix of pixels of dimensions B x ×B y . The size B x ×B y  of the blocks  18  will vary proportionally to the ratio of the size of the attacked stego-image  10 ′ to the original stego-image  10  such that the total number of blocks  18  used to extract data from the attacked version  10 ′ of the stego-image  10  is the same as the number of blocks used to hide data into the stego-image  10 .  
         [0050]     With reference to  FIG. 1E , during the processing of the attacked stego-image  10 ′, each of the blocks  18  is transformed to the frequency domain using the discrete cosine transform (DCT), producing low frequency coefficients  20 , mid-frequency coefficients  22 , and high frequency coefficients  24 . Each low frequency coefficient  20  contains most of host image&#39;s information, but does not contain any hidden data information. The hidden data information is stored in the mid-frequency coefficients  22 , which distorts the stego-image only minimally. No hidden data information is stored in the upper frequency coefficients  24 , since this region of the 2D-DCT-transformed image is most likely to be affected by data compression algorithms such as the JPEG standard, so little hidden data information is lost.  
         [0051]     With reference to  FIG. 1F , an extracted hidden data image  25  is reconstructed by the enhanced method of the present invention and contains data corresponding to the data  2  shown in  FIG. 1A  and embedded in the stego-image of  FIG. 1C . There will be some degradation to the hidden data. For example, the letter ‘O’ shows a missing pixel  26 , the letter ‘T’ shows extra dark pixels  27 , and some stray dark pixels  28  appear in the background  30 . However, this degradation is nominal, as the overall integrity of the hidden data image  25  is preserved.  
         [0052]     With reference to  FIG. 2 , a flow chart  31  of the basic steps of the enhanced method of the present invention is depicted. At step  32 , the received stego-image, represented as real-valued digital data bits, is read into a buffer. By the term “received stego-image,” it is meant a stego-image which has been transmitted through a communication channel and which may or may not have been attacked. By the term “original stego-image,” it is meant a stego-image that includes hidden data and which has not yet been transmitted and/or subject to an attack. At step  34 , the size of the received stego-image is determined. At step  36 , the optimal block size is computed based on the image dimensions determined in step  34 . At step  38 , after 2D-DCT transforming an individual block of optimal block size, appropriate 2D-DCT mid-band locations  22  (see  FIG. 1E ) are selected for further processing. At step  40 , the hidden data bits are extracted from the 2D-DCT mid-band locations  22 . The processing shown in  FIG. 2  can be repeated as necessary to process all blocks  18  of the received stego-image.  
         [0053]     With reference to  FIG. 3 , the step  36  of  FIG. 2  of computing the optimal block size based on the image dimensions is expanded into sub-steps. At step  44 , the number of blocks of the original stego-image image, n x ×n y , is determined, where n x  is the number columns of blocks and n y  is the number of rows of blocks. The number of columns of blocks, n x,  and the number of rows of blocks, n y,  can be determined from any one of the following information stored in the header of the received stego-image: (i) the values of n x  and n y , (ii) the ratio of n x  to n y  (or vice versa), or (iii) the dimensions, M 0 ×N 0  pixels, of the original stego-image. Further, if the dimensions of the block size, a×b, used to encode the host image is known (e.g., the 8×8 pixels used in the J. R. Hernandez et al. 2D-DCT data hiding technique), then the number of blocks of the original stego-image image can be calculated as  
           M   0     a     ×         N   0     b     .         
 
         [0054]     The received stego-image has dimensions M w ×N w . At step  46 , a temporary variable, b x * is calculated, equal to M w  pixels divided by n x  blocks. Likewise, at step  48 , a temporary variable, b y * is calculated, equal to N w  pixels divided by n y  blocks. At step  50 , the question is asked whether the value of b x * is an integer. If it is not, then step  52  occurs, wherein the quantity B x *, representing the x dimension size of a block to be used in the enhanced extraction method of the present invention, is calculated from the floor function operating on b x * (the floor function being the truncated value of a real number, or the decimal part without the fraction beyond the decimal). If b x * is an integer, then at step  54 , B x * is set to b x *. Likewise, at step  55 , the question is asked whether the value of b y * is an integer. If it is not, then step  56  occurs, wherein the quantity B y *, representing the y dimension size of a block to be used in the enhanced extraction method of the present invention, is calculated from the floor function operating on b y *. If b y * is an integer, then at step  57 , B y * is set to b y *. At step  58 , the residual in the x direction, β, is computed, where βis defined as: 
 
β= M   w −(└ B   x   *┘*n   x ) 
 
         [0055]     Finally, at step  59 , the residual in the y direction δ is computed, where δ is defined as: 
 
δ= M   W −(└ B   y   *┘*n   y ) 
 
 As an example, if the original stego-image had overall dimensions M 0 ×N 0  of 1024×1024 pixels and the received stego-image was down-scaled to dimensions M w ×N w  of 512×512 pixels, then the original number of blocks, n x ×n y , assuming an 8×8 block size, is M 0 /8×N 0 /8=1024/8×1024/8=128×128=16384 blocks. The block size to be used to extract the hidden data from the received stego-image using the enhanced method is no longer 8×8, but  
           B   x   *     =       ⌊     b   x   *     ⌋     =       ⌊       M   W       n   x       ⌋     =       ⌊     512   128     ⌋     =   4           ,     
     ⁢       B   y   *     =       ⌊     b   y   *     ⌋     =       ⌊       N   W       n   y       ⌋     =       ⌊     512   128     ⌋     =   4               
 
 for a 4×4 block size. The residuals β and δ would be 
 
β= M   W −(└ B   x   *┘*n   x )=512−(└4┘*128)=0, δ=512−(└4┘*128)=0, 
 
         [0056]     As another example, if the original stego-image had overall dimensions M 0 ×N 0  of 1024×1024 pixels and the received stego-image was up-scaled to dimensions M w ×N w  of 2048×2048 pixels, then the original number of blocks is M 0 /n x ×N 0 /n y =1024/8×1024/8=128×128=16384 blocks so the block size to be used to extract the hidden data from the received stego-image using the enhanced method is no longer 8×8, but  
           B   x   *     =       ⌊     b   x   *     ⌋     =       ⌊       M   W       n   x       ⌋     =       ⌊     2048   128     ⌋     =   16           ,     
     ⁢       B   y   *     =       ⌊     b   y   *     ⌋     =       ⌊       N   W       n   y       ⌋     =       ⌊     2048   128     ⌋     =   16               
 
 for a 16×16 block size. The residuals β and δ would be 
 
β= M   W −(└ B   x   *┘*n   x )=2048−(└16┘*128)=0, δ=2048−(└16┘*128)=0, 
 
         [0057]     Now referring to  FIG. 4 , the step  38  of choosing the appropriate 2D-DCT mid-band locations is expanded into sub-steps. At step  60 , the received stego-image image is down-scaled to eliminate β rows and δ columns. At step  62 , the image is bilinear-interpolated. At step  64 , the resulting image from steps  62  and  64  is divided into n x ×n y  blocks. At step  66 , the 2D-DCT is taken for each block. At step  68 , the mid-band frequency components from each block are extracted.  
         [0058]     Now referring to  FIG. 5 , the step  40  of extracting the hidden data bits is expanded into sub-steps. At step  70 , the mid-band coefficients of a 2D-DCT block matrix are correlated with the known PN sequence representing a ‘1’ bit. At step  72 , the same mid-band coefficients of the same 2D-DCT block matrix are correlated with the known PN sequence representing an ‘0’ bit. At step  74 , the correlation of step  70  is compared with that of step  72 . If the value of correlation with the PN sequence representing a ‘1’ bit is greater than that of the PN sequence representing a ‘0’ bit, then at step  76 , the hidden data bit is set to ‘1’, otherwise, the hidden data bit is set to ‘0’ at step  78 . At step  80 , if all the 2D-DCT blocks have been examined, then the hidden data has been completely extracted, otherwise, processing continues with step  81  at the next block.  
         [0059]     With reference to  FIG. 6 , an apparatus implementing the enhanced hidden data extraction method of the present invention is depicted. A processor  82  reads in the received stego-image from communications channel  84  via a network interface card  86  (NIC) and stores the image in memory  88 . Communications channel  84  is often a local area network or the Internet, so that NIC  86  can be an Ethernet Card. In wireless communications, the communication channel  84  is airspace and the NIC  86  is a WiFi or Bluetooth transceiver. In still other applications, communications channel 84 is a telecommunication network and NIC  86  is a dial-up modem. Processor  82  can reside within an embedded system, a personal computer, work station, a minicomputer, or a main frame. For example, a suitable processor could include a Sun SPARCstation™ 60 having 512 megabytes of memory, running the Solaris™ operating system. Memory  88  can be a combination of random access memory and/or a machine-readable medium, such as a hard disk. Memory  88  is used for storing and the data received from the communication channel  84  and for storing the enhanced hidden data extraction program of the present invention. After processor  82  operates on the image and extracts the hidden data, the hidden data can be shown on a display  89  such as a monitor, stored back in memory  88 , or sent back over communication channel  84  via NIC  86 . The method of the present invention could be carried out using software written in any suitable high or low level language, and stored in executable object code in the memory  88 .  
         [0060]      FIG. 7  is a flow chart showing another embodiment of the present invention, indicated generally at  100 . In this embodiment, the extraction method of the present invention is incorporated into a system for sending and receiving data across any suitable communications channel. In step  102 , a generic, block-based 2D-DCT data hiding algorithm is performed on a host image in a memory (e.g., an image stored in memory  88  of  FIG. 6 ) to produce a stego-image. This stego-image is sent out through a communications channel via a processor and a NIC at step  104  (using, for example, the components shown in  FIG. 6 ). The stego-image is then received over the communications channel and stored in memory. The processor then performs the enhanced hidden data extraction method of the present invention. Finally, at step  108 , the extracted hidden data is presented on a display.  
         [0061]     One advantage of the enhanced hidden data extraction method over the generic method is performance. To gauge the performance of the enhanced hidden data extraction method of the present invention over the generic method, reference is made to  FIGS. 8-11 .  FIGS. 8-11  summarize the results obtained after Category-1 and Category-2 scaling attacks on three stego-images having sizes of 512×512 pixels. Random bit sequences ranging in size from 8000 to 14400 bits were used as hidden data.  
         [0062]     Referring now to  FIG. 8 , a graph of bit error rates (BER) versus scaling factors is depicted for the case of a Category-1 Down-Scaling attack. The enhanced method (i.e., the hidden data extraction method of both disclosed embodiments) of the present invention and the generic (i.e., the prior art) method performed equally well, so that for a down-scaling factor of 85%, both methods retrieve about 90% of the embedded hidden data correctly (what is meant by a recovery rate of 90% is that the Bit Error Rate (BER) was about 0.1, or 100 errors per 1000 bits of hidden data).  
         [0063]     Referring now to  FIG. 9 , a graph of bit error rates (BER) versus scaling factors is depicted for the case of a Category-1 Up-Scaling attack. The enhanced method of the present invention and the generic method performed equally well, so that for a down-scaling factor of 85%, both methods retrieve about 99.4% of the embedded hidden data correctly for a BER of about 0.005, or 5 errors per 1000 bits of hidden data.  
         [0064]     Referring now to  FIG. 10 , a graph of bit error rates (BER) versus scaling factors is depicted for the case of a Category-2 Down-Scaling attack. The enhanced method of the present invention far out-performs the generic method for all cases of down-scaling between 6% and 100%. Down-scaling the stego-image with the generic method by a mere 4% causes the generic method to loose 50% of the hidden data. At this percentage of down-scaling, the enhanced method of the present invention has a near 0% error, and even a 66% down-scaling causes a 0.11 BER for a recovery rate of 89%.  
         [0065]     Referring now to  FIG. 11 , graphs of bit error rates (BER) versus scaling factors are depicted for the case of a Category-2 Up-Scaling attack. The enhanced method of the first embodiment of the present invention, shown in the graph to the right, far out-performs the generic method, shown in the graph to the left, for all cases of up-scaling between 100% and 400%. Up-scaling the stego-image with the generic method in nearly all up-scaling attacks resulted in a 50% recovery rate, while the enhanced method of the present invention had a BER no greater than 0.007 for a recovery rate of 99.3%.  
         [0066]     The performance of the enhanced method of the present invention compared to the generic method using a combination of attacks is summarized in Table 1, below. Here, the stego-image was subjected to several other popular attacks known in the art before down-scaling the stego-image by a factor of 50%. In all cases, the enhanced method of the present invention fared better than the generic method.  
                                                   TABLE 1                           PERFORMANCE RESULTS FOR COMBINATION ATTACKS                    BER for the                   Method of the   BER for the               Present   Generic           Test   Invention   Method                            JPEG (Q.90)   0.057   0.667           JPEG (Q-50)   0.059   0.685           JPEG (Q-20)   0.066   0.694           Sharpening   0.086   0.658           Despeckle   0.095   0.631           Smart Blur (Rad. 5)   0.104   0.730           Median Filtering   0.154   0.676           Uniform Noise (10%)   0.229   0.775           Uniform Noise (15%)   0.285   0.793           Gaussian Noise (10%)   0.301   0.820           Gaussian Noise (15%)   0.325   0.856           Motion Blur (5°)   0.362   0.802                      
 
         [0067]     An advantage of the enhanced method over other hidden data extraction methods is its minimal computational complexity. Only two additional divisions are needed compared to the generic method.  
         [0068]     It will be understood that the embodiments described herein are merely exemplary and that a person skilled in the art may make many variations and modifications without departing from the spirit and scope of the invention. All such variations and modifications are intended to be included within the scope of the present invention as defined in the appended claims.