BLIND CONSISTENCY-BASED STEGANOGRAPHY FOR INFORMATION HIDING IN DIGITAL MEDIA

BLIND CONSISTENCY-BASED STEGANOGRAPHY FOR INFORMATION HIDING INDIGITAL MEDIAHairong QiECE DepartmentThe University of Tennessee Knoxville,TN37996hqi@Wesley E.Snyder,William A.SanderATTN:AMSRL-RO-TU.S.Army Research Office,PO Box12211 Research Triangle Park,NC27709-2211SnyderWE,sander@ABSTRACTWe propose a new approach to steganography for information hid-ing in digital media.We refer to it as blind consistency-based steganography(BCBS).Our main concerns in designing BCBS is high imperceptibility,high security level,and large capacity. Steganography differs from digital watermarking because both the information and the very existence of the information are hidden. Even though the discussion focuses on digital images,BCBS can be applied to any digital media.While existing steganographic approaches all have different advantages for specific applications, they also suffer a similar problem:such systems are unable to han-dle subterfuge attacks,i.e.,they cannot deal with the opponents who not only detect a message,but also render it useless,or even worse,modify it to the opponent’s favor.The breakthrough of BCBS is that it not only decodes the message exactly,it also de-tects if the message has been tampered without using any extra error correction.The detection is integrated into the process of decoding.Another advantage of BCBS is the“blindness”of the decoding process,meaning the decoding can be operated without access to the cover image.The encoding and decoding process are detailed in the paper,along with the analysis on imperceptibility, security,and capacity.Experimental results are provided as well.1.INTRODUCTIONSteganography deals with hiding information in a cover so that not only the information,but the very existence of the informa-tion is hidden.It differs from digital watermarking for its different requirements on imperceptibility(including both visual impercep-tibility and statistical imperceptibility),robustness(robust against cover modifications),security(how easy it is to break the embed-ded message),and capacity(how much information can be hidden in a certain media)[1,2,3].Steganography needs to achieve large capacity,high security level,and high imperceptibility,but does not have to be robust against cover modifications.While digital watermarking has relatively low requirements on imperceptibil-ity,security and capacity,it must be robust against both acciden-tal faults(e.g.noise)and malicious faults(e.g.attacks like clip-ping,scaling of the cover).Steganography is sometimes referred to as covert communication[1].A typical application example is to transfer secret messages embedded in images using a public web-site.Although the images are accessible to all users,only those with the secret key(s)can view the hidden information.This paper describes a new approach to steganography.Therefore,our main concerns are high imperceptibility,high security level,and large capacity.Even though the discussion is based on digital images, the algorithm can be applied to any kinds of digital media.The area of steganography has a long history.It can be traced back to techniques like invisible ink and microdots used by spies [4].Common approaches to hide information in digital images in-clude least significant bit insertion(LSB),masking(in a manner similar to paper watermarks),and information hiding in transfor-mations(DCT,FFT,WT,etc.)[5,6].While they all have differ-ent advantages for specific applications,they also suffer a similar problem:such systems are unable to deal with subterfuge attacks (collusion and forgery)[7,8],that is,they cannot deal with the op-ponents who not only detect a message,but also render it useless, or even worse,modify it to the opponent’s favor.In this paper,we propose a new approach to steganography,re-ferred to as blind consistency-based steganography(BCBS).At the sender’s side,the message is hidden in specific columns/rows of an image.After a slightly global blur operation,those columns/rows are discarded and replaced by their neighboring pixels chosen ran-domly in order to make the marked columns/rows unpredictable. Locations of those message hiding places and the blur kernel are the two stego-keys.The decoding process is an ill-posed problem. We propose the separable deblurring based consistency method to decode the message at the receiver’s side,which transforms the ill-posedness to a well-posed one by using separable blur kernel and integer-type cover images.Therefore,exact and unique solution can be guaranteed in the decoding process.The breakthrough of the BCBS approach is that it not only decodes the message exactly, it also detects if the message has been tampered without using any extra error correction.The detection is integrated into the process of decoding.Another advantage of the BCBS approach is that the decoding process can be operated blindly without access to the cover image,which enhances the imperceptibility.That is,it elim-inates the possibilities of malicious attackers obtaining both the cover image and the stego image and do a bit-by-bit comparison to discover the potential existence of hidden messages.The message encoding and decoding processes are detailed in Sec.2.Experimental results and stegoanalysis are provided in Sec.3.2.MESSAGE ENCODING AND DECODING Figure1illustrates the general procedure of BCBS.For purposes of this explanation,message()is hidden in specific columns of the cover image(),which is then undergone a slightly blur oper-ation.In the resulting image,the message hiding columns are re-placed by pixels chosen randomly from their neighbors to generatethe stego image().In the decoding process,separable deblurringbased consistency method is designed to convert the ill-posed de-coding problem to a well-posed one in order to uniquely extract thehidden message.The message hiding columns and the blur kernelare the two stego keys used at the receiver’s side for decoding.Fig.1.Block diagram of BCBS.2.1.Message EncodingThe encoding process uses both the distortion and substitutiontechniques.Based on the notation adopted in Fig.1,the messageencoding process can be summarized into the following four steps. The cover image is of size.The length of the hiddenmessage is of bits.Without loss of generality,we assumeis hidden in one column(column)of and that.We also assume each pixel in the cover image carries one bit of the hidden message.Step1:Replace each pixel in column of image with thepixel in column of the same row.Step2:Add the th bit of the message(either0or1)to the least significant bit of the th pixel of column,where.Step3:Blur the image generated from step2using a blurkernel offinite size.This process helps spread the message bitsto the neighboring pixels.Step4:Discard column from the image generated by step3,and replace it with neighbor pixel brightness value where theneighbor is chosen randomly.The resulting image from step4iscalled the stego image().In the encoding process,the message hiding column and theconvolution kernel are the two stego keys.Based on the abovedescription,we can formulate the message encoding process intoEq.1,where denotes that the message()is hidden in thecover image(),indicates the convolution with the blur kernel, and denotes the further process on column described in step 4.The blur kernel is discrete and offinite support.(1)2.2.Message DecodingMessage decoding from images is basically an ill-posed[9,10]problem,since a little change in the input data can dramatically af-fect the solution.Ill-posedness comes from the ill-conditioning ofthe matrix constructed from the blur kernel.The most popular so-lution to ill-posedness is regularization.Generally speaking,any regularization method tries to analyze a related well-posed prob-lem whose solution approximates the original ill-posed problem. According to[11],one of the methods to achieve well-posedness is to insert some restrictions on the data.In the decoding process of BCBS,by putting some restrictions on the cover image and the blur kernel,we are able to transform the ill-posed decoding prob-lem into a well-posed one.Eq.1can be simplified into Eq.2if we regard as little dis-turbance in the stego-image(),and.Both and are matrices.If the system is well-conditioned,the little disturbance in will not affect the solution.(2)In order to transform the decoding problem into a well-posed one,we add two restrictions on the cover image and the blur ker-nel:(1)the blur kernel()should be separable;and(2)the cover image()is of integer type.The separability property of the blur kernel leads to the sep-arable convolution as shown in Eq.3,where and are the separated vertical and horizontal components of,and denotes matrix multiplication.(3)If is an image and is an blur kernel,the convolution between image and can be equally achieved by a matrix multiplication between and an(,)-matrix generated from;and the convolution with can be similarly achieved by a matrix multiplication with an (,)-band matrix generated from.For example,if the image is of dimension and the separable blur kernel of dimension:the matrices and then look like:With and,we can rewrite Eq.3into Eq.4.Eq.5is the inverse problem to Eq.4.If matrices and are both well-conditioned,the solution should be unique and stable.The well-conditioning of matrices and are shown in[12].(4)(5)To actually solve the system of Eq.4,we use Householder triangularization based QR factorization(HHQR)algorithm[13].HHQR has been proved to be backward-stable which means if thelinear system is well-conditioned,this algorithm can provide theaccurate solution.In the decoding process of BCBS,HHQR algo-rithm is used twice to solve the two linear systems derived fromEq.4.Step1:Solve for.This step is to deblur thestego image in the vertical direction.Step2:Solve for.In this step,HHQR can-not be used directly since there is one column of message hidingpixels in.Instead,we solve linear systems where is therow number of image.For the example we took earlier in this section,one of the linear systems can be written as Eq.6(6)where is the th row in.Assume the cover image has onlyinteger brightness values,and these values are within[0,255],alsoassume the message is hidden in the3rd column,we then have5 unknowns(,,,and)but only4equations in the linear system.To solve this problem,weneed tofind another condition.Since we already know thatshould be an integer between0and255,an exhaustive search can be carried out by assuming is each one of them,which gives us4unknowns and4equations.Solve the new linear system by HHQR,and check the solution to see if it satisfies the consis-tency criterion,that is,the solutions(,,) are all between0and255and are all integers.If they do,then we can continue and solve the next row;otherwise,next value of is attempted.The well-conditioned problem and the backward-stable algorithm assure that the solution is unique and accurate.3.EXPERIMENTAL RESULTS AND STEGOANALYSIS The proposed BCBS technique,as described in Sec.2is imple-mented,tested,and verified.In the following experiments,we use“Hello,World!”as the hidden message,whose ASCII code is105-bit long.We choose the cover image“barbara”of size .Different numbers of message hiding columns and message hiding bits are tested.For all these cases,BCBS is able to extract the hidden message successfully.Figures2shows the results including the cover image,the stego image,and the hid-den message.We used a Gaussian blur kernel with com-ponent and.Imperceptibility,capacity, and security of BCBS are analyzed based on these experimental results.24 hidden columns1 bit/pixel24 hidden columns2 bits/pixel24 hidden columns1 bit/pixel24 hidden columns2 bits/pixelcover image stego−image hidden message stego−image hidden messageFig.2.Experimental results using barbara()as the cover image.3.1.ImperceptibilityImperceptibility takes advantages of human psychovisual redun-dancy.It is difficult to quantify.For image steganography,exist-ing metrics to measure imperceptibility include mean-square-error (MSE)and peak-signal-to-noise ratio(PSNR)[3]defined in Eq.7 and Eq.8,(7)(8) where,are the row and column numbers of the cover image, is the pixel value from the cover image,is the pixel value from the stego-image,and is the peak signal level of the cover image(for8-bit gray-scale images,).Signal-to-noise ratio(SNR)(Eq.9)is another way to quantify imperceptibility, where the message is regarded as the signal(-variance of the signal),and the cover image as the noise(-variance of the noise).Therefore,the higher the SNR,the more perceptible the message is.(9)Figure3illustrates the relationship between SNR and the num-ber of message hidden columns.For a given number of message hidden bits per pixel,the more columns of hidden messages,the larger the SNR.For afixed number of message hidden columns, the more bits used to hide message,the larger the SNR.Figure4 shows the relationship between SNR and MSE.In general,theFig.3.SNR vs.number of message hidden columns.3.2.Channel capacityBased on the conditioning analysis in[12],the size of the blur kernel needs to be greater than,and the distance between adjacent message hidden columns should be greater than twice the radius of the blur kernel.Therefore,we can quantize the capacity of BCBS as Eq.10:(10)Fig.4.MSE vs.SNR.where is the number of bits per pixel used to hide the message, is the size of the blur kernel,and are the number of rows and columns in the cover image.A smaller will improve the imperceptibility.Figure5shows the relationship between capacityFig.5.Capacity vs.SNR.3.3.SecurityThe message decoding algorithm is based on the combination of two stego-keys:the blur kernel,and the location of message hiding columns.Without either of them,it would be impossible to decode the message.The elements of the blur kernel can be either inte-gers or selectedfloating point numbers.An exhaustive searching method used to determine the blur kernel would take a very long time.One could envision attempting to determine the blur kernel by an optimization/estimation technique such as“blind deconvo-lution”.This approach is infeasible in our application since two blurs are actually conducted in the stego image.The cover image, prior to our insertion of data,has already been slightly blurred-all optical systems,whether they be lenses or“finite point”sources, impose some blur into the image.Therefore,the blind deconvo-lution would not be able to extract the blur that BCBS conducted from the stego image.4.CONCLUSIONSeparable deblurring based consistency method is proposed to de-code messages embedded in a digital image that undergone a global blur operation and a local pixel corruption.Based on the experi-ments,we conclude that if(1)the blur kernel is separable,(2)the cover image is of integer 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