Watermarking and encryption of color images in theFibonacci domain

F. Battistia, M. Cancellaroa, M. Carlia, G. Boatob, and A. Neria

aApplied Electronics Dept.,Universita degli Studi Roma TRE, Roma, Italy;bDept. of Information Engineering and Computer Science, University of Trento, Trento, Italy

ABSTRACT

In this paper a novel method for watermarking and ciphering color images is presented. The aim of the system isto allow the watermarking of encrypted data without requiring the knowledge of the original data. By using thismethod, it is also possible to cipher watermarked data without damaging the embedded signal. Furthermore, theextraction of the hidden information can be performed without deciphering the cover data and it is also possibleto decipher watermarked data without removing the watermark. The transform domain adopted in this work isthe Fibonacci-Haar wavelet transform. The experimental results show the effectiveness of the proposed scheme.

Keywords: Encryption, watermarking, key-dependent domain, Fibonacci-Haar transform.

1. INTRODUCTION

Increasing use and distribution of multimedia data, through Internet or widely-used communication systemsand media, is raising several problematic aspects concerning security. Nowadays, it is very easy to create anunlimited number of copies of digital data and their distribution or sharing does not require complex operations.Furthermore, friendly software editing tools allow to easily modify the content of multimedia data. Therefore, itis necessary to develop techniques able to protect sensitive data from unauthorized use. As described in ITU-T,Rec. X.8001 and IETF RFC 28282 , another crucial aspect in information security is the data confidentialityservice that provides data protection from unauthorized disclosure.

Typical mechanisms considering these security aspects are watermarking and cryptography, respectively. Thefirst one aims to insert a secret message, the watermark, into the to-be-protected data so that its existence iskept secret. To be effective, a watermark should not introduce perceivable artifacts in the host data and it shouldbe detectable also if unintentional or intentional modifications of the watermarked signal occurred. State of theart watermarking methods embed the watermark bits into the most significant portions of the digital data, sothat they cannot be removed without impairing the original content.

Cryptography is used to hide the information of a message, but its existence, allowing the access to theoriginal content only to authorized users.

In order to provide both levels of data protection, we propose a new commutative watermarking and encryp-tion method for color images. Our aim is to combine the robustness of a Singular Value Decomposition (SVD)watermarking method with the security provided by a suitable encryption algorithm.

The rest of the paper is organized as follows. In Section 2 a review of works concerning the use of watermarkingschemes together with encryption techniques is presented. In Section 3 the proposed method is described, whilein Section 4 the experimental results are reported. Finally, some conclusions are drawn in Section 5.

Further author information: send correspondence to (federica.battisti, michela.cancellaro)@uniroma3.it

2. PREVIOUS WORK

Different methods have been proposed in literature to protect digital data exploiting the advantages of encryptionand watermarking techniques. Non commutative schemes are usually proposed: either the cipher text is used assecret information to be embedded or a watermarked document is ciphered and deciphered by an authorized user.

Puech and Rodrigues3 encrypt the secret key with an encryption method based on public-private keys. Then,this secret key is embedded in the encrypted image by using a Discrete Cosine Transform (DCT) based water-marking method. The same authors in4 propose a lossless joint crypto-data hiding method for medical imagein which the image is decomposed in bit planes: the first semipixel image (the four Most Significant Bit planes)is compressed with a similar Run Length Encoding algorithm and stenographed with the patient information;then, this image is ciphered with a secret-key and scrambled with the remaining semipixel image (the four LSBplanes).In5 an hybrid image protection algorithm is proposed. A pre-positioned secret sharing scheme is used to re-construct encryption secret keys by communicating different activating shares. The activating share is used tocarry copyright or usage rights data that are embedded in the content as a visual watermark. A Singular ValueDecomposition based watermarking scheme is used to insert the watermark. When the encryption key needs tobe changed, the data source generates a new activating share and embeds the corresponding watermark into themultimedia stream. Before transmission, the composite stream is encrypted with the key constructed from thenew activating share. Once both the activating share and the encrypted content are obtained, each receiver isable to reconstruct the decryption key, decrypt the content and extract the watermark.In6 the image is divided into blocks of size 16x16 pixels and the DCT of each block is computed. The watermark isembedded into the encrypted LSBs of High-DCT-data (the highest and the second highest frequency coefficients)of each block in order to replace one bit every 8 with one bit of the watermark; the encryption is performedwith RSA? algorithm by using a private key. Then the watermarked encrypted LSBs is decrypted using thecorresponding private key and then the watermarked DCT coefficients are obtained combining High-DCT-datawith original Low-DCT-data.

All described methods propose a non commutative scheme. On the contrary, in7 the authors propose todecompose an image in the Discrete Wavelet Transform, to cipher the subbands in the lowest level with AdvancedEncryption Standard (AES), a NIST-standard cryptographic block cipher?, to cipher the subbands in the highlevel with sign encryption and to encrypt and to watermark at the same time the subbands in the middle level.Lian et al.8 recently designed a combined approach for video encryption and watermarking.

3. PROPOSED METHOD

In the following the proposed method is described. As mentioned before our goal is to create a joint commutativeembedding-encryption scheme that allows us to perform independently the two operations, in order to allowwatermark insertion and extraction without interfering with the encryption scheme and viceversa.To increase the security of the method, a key-dependent transform domain, the Fibonacci-Haar transform,has been used for both procedures. This is a generalization of the Haar transform9 in which the subbanddecomposition depends on the particular Fibonacci p-sequence Fp(n) that is defined by the following recurrence:

Fp(n) =

0, n < 0;1, n = 0;Fp(n− 1) + Fp(n− p− 1), otherwise.

(1)

The decomposition of a signal of length L is performed by choosing a particular sequence to whom L belongs.Once p is chosen, the signal is decomposed in an average and a detail subband as in the classical waveletdecomposition. In the case of image transform, if the cover image size is NxN , where N is a Fibonacci number,once p is chosen, the subband size will be:

LL: Nn−1 × Nn−1 pixels;LH : Nn−1 × Nn−p−1 pixels;HL: Nn−p−1 × Nn−1 pixels;HH : Nn−p−1 × Nn−p−1 pixels.

(2)

where Nn−1 is the number preceding N in the considered p-sequence and Nn−p−1 is the number preceding Nof p− 1 positions in the p-sequence. In Figure 1 the first order Fibonacci-Haar decomposition of a test image isshown. The original image X, of size 256× 256 pixels, is decomposed using the Fibonacci sequence for p = 24,that is:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 28, 31, 35, 40, 46, 53, 61, 70, 80, 91,

103, 116, 130, 145, 161, 178, 196, 215, 235, 256, ...

As already described, in this case the subband dimensions are:

LL: 235 × 235 pixels;LH : 235 × 21 pixels;HL: 21 × 235 pixels;HH : 21 × 21 pixels.

Notice that the knowledge of the exact p-sequence used in the embedding process is crucial for the securityof the method: without disclosing it, the performed decomposition of the image is kept secret. As an examplethe same number 256 can be obtained as 46th element of the p = 24 Fibonacci sequence, or as 66th element ofthe p = 45 Fibonacci sequence:

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36,

37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 52, 56, 61, 67, 74, 82, 91, 101, 112, 124, 137, 151, 166, 182, 199, 217, 236, 256...

The two decompositions obtained when p = 24 and p = 45 are shown in Figure 1(a)-(b). Other representationsare also feasible: for example, in Figure 1(c) it is depicted the case p = 0 (256 is the 9th element) that correspondsto the classical Haar decomposition.

(a) p=24 (b) p=45 (c) p=0

Figure 1. First order Fibonacci Haar transform.

Let us consider a color image X and let us denote with Xc its color components where c = R, G, B. Let thewatermark W be a binary signal of entries (0, 1). W is partitioned in three parts Wc according to the capacityof each color component.

The embedding-encryption procedure, performed on each Xc, can be summarized as follows (see Figure 2):

Figure 2. Proposed scheme.

1. The first order decomposition of Fibonacci-Haar transform of Xc is computed according to the chosenp-sequence (pc). Let us indicate with Xc the correspondent transform of the color component.

2. The LLc subband is encrypted by using the AES standard. In the performed tests we used a key length of128-bits.

3. To increase the embedding capacity, the subbands LHc, HLc and HHc are partitioned in

B =⌊

Nn−1

Nn−p−1

⌋· 2 + 1 (3)

blocks of size Nn−p−1xNn−p−1 pixels, where Nn−1 is the larger dimension of the LHc, HLc subbandsand Nn−p−1 is the smaller dimension of the LHc, HLc subbands. Each block is decomposed throughthe Singular Value Decomposition (SVD). According to this representation every real matrix A can beexpressed as product of three matrices:

A = USV T (4)

where U and V are orthogonal matrices and S is a diagonal matrix whose singular values S = [s1, ..., sNn−p−1 ],are disposed in decreasing order. In our scheme, the only component of the SVD that is involved in theembedding procedure is S. Since the largest singular values have a strong impact on the perceived imagequality, and the smallest ones are extremely sensitive to noise, we have selected the middle singular valuesto embed the watermark. The embedding is performed according to the SVD watermarking scheme pro-posed in10 as follows:

sij = sij−1 − 1.25∆,sij = sij ,sij = sij−1 − 0.25∆,sij = sij

ifififif

Wck= 1,

Wck= 1,

Wck= 0,

Wck= 0,

sij−1 − sij < 1.25∆sij−1 − sij > 1.25∆sij−1 − sij > 0.75∆sij−1 − sij ≤ 0.75∆

(5)

where i = 1, ..., B, j = l, ..., m with l and m are the index boundaries of the singular values involved in theembedding, ∆ is the selected threshold, sij and sij are the singular values of Si of the watermarked and ofthe original block, respectively, Wck

is the watermark of length B(m− l).

4. Find the smallest singular value a = siz , with l < z < m in the range [sil, sim ]; in order to maintain the

decreasing order of the singular values, find the first b = sih< a, where h > m. Replace the singular values

[siz+1 , sih−1 ] by linear interpolation between a and b.

5. The inverse SVD of each block is computed.

6. The inverse Fibonacci-Haar is computed in order to obtain the c component of the watermarked-encryptedimage.

(a) R component (b) Watermarked-encrypted Rcomponent

(c) G component (d) Watermarked-encrypted Gcomponent

(e) B component (f) Watermarked-encrypted B com-ponent

Figure 3. RGB original and processed components.

Figure 3 shows the RGB components before and after the watermarking-encryption process.

The extraction of the watermark and the decryption procedures are performed individually by analyzing theRGB components of the watermarked-encrypted image X. The following steps have been performed on eachcolor component Xc (c = R,G, B):

1. The first order Fibonacci-Haar decomposition, Xc, is performed according to the secret key pc, which allowsthe receiver to recover the Fibonacci sequence used in the embedding-encryption procedure.

2. The LLc subband undergoes an inverse AES performed with the same 128-bits secret key used by thesender.

3. The subbands LHc, HLc and HHc are partitioned in B blocks as previously described and each block isdecomposed through the SVD. The watermark Wc is extracted from the singular values as:

ifif

sij−1 − sij> ∆,

sij−1 − sij≤ ∆,

Wck= 1,

Wck= 0.

(6)

where i = 1, ..., B, j = l, ..., m with l and m are the index boundaries of the singular values involved in theembedding, ∆ is the selected threshold and k = 1, ..., B · (m− l).

The three components of the extracted watermark Wc are combined and the normalized correlation coefficientbetween the original watermark W and the extracted one W is computed as follows:

ρ =

∑i

∑j

(W −W

) (W − W

)

√∑i

∑j

(W −W

)2(W − W

)2, (7)

where W and W are the average values of W and W .

The presence of the watermark is revealed by comparing the obtained value with a suitable threshold definedby the Neyman Pearson criterion.

4. EXPERIMENTAL RESULTS

To verify the effectiveness of the proposed method several tests have been carried out. Our aim is to showthat the image is non-intelligible for an unauthorized user unless the secret keys pc are known. Moreover, it isimportant to underline that the knowledge of the encryption keys used for the AES procedure is strictly requiredin order to decrypt the color components.

The experimental tests have been performed on different color images of size 256x256 pixels; the watermarkis a pseudo-random binary matrix of size 32x32 pixels generated by a secret seed. The chosen p-sequences arepR = 45, pG = 24 and pB = 0; the decomposition obtained are shown in Figure 1. In order to embed the chosenwatermark the following singular values have been modified:

• the decomposition pR = 45 allows to obtain 23 blocks and in each block the values from the 2nd to the17th are modified with ∆ = 10;

• the decomposition pG = 24 allows to obtain 23 blocks and in each block the values from the 2nd to the17th are modified with ∆ = 10;

• the decomposition pB = 0 allows to obtain 3 blocks and in each block the values from the 10th to the 105thare modified with ∆ = 10.

In the following the results for the Figure 4(a) are shown. Figure 4(b) shows the watermarked-encrypted image.The encryption of the most perceptually significant subbands LLc results in an image that is non intelligible.Figure 4(c) shows the decrypted-watermarked image. The Peak Signal to Noise Ratio (PSNR) and the WeightedPeak Signal to Noise Ratio (WPSNR) are adopted to evaluate the watermark invisibility. The computed valuesfor the watermarked images when no manipulations are performed are:

• Red component: PSNR=47dB WPSNR=42dB;

• Green component: PSNR=46dB WPSNR=35dB;

(a) Original image (b) Watermarked-encrypted image (c) Watermarked image

Figure 4. Experimental results.

• Blue component: PSNR=57dB WPSNR=58dB.

To underline the importance of the secret key pc, we have tried to extract the watermark by using a differentpc from the one used in the embedding-encryption procedure. For example, by using pR = 24, pG = 0, andpB = 45 the correlation value decreases from 0.998 (computed by using the correct pc, that is pR = 45, pG = 24and pB = 0) to 0.009.

To evaluate the robustness of the embedding method different attacks have been performed individually onthe decrypted color component of the image. This choice is due to the fact that it is infeasible for an attackerto recover all the keys needed for the deciphering process and watermark extraction from Xc. Simulations showsimilar performances for the three color components when the same attack is performed. As an example seeFigure 5 for the equalization attack. Therefore we report some results just considering the green component. InTable 1 the correlation values for different kind of attacks are presented.

Attack Parameters ρMotion linear motion of a camera by 10 pixels 0.71Gaussian mean=0, and standard deviation =0.005 0.75Blurring using a circular averaging filter within the square matrix of size=5 0.73Sharpening 3-by-3 contrast enhancement filter 0.75

Table 1. Simulation results.

The JPEG compression attack has been performed on the watermarked image with increasing quality factorfrom 10 to 100 with step 10 and rotation attack has been executed with rotation angle from 0 to 90 degreeswith step 10 degrees. The detector response has been tested with 500 random watermarks and in Figure 6 thefirst and the second highest correlation peaks are depicted for both (a) JPEG and (b) rotation attack. Resultsshow that it is always possible to extract the inserted watermark, thus verifying the robustness of the proposedmethod.

5. CONCLUSIONS

In this work we proposed a new joint watermarking and encryption technique for color images, which exploitsthe Fibonacci-Haar wavelet transform domain to increase its security. The three RGB color components areciphered with the standard block cipher AES, while they are marked via a SVD-based blind watermarkingmethod. Experimental results show the effectiveness of the proposed method and the robustness of the adoptedwatermarking procedure.

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Figure 5. Equalization attack. 500 random watermarks are presented to the detector. The highest peak corresponds tothe original watermark.

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Figure 6. Experimental results.

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