Hybrid Successive CFA Image Encryption-Watermarking Algorithm Based on the Quaternionic Wavelet Transform (QWT)

In this paper, we present a new robust hybrid algorithm combining successively chaotic encryption and blind watermarking of images based on the quaternionic wavelet transform (QWT) to ensure the secure transfer of digital data. The calculations of the different evaluation parameters have been per-formed in order to determine the robustness of our algorithm to certain attacks. The application of this hybrid algorithm on CFA (Color Filter Array) images, allowed us to guarantee the integrity of the digital data and to pro-pose an autonomous transmission system. The results obtained after simulation of this successive hybrid algorithm of chaotic encryption and then blind watermarking are appreciated through the values of the evaluation parameters which are the peak signal-to-noise ratio (PSNR) and the correlation coefficient (CC), and by the visual observation of the extracted watermarks before and after attacks. The values of these parameters show that this successive hybrid algorithm is robust against some conventional attacks.


Introduction
The transfer or archiving of digital data is sometimes insecure. It is therefore essential to have secure systems for the transfer of these data and the protection of the rights holders [1] [2]. For this purpose, several researchers have been interested in securing digital data through different simple protection techniques such as steganography, encryption, and watermarking; and even through different hybrid techniques such as steganography encryption and encryption-watermarking [3]- [16].
Faced with all these difficulties, the robust hybrid method combining successively encryption and watermarking has very naturally appeared as an alternative or complementary solution to strengthen the security of these digital data. Most contributions were made to grayscale images and even more medical images.
However, to our knowledge, the CFA (Color Filter Array) images generated by digital photography [17] have not yet been successive encryption-watermarking based on the quaternionic wavelet transform (QWT). The successive hybrid method of encryption-watermarking is the one we will study in our work with the aim of ensuring the secure transfer of photographic images and obtaining a better compromise between invulnerability (robustness and security) and the amount of information to insert (capacity and imperceptibility). CFA images are important for image analysis because these raw images have not undergone any processing (interpolation, demosaicking, etc. [18] [19] [20]) that might alter their reliability [17] [21]. In the rest of this paper, we will introduce the properties of the quaternionic wavelet transform firstly, and then present the proposed successive encryption-watermarking methodology, the presentation of the results obtained after the simulation of this algorithm and finally the analysis, and discussion of our obtained results.

Definition and Properties of Quaternions
Quaternions are an extension of the complex numbers [Lord William Hamilton in the 19th century] with a real part and three imaginary parts as follows: q a ib jc kd The multiplication of two of these imaginary numbers , , i j k behaves like the vector product of orthogonal unit vectors: The polar writing of a quaternion is, analogous to the exponential complex: e i j k q q ϕ θ β

Quaternionic Structure of an Image
The QWT integrates the concept of phase in a break down into wavelets. Defined from an analytical quaternionic mother wavelet, the QWT provides qualit- Hence, the following quaternionic matrix Q representing the scale function and the corresponding actual additives of the wave function: We, therefore, obtain the matrix w of the different coefficients (a real LL part corresponding to the approximate component and three imaginary parts LH, HL, HH corresponding to the components of details) of the transformed into quaternionic wavelets [26] [27]: In order to display the image after being transformed into a quaternionic wavelet, we arrange the quaternionic coefficients of the matrix w as follows: Two complementary filter banks, one using an even filter, the other an odd filter, lead to four separable 2D filter banks [28], slightly offset from each other.
These shifts correspond theoretically to the phase shifts of the 2D Hilbert transforms. One obtains a sub-pixel precision, translated indirectly in the notion of phase [24]. The original image I 0 is decomposed as shown in Figure 1(A) by a set of quaternion filter banks connected by operators ↓ 2 of data subsampling (downsampling), low-pass (h i ) and high-pass (g i ) filters for the analysis (i taking the values 1 and 2) the signs of interpolation. Likewise, in order to reconstruct the filter banks and the decomposed image, we use the reconstruction structure (Synthesis) given by Figure 1(B), a phase of dilation of the data with insertion of zeros (upsampling), obtained using of the operator ↑ 2 and the low-pass ( i h  ) and high-pass ( i g  ) filtering operations. This allows us to obtain the quaternionic decomposition (Analysis) and reconstruction (Synthesis) structure of an image I 0 given by Figure 1 below.

Chaotic Encryption
The cryptographic method used here is the symmetrical chaotic cryptography.

Blind Watermarking
The watermarking algorithm used in this article is the substitution method in the frequency domain. The coefficients (pixels) of the watermark (tiers-person data, encryption key K, etc.) were embedded by replacing the coefficients of the host image (HH sub-mark) with those of the watermark, using a secret key q.
This key is to determine where the watermark elements should be embedded.
This method also requires a coefficient of strength in order to control the visibility of the watermark. The extraction method used for this method is blind. We only need the secret key to extract the hidden watermark [32].

Tools Used
The raw CFA images of a size of 512 * 512 and 1024 * 1024 pixels used ( Figure   2) in this work come from color images obtained by 3CCD cameras [18] [19].

Proposed Hybrid Successive Image Encryption-Watermarking Algorithm
In this paper, we now present a new hybrid encryption-watermarking algorithm of CFA images successively combining the technologies of chaotic encryption and blind watermarking. However, this algorithm can also be applied to grayscale images. The proposed algorithm is described by the emission and the reception process. Consider the original image I 0 , a CFA image of m n * pixels and the watermark image M, a grayscale image of k l * pixels. The block diagram of the emission process is shown in Figure 3, and is summarized by the following steps: 1) Define a chaotic system and the encryption key k [4]; 2) Encrypt (confuse and broadcast) the original image using the key k: en- The reception process is the reverse of this emission process scheme to obtain reconstructed image I r .

Results and Discussion
The objective of our work was therefore to develop a robust algorithm combining successively encryption and watermarking of digital photography images using quaternions allowing the secure transfer of CFA images. The results obtained where MSE is mean squared error between original and reconstructed images, which is defined as follow: In the next, we will present an example of the application of this hybrid algorithm on image 2 illustrated above Figure 2.
According to the human visual system, we note that from Figure 4, that it is difficult to differentiate the original image from the reconstructed image and the same to the watermark from the extracted watermark after encryption and then watermarking. According to the calculated evaluation parameters, we find that the operation generates an information loss equivalent to the correlation coefficient CC = 0.9996 (with CC ≈ 1) and a peak signal-to-noise ratio PSNR = 42.4562 dB (already > 30 dB). So, we can say that our algorithm for successive encryption-watermarking of CFA images was successful depending on the standards described in the literature.    Table 1 below. We compare our results obtained by our hybrid successive encryption then watermarking algorithm with those of the works of A. Khalfallah et al. [34], W. Puech et al. [35] and Mohamed et al. [36]. The results obtained are presented in Table 2 below: We can see from Table 2 that our results are better on the quality of the reconstructed image since our value (in bold) of PSNR is largely above theirs.

Conclusion
At the end of our work, we were able to achieve our goal by developing a hybrid successive, reversible, and robust encryption-watermarking algorithm applied to CFA images using quaternions.