**1. Introduction**

Several image encryption algorithms are being developed today to meet privacy needs in multimedia communications [1–33]. With the rapid expansion of the Internet, innovative technologies, and cryptanalysis, it has become necessary to build new and appropriate cryptosystems for secured data transfer, especially for digital images. Nowadays, a large quantity of images is produced in various fields and exchanged sometimes with text through different channels, favoring the development of multiple-image encryption (MIE) instead of single-image encryption (SIE). A secure technique to protect the large amounts of data (image and text) exchanged in unsecured communication channels is to combine cryptography and watermarking [26, 27]. These two combined approaches help to produce a two-level security of the text and image, especially when the message is hidden in the image to be encrypted. Various watermarking techniques are proposed in the literature [28–32], and the most used are discrete wavelet transformation (DWT) and discrete cosine transformation (DCT). For instance, if an information, such as a signature, a logo, or a text is embedded in low- or medium-frequency DCT coefficients, then it may be recovered without any loss; however, only high-frequency DCT coefficients are lost in low-pass filtering.

compaction property, which means that the low-frequency coefficients are located around the top-left corner of its spectral plane [24]. In 2018, Jridi and Alfalou [14] proposed a cryptosystem to improve a Simultaneous Fusion,

*Multiple-Image Fusion Encryption (MIFE) Using Discrete Cosine Transformation (DCT)…*

performance in terms of robustness as the number of images to multiplex increases, but suffered from reduced key space and poor quality of images recovered. Mehra and Nishchal [17] proposed an image fusion encryption based on wavelets for securing multiple images through asymmetric keys. It offers a large key space, which enhances the security of the system. In 2016, Qin et al. [18] proposed an optical multiple-image encryption scheme in diffractive imaging

using spectral fusion and nonlinear operations.

*DOI: http://dx.doi.org/10.5772/intechopen.92369*

cipher, on the byte level.

made dependent on the plain images.

**23**

Compression and Encryption (SFCE) scheme [15] in terms of time consumption, bandwidth occupation, and encryption robustness. In [16], Dongfeng et al. proposed a new scheme for simultaneous fusion, imaging and encryption of multiple target images using a single-pixel detector. This algorithm achieves good

More recently, Zhang and Wang [19, 20] proposed two schemes of multipleimage encryption (MIE): the first algorithm based on mixed image element and permutation, and the second MIE algorithm based on mixed image element and chaos. The cryptosystem shows good performances, but can be improved in terms of compression to reduce the size of the multiplex big image when the number of target images increases. In [21], Zhu and Zhang proposed an encryption algorithm of mixed image element based on an elliptic curve cryptosystem. Experimental results and theoretical analysis show that the algorithm possesses a large key space and can accomplish a high level of security concerning information interaction on the network platform, but the encryption and decryption computational time is long. In 2013, Abdalla and Tamimi [22] proposed a cryptosystem, which combines two or more images of different types and sizes by using a shuffling-substitution procedure. Here, the process of mixing image combines stream cipher with block

After analyzing most MIE algorithms operating in the spectral domain, the robustness of the cryptosystem increases with the number of input images. Consequently, the quality of decrypted images is degraded. Therefore, it is important to design cryptosystems that can keep a good compromise between a large number of images added to text to encrypt, a small MSE after decryption,

As a result, this chapter suggests a new MIE algorithm based on the spectral fusion of different types of watermarked images of same size using discrete cosine transformation (DCT) associated with a low-pass filter and chaotic maps. The proposed scheme has several strengths: it is robust, combines watermarking and cryptography, which produce a two-level security, uses chaotic maps with good properties, encrypts a large number of watermarked images into two hybrid ciphered images, and the quality of the reconstructed images and text is good (reduced MSE). The encryption process comprises three main steps: in the first step, target images are fused into two images through DCT and low-pass filter; in the second step, the small blocks with the size of (4 4) images are permuted in a certain order; and in the last step, which is the diffusion phase, the two scrambled images are fused by a nonlinear mathematical expression based on Cramer's rule to obtain two hybrid encrypted images. The key generation of the cryptosystem is

The rest of the chapter is organized as follows: Section 2 presents an overview of

watermarking process. In Section 3, spectral fusion of plain images is detailed. The proposed encryption/decryption scheme is given in Section 4. In Section 5, experimental results and algorithm analyses are presented, then compared with others in

chaotic generators used in the cryptosystem and the description of the

the literature. We end with a conclusion in Section 6.

and a good performance in terms of robustness and efficiency.

In literature, many encryption algorithms, such as International Data Encryption Algorithm (IDEA), Advanced Encryption Standard (AES), and Data Encryption Standard (DES) have been proposed [1]. However, these standard algorithms do not seem to be appropriate for image encryption, because of the intrinsic features of images, such as huge data capacity, high redundancy, strong correlation among adjacent pixels, and low entropy [2]. Some basic properties of chaotic systems such as the sensitivity to the initial condition and control parameters, sensitivity to plain text, ergodicity and randomness behavior, meet the requirements for a good cryptosystem. Consequently, several cryptosystems were developed by researchers, based on chaotic systems because the latter provided a good combination of speed, high security, complexity, reasonable computational overheads, and computational power [3]. With these features, chaotic-based cryptosystems have excellent properties of confusion and diffusion, which are desirable in cryptography. Therefore, many techniques involving different chaotic systems have been published [2–12, 23], and we can distinguish one-dimensional (1D) chaotic maps and highdimensional (HD) chaotic maps.

Among the chaotic encryption algorithms developed, the ones using a onedimensional (1D) chaotic system like Logistic, May, Tent, and Sine map have proven to have some strengths, such as: high-level efficiency, simplicity, and highspeed encryption. 1D chaotic structures have been widely used [4] due to their simple structures, as opposed to the complex ones of higher dimensional chaotic system (which causes a relative slowness in computation). However, some schemes using the 1D map have been broken due to their weaknesses like nonuniform data output, small key space, periodic data output, and poor ergodicity properties for some ranges of control parameters [5, 6]. To overcome this drawback, some researchers stated that the 1D chaotic map should not be used alone [7, 8]. Others proposed new 1D chaotic systems with better properties like Spatiotemporal chaos in [9], coupled with the 1D chaotic map [6], the Nonlinear Chaotic map Algorithm (NCA) [10], and, more recently, nonlinear combinations of two different 1D chaotic maps [3, 11, 12]. For example, Abanda and Tiedeu [3] combined outputs of Duffing and Colpitts chaotic systems to encrypt gray and color images. Kamdeu and Tiedeu [11] proposed a fast and secured encryption scheme using new 1D chaotic systems obtained from Logistic, May, Gaussian, and Gompertz maps. In [12], Chenaghlu et al. proposed a polynomial combination of 1D chaotic maps for image encryption using dynamic functions generation.

Recently, in order to increase the efficiency of cryptosystems for multiple images, some authors proposed algorithms integrating the concept of fusion or mixing images as a step in the encryption process. Image fusion has been proven to have potential for encryption in both spatial and frequency domains. In the last 8 years, much effort has been devoted to compressing and encrypting images at the same time [13], which is considered as a new tool used to reduce the amount of data to be transmitted and protecting the use of these data against unauthorized access. In particular, the discrete cosine transformation (DCT) is employed as a useful tool for spectral fusion in most of these methods. The widely used application DCT for image compression is mainly based on its energy

*Multiple-Image Fusion Encryption (MIFE) Using Discrete Cosine Transformation (DCT)… DOI: http://dx.doi.org/10.5772/intechopen.92369*

compaction property, which means that the low-frequency coefficients are located around the top-left corner of its spectral plane [24]. In 2018, Jridi and Alfalou [14] proposed a cryptosystem to improve a Simultaneous Fusion, Compression and Encryption (SFCE) scheme [15] in terms of time consumption, bandwidth occupation, and encryption robustness. In [16], Dongfeng et al. proposed a new scheme for simultaneous fusion, imaging and encryption of multiple target images using a single-pixel detector. This algorithm achieves good performance in terms of robustness as the number of images to multiplex increases, but suffered from reduced key space and poor quality of images recovered. Mehra and Nishchal [17] proposed an image fusion encryption based on wavelets for securing multiple images through asymmetric keys. It offers a large key space, which enhances the security of the system. In 2016, Qin et al. [18] proposed an optical multiple-image encryption scheme in diffractive imaging using spectral fusion and nonlinear operations.

More recently, Zhang and Wang [19, 20] proposed two schemes of multipleimage encryption (MIE): the first algorithm based on mixed image element and permutation, and the second MIE algorithm based on mixed image element and chaos. The cryptosystem shows good performances, but can be improved in terms of compression to reduce the size of the multiplex big image when the number of target images increases. In [21], Zhu and Zhang proposed an encryption algorithm of mixed image element based on an elliptic curve cryptosystem. Experimental results and theoretical analysis show that the algorithm possesses a large key space and can accomplish a high level of security concerning information interaction on the network platform, but the encryption and decryption computational time is long. In 2013, Abdalla and Tamimi [22] proposed a cryptosystem, which combines two or more images of different types and sizes by using a shuffling-substitution procedure. Here, the process of mixing image combines stream cipher with block cipher, on the byte level.

After analyzing most MIE algorithms operating in the spectral domain, the robustness of the cryptosystem increases with the number of input images. Consequently, the quality of decrypted images is degraded. Therefore, it is important to design cryptosystems that can keep a good compromise between a large number of images added to text to encrypt, a small MSE after decryption, and a good performance in terms of robustness and efficiency.

As a result, this chapter suggests a new MIE algorithm based on the spectral fusion of different types of watermarked images of same size using discrete cosine transformation (DCT) associated with a low-pass filter and chaotic maps. The proposed scheme has several strengths: it is robust, combines watermarking and cryptography, which produce a two-level security, uses chaotic maps with good properties, encrypts a large number of watermarked images into two hybrid ciphered images, and the quality of the reconstructed images and text is good (reduced MSE). The encryption process comprises three main steps: in the first step, target images are fused into two images through DCT and low-pass filter; in the second step, the small blocks with the size of (4 4) images are permuted in a certain order; and in the last step, which is the diffusion phase, the two scrambled images are fused by a nonlinear mathematical expression based on Cramer's rule to obtain two hybrid encrypted images. The key generation of the cryptosystem is made dependent on the plain images.

The rest of the chapter is organized as follows: Section 2 presents an overview of chaotic generators used in the cryptosystem and the description of the watermarking process. In Section 3, spectral fusion of plain images is detailed. The proposed encryption/decryption scheme is given in Section 4. In Section 5, experimental results and algorithm analyses are presented, then compared with others in the literature. We end with a conclusion in Section 6.

exchanged in unsecured communication channels is to combine cryptography and watermarking [26, 27]. These two combined approaches help to produce a two-level security of the text and image, especially when the message is hidden in the image to be encrypted. Various watermarking techniques are proposed in the literature [28–32], and the most used are discrete wavelet transformation (DWT) and discrete cosine transformation (DCT). For instance, if an information, such as a signature, a logo, or a text is embedded in low- or medium-frequency DCT coefficients, then it may be recovered without any loss; however, only high-frequency DCT coefficients

In literature, many encryption algorithms, such as International Data Encryption Algorithm (IDEA), Advanced Encryption Standard (AES), and Data Encryption Standard (DES) have been proposed [1]. However, these standard algorithms do not seem to be appropriate for image encryption, because of the intrinsic features of images, such as huge data capacity, high redundancy, strong correlation among adjacent pixels, and low entropy [2]. Some basic properties of chaotic systems such as the sensitivity to the initial condition and control parameters, sensitivity to plain text, ergodicity and randomness behavior, meet the requirements for a good cryptosystem. Consequently, several cryptosystems were developed by researchers, based on chaotic systems because the latter provided a good combination of speed, high security, complexity, reasonable computational overheads, and computational power [3]. With these features, chaotic-based cryptosystems have excellent properties of confusion and diffusion, which are desirable in cryptography. Therefore,

many techniques involving different chaotic systems have been published [2–12, 23], and we can distinguish one-dimensional (1D) chaotic maps and high-

Among the chaotic encryption algorithms developed, the ones using a onedimensional (1D) chaotic system like Logistic, May, Tent, and Sine map have proven to have some strengths, such as: high-level efficiency, simplicity, and highspeed encryption. 1D chaotic structures have been widely used [4] due to their simple structures, as opposed to the complex ones of higher dimensional chaotic system (which causes a relative slowness in computation). However, some schemes using the 1D map have been broken due to their weaknesses like nonuniform data output, small key space, periodic data output, and poor ergodicity properties for some ranges of control parameters [5, 6]. To overcome this drawback, some researchers stated that the 1D chaotic map should not be used alone [7, 8]. Others proposed new 1D chaotic systems with better properties like Spatiotemporal chaos in [9], coupled with the 1D chaotic map [6], the Nonlinear Chaotic map Algorithm (NCA) [10], and, more recently, nonlinear combinations of two different 1D chaotic maps [3, 11, 12]. For example, Abanda and Tiedeu [3] combined outputs of Duffing and Colpitts chaotic systems to encrypt gray and color images. Kamdeu and Tiedeu [11] proposed a fast and secured encryption scheme using new 1D chaotic systems obtained from Logistic, May, Gaussian, and Gompertz maps. In [12], Chenaghlu et al. proposed a polynomial combination of 1D chaotic maps for image

Recently, in order to increase the efficiency of cryptosystems for multiple images, some authors proposed algorithms integrating the concept of fusion or mixing images as a step in the encryption process. Image fusion has been proven to have potential for encryption in both spatial and frequency domains. In the last 8 years, much effort has been devoted to compressing and encrypting images at the same time [13], which is considered as a new tool used to reduce the amount

unauthorized access. In particular, the discrete cosine transformation (DCT) is employed as a useful tool for spectral fusion in most of these methods. The widely used application DCT for image compression is mainly based on its energy

of data to be transmitted and protecting the use of these data against

are lost in low-pass filtering.

*Multimedia Information Retrieval*

dimensional (HD) chaotic maps.

encryption using dynamic functions generation.

**22**
