Medical image encryption algorithm based on hyper‐chaotic system and DNA coding

Cognitive Computation and SystemsVolume 4, Issue 4 p. 378-390 ORIGINAL RESEARCHOpen Access Medical image encryption algorithm based on hyper-chaotic system and DNA coding Mingzhen Li, Mingzhen Li School of Information Engineering, Henan University of Science and Technology, Luoyang, China Lushi Chinese Medicine Hospital, Sanmenxia, ChinaSearch for more papers by this authorShuaihao Pan, Shuaihao Pan School of Computer, Harbin Engineering University, Harbin, ChinaSearch for more papers by this authorWeiming Meng, Weiming Meng School of Information Engineering, Henan University of Science and Technology, Luoyang, ChinaSearch for more papers by this authorWang Guoyong, Corresponding Author Wang Guoyong [email protected] orcid.org/0000-0002-7784-9294 School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang, China Correspondence Wang Guoyong, School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang 471023, China. Email: [email protected]Search for more papers by this authorZhihang Ji, Zhihang Ji School of Information Engineering, Henan University of Science and Technology, Luoyang, ChinaSearch for more papers by this authorLin Wang, Lin Wang School of Information Engineering, Henan University of Science and Technology, Luoyang, ChinaSearch for more papers by this author Mingzhen Li, Mingzhen Li School of Information Engineering, Henan University of Science and Technology, Luoyang, China Lushi Chinese Medicine Hospital, Sanmenxia, ChinaSearch for more papers by this authorShuaihao Pan, Shuaihao Pan School of Computer, Harbin Engineering University, Harbin, ChinaSearch for more papers by this authorWeiming Meng, Weiming Meng School of Information Engineering, Henan University of Science and Technology, Luoyang, ChinaSearch for more papers by this authorWang Guoyong, Corresponding Author Wang Guoyong [email protected] orcid.org/0000-0002-7784-9294 School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang, China Correspondence Wang Guoyong, School of Computer and Information Engineering, Luoyang Institute of Science and Technology, Luoyang 471023, China. Email: [email protected]Search for more papers by this authorZhihang Ji, Zhihang Ji School of Information Engineering, Henan University of Science and Technology, Luoyang, ChinaSearch for more papers by this authorLin Wang, Lin Wang School of Information Engineering, Henan University of Science and Technology, Luoyang, ChinaSearch for more papers by this author First published: 24 August 2022 https://doi.org/10.1049/ccs2.12070AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract With the international development of the medical service informatisation, medical information sharing has become the key standard to measure the degree of medical informatisation. In this process, it is important to ensure the security of patients' medical information such as patients' records, examination reports, images and so on. In this article, an image encryption scheme based on Secure Hash Algorithm 3 (SHA-3), DNA coding and high dimensional chaos system is proposed to promote the security level of medical images in information sharing processes such as over the network. First, SHA-3 algorithm is used to calculate the hash value of the input image, and the result is taken as the initial value of the hyper-chaotic system. Second, the intensity value of the input image is converted into a serial binary digital stream. Third, the pseudo-random sequence generated by a 4-dimensional hyper-chaotic system is used to perturb the bit stream globally so as to achieve the purpose of hiding the effective information of the input image. During the operation of hyper-chaotic sequence and DNA sequence, algebraic and complementary operations are performed on DNA encoding values to enhance encryption performance. Finally, simulations have been applied on an open-source medical image database, and the results demonstrate obvious encryption effectiveness and high security level of the proposed encryption algorithm in the robustness of noise and clipping attacks. 1 INTRODUCTION Under the background of health and medical big data, the construction of medical informatisation is bound to break the traditional data island and move towards sharing and opening. Therefore, health and medical big data has shown an increasingly active 'flow' trend and played a value in the 'flow'. For example, new type of businesses such as hierarchical diagnosis and treatment, telemedicine, health management certainly will drive the orderly movement, rational utilisation and security share of medical data. There are many potential safety hazards in the process of data 'flow': for individuals, they are especially concerned about data privacy disclosure; for medical institutions and competent authorities, they are concerned about whether the data is 'healthy', that is, whether the data is true, complete and reliable. Therefore, security has become the core concern of health and medical big data. However, health and medical big data is facing unprecedented security challenges at present. In the 'Internet +' era, the boundary of data becomes more and more blurred and open, attracting more and more advantaged, secret and utilitarian means of network attacks [1]. In the case of medical images, the risk of privacy disclosure is increasing year by year. For example, Greenbone's research has revealed that 1.19 billion confidential medical images were divulged in November 2019 alone, which are stored on the security of image archive and communication system (PACS) servers used by worldwide healthcare providers to store X-ray images, as well as CT, MRI and other medical scans [2]. And according to an April report from the USA department of health and human services, the average value of health records on the dark web is $25 to $1000, which can reflect the attackers' strong interest in such information from the side. The serious degree of medical image information theft makes people realise that it is imperative to solve the medical image information security transmission problem. As it is well known that one effective way is to encrypt the image. Encryption technology plays an important role in the field of information security. The continuous innovation of image encryption is particularly important because the widely existing image information encryption algorithms, such as data encryption standard, advanced encryption standard, Rivest-Shamir-Adleman public-key cryptosystem and other traditional encryption algorithms cannot meet the current requirements of image encryption already. Medical images concern patients' privacy, so more suitable encryption methods are needed in terms of encryption. Therefore, the exploration of secure and efficient image encryption algorithm has become a research hotspot. In recent years, many image encryption algorithms have been proposed based on such as chaos theory [3-8] or DNA sequence [9]. For the first type of image encryption methods, there is a close relationship between chaos and cryptography, because the characteristics of chaotic systems are consistent with the requirements of cryptography such as sensitivity to initial values, strong dispersion and unpredictability of orbit and good pseudo-random properties and so on. Therefore, chaos cryptography has been studied and applied to image encryption fields. For example, in Ref. [3, 4], the key associated with the plain image is used as the initial value of the non-linear chaotic system Henon, and a cross-component dislocation and diffusion strategy are applied to the measurements using the chaotic sequences generated by Henon to obtain the secret image to enhance the ability of the algorithm to resist chosen-plaintext attack. However, the dispersion of random sequence generated by the low-dimensional chaotic system is poor and the chaos interval is narrow, which result in small key space, uneven ciphertext distribution, poor security performance and easy cracking. In order to increase the randomness of chaotic sequences and expand the key space, scholars have designed image encryption algorithms based on hyper-chaos [10] and multilevel chaos [11]. Among them, the hyper-chaotic system has two or more Lyaponuv index due to large key space, better chaos characteristics and security, so it has been widely used in biology, mathematics, engineering, information technology, economics, robotics and other fields. It's worth noting that the weakness of low sensitivity to keys in hyper-chaotic systems is gradually exposing with the development of cryptography. For the second type of image encryption methods, the DNA coding algorithm proposed by Adleman [12] in 1994 has provided a new development idea and technology for cryptography and been widely in image encryption field because of its low-consumption and high-density information storage capacity. DNA coding is one of the fastest developing new technologies in the field of genetic research [13]. In Ref. [14], a fast encryption algorithm based on hyper-chaotic images was proposed to improve the performance of correlation coefficients by scrambling pixel positions into pixel positions. Ref. [15] proposed a new image encryption algorithm based on chaos system. By using logical mapping to generate row coordinates and column coordinates, the plane image is scrambled, and the logical chaotic mapping is generated into a matrix with the same size as the original image. exclusive OR (XOR) operation is used to diffuse scrambled pixel matrix, while, due to the simple structure of low-dimensional chaotic system, the key space is small and the security is poor. In Ref. [16] proposed a new image encryption algorithm based on hyper-chaos system and ciphertext staggered diffusion, which improves the key space through two pixel replacement and diffusion operations. In Ref. [17] proposed an image encryption algorithm based on chaos and DNA dynamic coding, but the single DNA operation rules led to easy cracking. In Ref. [18] proposed an improved algorithm for image encryption based on DNA encoding and multi-chaotic mapping, which adopted quaternion encoding to improve efficiency and embedded key encryption in the encryption process. But the ciphertext security performance is poor due to the low correlation between the key and plaintext. In Ref. [19] pointed out that the current encryption algorithm based on chaos and DNA coding theories for true-colour map has low sensitivity to plaintext and key, resulting in vulnerable to plaintext attacks. In Ref. [20], a global scrambling method was used for image encryption by cross-using hyper-chaos and DNA sequence, which has improved the encryption performance of images greatly. In order to promote the efficiency of medical image encryption and decrypt the correct plaintext images under the influence caused by crop impacts or noise accumulation in transmission, a novel image encryption (S-HC-DNA) method based on Secure Hash Algorithm 3 (SHA-3), hyper-chaotic sequences and DNA sequence is proposed in this article. And experimental results show that the S-HC-DNA method achieves better image encryption performance compared with other existing methods. The rest of the article is organised as follows. Section 2 surveys the related work about the proposed method. Section 3 elaborates the whole framework of the proposed method. Section 4 presents the experiments in detail and discusses the results. Finally, concluding remarks are given in Section 5. 2 THEORETICAL PRINCIPLE SHA-3 algorithm Medical images usually have large contiguous areas with the same value of pixels. If the algorithm simply generates ciphertext by XOR operations of the encrypted sequence and plaintext, the attackers can easily analyse the corresponding key sequence according to this contiguous area. Therefore, the encryption algorithm should change the situation where the plaintext causes a single change in the ciphertext in some way. Therefore, the hashing algorithm is used in this work to expand the secret key space to overcome the above problem. The hashing algorithm is an important part of information security field, mainly including generating and verifying digital signatures, and key derivation and pseudorandom bit generation of three steps. Hash algorithms are very sensitive to small changes in the image. Any change in the value of a pixel will completely change the calculated hash value. The SHA-3 algorithm is the third generation of standard hash function in SHA family based on sponge structure [21], which has been widely used in information interaction. Unlike previous hashing algorithms, SHA-3 is a permutation-based encryption function. It has the advantages of low overhead, fast encryption speed and no limit on message length. Hyper-chaotic system Since Lorenze discovered the first chaotic system in 1963, many new chaotic systems have been discovered, such as Chuan system, Chen system and Lű system. The chaotic system has a Lyapunov exponent, and its phase trajectory is separated in one direction and dynamics is complex, which can be used for secure communication. In 2011, the authors in Ref. [22] constructed a new 4-dimensional hyper-chaotic system based on the Yang-Chen chaotic system, which can generate complex dynamic behaviours with the change of parameters, and the trajectory has a large ergodic range in its phase space. The mathematical model of the hyper-chaotic system is described as follows. { x ̇ 1 = α x 2 − x 1 + λ 1 x 4 x ̇ 2 = ξ x 1 − x 1 x 3 + λ 2 x 4 x ̇ 3 = − β x 3 + x 1 x 2 + λ 3 x 4 x ̇ 4 = − τ x 1 $\begin{array}{l}\left\{\begin{array}{l}{\dot{x}}_{1}=\alpha \left({x}_{2}-{x}_{1}\right)+{\lambda }_{1}{x}_{4}\hfill \\ {\dot{x}}_{2}=\xi {x}_{1}-{x}_{1}{x}_{3}+{\lambda }_{2}{x}_{4}\hfill \\ {\dot{x}}_{3}=-\beta {x}_{3}+{x}_{1}{x}_{2}+{\lambda }_{3}{x}_{4}\hfill \\ {\dot{x}}_{4}=-\tau {x}_{1}\hfill \end{array}\hfill\right. \end{array}$ (1) The system (1) is 4-dimensional and contains 2 non-linear product terms. The coefficients in the formula are normal numbers, where α, β, ξ, τ, λ1, λ2 and λ3 are the system control parameters, and x1, x2, x3 and x4 are the change rate of system state variables with time. When the parameters α = 35, β = 3, ξ = 35, τ = 5, λ1 = 1, λ2 = 0.2 and λ3 = 0.3, there are two positive Lyapunov indices [23]. The system is in hyper-chaotic state and the values of hyper-chaotic attractor are shown in Figure 1. FIGURE 1Open in figure viewerPowerPoint Phase diagrams of hyperchaotic systems. x1 − x2 plane, x1 − x3 plane, and x2 − x3 plane from top to bottom [22] DNA encoding DNA is a double-stranded polymer whose sequence contains 4 bases: adenine (A), cytosine (C), guanine (G), and thymine (T), where A is complementary to T and C is complementary to G [24]. The value of each pixel in the grey-scale image can be represented as an 8-bit binary number, since 0 and 1 are also complementary in the binary system, so 00 and 11, 01 and 10 are complementary. A DNA base can be represented by two binary digits. Even there are 24 encoding rules in total, only 8 rules satisfy the complementary relationship between DNA bases [25], as shown in Table 1. TABLE 1. DNA coding rules Rule 1 2 3 4 5 6 7 8 00 A A C C G G T T 01 C G A T A T C G 10 G C T A T A G C 11 T T G G C C A A DNA sequence algebraic operation In DNA computing, the traditional binary addition and subtraction algorithm are applied to DNA addition, subtraction and XOR. The addition, subtraction and XOR operation rules of DNA are shown in Tables 2–4, respectively [26]. TABLE 2. DNA sequence adding rule ++ A G C T A A G C T G G C T A C C T A G T T A G C TABLE 3. IDNA sequence subtracting rule - - A G C T A A T C G G G A T C C C G A T T T C G A TABLE 4. DNA XOR operation rule ⊕ A G C T A A G C T G G A T C C C T A G T T C G A 3 S-HC-DNA IMAGE ENCRYPTION SCHEME The whole schematic diagram of the proposed S-HC-DNA image encryption method is shown in Figure 2. First, the SHA-3 algorithm is used to calculate the hash value of the input image, and the initial hyper-chaotic key sequence of the hyper-chaotic system is calculated. Second, the intensity value of the input image is converted into a serial binary digital stream. Third, a hyper-chaotic key sequence was regarded as the inputs of global bit scrambling (GBS), DNA addition, DNA complement and Binary XOR modules after different operations. Then, the pseudo-random sequence generated by a 4-dimensional hyper-chaotic system is used to perturb the bit stream globally. Here, the GBS algorithm is used to realise pixel position scrambling and pixel value replacement. DNA addition, DNA complement, and Binary XOR are used to solve the problem of low correlation between adjacent pixels to achieve good encryption efficiency. FIGURE 2Open in figure viewerPowerPoint Flow chart of S-HC-DNA encryption algorithm Hyper-chaotic initial value generation An 8-bit grey-scale image P size of L = m × n with an intensity value in the range [0, 255] is regarded as the initial input, where m is the width and n is the height of the image, respectively. The input image will be calculated with the SHA-3 algorithm to obtain a set of 256-bit hash value H, which is used to generate the initial values of the hyper-chaotic system. A sequence h is acquired as h1, h2, h3, …, h32 by dividing the hash value H into 32 pieces. Supposing the number of horizontal pixels in the image is ψ, the calculation formulas of initial values of hyper-chaos are described as follows. x 1 = h 1 ⊕ h 2 ⊕ ⋅ ⋅ ⋅ ⊕ h 8 / 2 ψ + x 0 x 2 = h 9 ⊕ h 10 ⊕ ⋅ ⋅ ⋅ ⊕ h 16 / 2 ψ x 3 = h 17 ⊕ h 18 ⊕ ⋅ ⋅ ⋅ ⊕ h 24 / 2 ψ x 4 = h 25 ⊕ h 26 ⊕ ⋅ ⋅ ⋅ ⊕ h 32 / 2 ψ $\begin{array}{rl}\hfill & {x}_{1}=\left({h}_{1}\oplus {h}_{2}\oplus \cdot \cdot \cdot \oplus {h}_{8}\right)/{\mathrm{2}}^{\psi }+{x}_{0}\hfill \\ \hfill & {x}_{2}=\left({h}_{9}\oplus {h}_{10}\oplus \cdot \cdot \cdot \oplus {h}_{16}\right)/{\mathrm{2}}^{\psi }\hfill \\ \hfill & {x}_{3}=\left({h}_{17}\oplus {h}_{18}\oplus \cdot \cdot \cdot \oplus {h}_{24}\right)/{\mathrm{2}}^{\psi }\hfill \\ \hfill & {x}_{4}=\left({h}_{25}\oplus {h}_{26}\oplus \cdot \cdot \cdot \oplus {h}_{32}\right)/{\mathrm{2}}^{\psi }\hfill \end{array}$ (2)where x1, x2, x3, and x4 are the initial values of the hyper-chaotic system and x0 is set to 0.12 in this work. Hyper-chaotic key sequence generation Because the 4-dimensional hyper-chaotic system generates complex dynamic behaviours with the change of parameters and its phase space has a large traversal range, the generated sequence has excellent randomness and good statistical properties [27]. A pseudo-random sequence is generated by using a hyper-chaotic system. The steps are as follows. Step 1: Hyper-chaotic system preiterates t ≠ 0 times to eliminate the adverse effects of transient effects. Step 2: Start from t + 1, the hyper-chaotic system continues to be iterated L times to generate the 4 state values x 1 j , x 2 j , x 3 j , x 4 j $\left\{{x}_{1}^{j},{x}_{2}^{j},{x}_{3}^{j},{x}_{4}^{j}\right\}$ of the hyper-chaotic system. Step 3: Each state value x i j ${x}_{i}^{j}$ is used in the iterative process to generate two different key values s i a j , s i b j ∈ [ 0 , 255 ] , ( i = 1 , 2 , 3 , 4 ) $\left\{{\left({s}_{i}^{a}\right)}^{j},{\left({s}_{i}^{b}\right)}^{j}\right\}\in [0,255],(i=1,2,3,4)$ are calculated, respectively, as follows. s i a j = mod ⌊ | x i i | − ⌊ | x i i | ⌋ × 1 0 7 ⌋ , 256 s i b j = mod mod | x i i | − | x i j | × 10 15 , 10 8 , 256 $\begin{array}{rl}\hfill & {\left({s}_{i}^{a}\right)}^{j}=\,\mathrm{mod}\,\,\left\{\left(\lfloor \left(\vert {x}_{i}^{i}\vert -\lfloor \vert {x}_{i}^{i}\vert \rfloor \right)\times 1{0}^{7}\rfloor \right),256\right\}\hfill \\ \hfill & {\left({s}_{i}^{b}\right)}^{j}=\,\mathrm{mod}\,\,\left(\lfloor \,\mathrm{mod}\,\,\left\{\left[\left(\vert {x}_{i}^{i}\vert -\lfloor \vert {x}_{i}^{j}\vert \rfloor \right)\times {10}^{15}\right],{10}^{8}\right\}\rfloor ,256\right)\ \hfill \end{array}$ (3)where ⌊⋅⌋ denotes flooring operation and mod (⋅) denotes the modulo operation, which rounds the element to a nearest integer towards minus infinity. The generated key sequence value is applied to the generated vector in Equation (4). s j = s 1 a j , s 2 a j , s 3 a j , s 4 a j , ( s 1 b ) j , ( s 2 b ) j , ( s 3 b ) j , ( s 4 b ) j ${s}^{j}=\left[{\left({s}_{1}^{a}\right)}^{j},{\left({s}_{2}^{a}\right)}^{j},{\left({s}_{3}^{a}\right)}^{j},{\left({s}_{4}^{a}\right)}^{j},{({s}_{1}^{b})}^{j},{({s}_{2}^{b})}^{j},{({s}_{3}^{b})}^{j},{({s}_{4}^{b})}^{j}\right]$ (4) Step 4: After the iteration is completed, the generated sequence is applied to Equation (5) to generate K. k η = s 1 , s 2 , … , s L ${k}_{\eta }=\left[{s}^{1},{s}^{2},\text{\ldots },{s}^{L}\right]$ (5)where kη is used to represent the elements in K, η ∈ 1 , 8 $\eta \in \left[1,8\right]$ . Global bit scrambling The correlation between adjacent pixels of image P is reduced by globally scrambling the image intensity values pixel-by-pixel. At the same time, the intensity value of each pixel of image P changes in the GBS process, which means that the pixel replacement is implemented simultaneously by GBS. The GBS implementation steps are described as follows. Step 1: A binary image with 256 grey levels can be represented as an 8-bit binary sequence: α = ∑ i = 1 8 b i 2 i − 1 $\alpha =\sum\limits _{i=1}^{8}{b}_{i}{2}^{i-1}$ (6)where bi ∈ {0, 1}i = 1, 2⋯8; therefore, the grey image P can be decomposed into 8 bit-planes and the ith bit-plane consists of the ith bit of all grey values. Step 2: The intensity values of each pixel of image P are represented by binary numbers and arranged in order. So we have a one-dimensional binary sequence b0. The generated hyper-chaotic sequence is arranged in ascending order to obtain the index sequence k0. Step 3: A new one-dimensional binary sequence b1 is obtained by perturbing the intensity value sequence b0 globally according to the index sequence k0. b i 1 = b k i 0 0 , i ∈ [ 1 , 8 L ] ${b}_{i}^{1}={b}_{{k}_{i}^{0}}^{0},i\in [1,8L]$ (7) Image encryption The flow chart of S-HC-DNA encryption algorithm process is shown in Figure 2. The detailed encryption steps are as follows. Step 1: Input initial parameters. Input the original plaintext image P. A 256-bit hash sequence H is obtain by the SHA-3 algorithm and divided into 32 pieces. Then 4 bit sequences of length 8L with extremely randomness x1, x2, x3, x4 are generated according to Equation (2) and (4) random decimal sequences M1, M2, M3, M4 of length L are obtained by combining eight consecutive bits without repeating them, which is regarded as the initial values of the hyper-chaotic system. Finally, the hyper-chaotic key sequence K of length 8L is generated. Step 2: Preprocessing. The plaintext image P is decomposed into 8 bit-planes. Then convert the 256-bit hash sequence H0 into a decimal one Hd. Supposing H1 and H2 are the sum of odd and even terms of Hd, respectively. Take (H1 ⊕ H2) as seed to generate 8 random values of [0, 255] and carry out ascending processing on them, which will be regarded as the secret key H. Scrambling the 8 bit-planes according to the ascending sequence to achieve reordering and a new image P1 of size 8L is obtained according to Equation (6). Step 3: Global scrambling operation. The hyper-chaotic system key sequence K is divided into eight pieces, and each one is took as a scrambled sequence according to Equation (5). Then the GBS operation is performed to generate a binary sequence b1 for each bit-plane image. Step 4: DNA encoding. First, encode b1 using the DNA encoding rule 1 in Table 1 to generate a sequence d1. In this work, set d0 = A as the initial value and the "++" in the formula represents the addition of DNA. Finally, add DNA to each element of d1 by adopting rules in Table 2 to generate a new DNA sequence d2. The formula for addition is as follows. d 1 2 = d 0 + + d 1 1 d i 2 = d i − 1 2 + + d i 1 , i ∈ [ 2 , 4 L ] $\left\{\begin{array}{l}{d}_{1}^{2}={d}_{0}++{d}_{1}^{1}\quad \hfill \\ {d}_{i}^{2}={d}_{i-1}^{2}++{d}_{i}^{1},i\in [2,4L]\quad \hfill \end{array}\right.$ (8) Second, a decimal sequence ks = M1 ⊕ M2 ⊕ M3 ⊕ M4 is obtained and converted to binary sequence bk. Use the DNA coding rule 3 in Table 1 to encode bk to dk. The d3 sequence is obtained by DNA addition operation on d2 and dk. Step 5: DNA complement and decoding. First, define a threshold function as follows. f ( r ) = 0 , 0 ≤ r 255 ≤ 0.5 1 , 0.5 ≤ r 255 ≤ 1 $f(r)=\left\{\begin{array}{l}0,\quad \quad 0\le \frac{r}{255}\le 0.5\quad \hfill \\ 1,\quad \quad 0.5\le \frac{r}{255}\le 1\quad \hfill \end{array}\right.$ (9) A sequence is obtained from the hyper = chaotic key K, and [k1, k1⋯ , k4L] is converted to mask sequence w according to Equation (9). Then a new DNA sequence d4 is constructed by using d3 according to the DNA complementary rule in Table 5 when the mask element wi = 1. TABLE 5. DNA complementary rule - A G C T T C G A Second, Use the inverse of DNA encoding rule 1 in Table 1 to encode d4 to obtain a binary sequence b2. And an encrypted binary sequence b3 is generated by performing an XOR operation between b2 and bk. Step 6: Output. Finally the ciphertext image Z is obtained by converting the binary sequence b3. And the secret key K is also output for the decryption process. Image decryption The process of image decryption is just the reverse of encryption, using the secret key H to decrypt the ciphertext image. The specific decryption process of the proposed method is as follows. Step 1: Input initial parameters. The secret key H is used to generate the initial values of the hyper-chaotic system x1, x2, x3, x4 and the random sequence K required for the encryption process. And the ciphertext image Z is converted into binary sequence b3. Step 2: Preprocessing. bk can be obtained by doing the same as in Step 1 in encryption process. Then the binary sequence b2 can be acquired by performing an XOR operation between the sequences bk and b3. Step 3: Inverse of DNA decoding and complement. First, convert b2 into a decimal sequence DEC4 and encode it by the rule 1 in Table 1 to obtain the sequence d4. Second, generate the mask sequence w according to Equation (9) and then obtain d3 by using mask sequences w and d4. Step 4: Inverse of DNA encoding. Encode the hyper-chaotic key sequence K by rule 3 in Table 1 to obtain dk. Then sequence d2 can be acquired by using the DNA subtracted d3 from dk according to the rules in Table 3. Step 5: Inverse of Global scrambling operation. Subtract DNA to each element of d2 by adopting rules in Table 3 to generate a new DNA sequence d1. The formula for addition is as follows. d 1 1 = d 0 − − d 1 2 d i 1 = d i 2 − − d i + 1 2 , i ∈ [ 1 , 4 L − 1 ] $\left\{\begin{array}{l}{d}_{1}^{1}={d}^{0}--{d}_{1}^{2}\quad \hfill \\ {d}_{i}^{1}={d}_{i}^{2}--{d}_{i+1}^{2},i\in [1,4L-1]\quad \hfill \end{array}\right.$ (10) Then decode the sequence d1 by using the inverse of DNA encoding rule 1 in Table 1 to obtain the sequence b1. Step 6: Output. Finally, reshape the binary sequence b1 to b0 according to the secret key H and convert the b0 into 8 bit-plane images, which can be regrouped to the original image P. 4 EXPERIMENTAL RESULTS Experimental setup In this work, the proposed method, S-HC-DNA algorithm, is simulated with Matlab2016b software in a regular laptop with 64-bit Windows 10 operating system, Intel Core i7 CPU of frequency 1.8GHz and 64GB RAM. First, the initial value of the hyper-chaotic system is calculated based on the generated 256-bit hash value of the input image with an iteration time step 0.001. And the initial value of DNA code is set as d0 = "A". Second, two typical medical brain images of size 1448 × 1412 and 1222 × 1192, respectively, are used as the test images. Finally, the experimental results of S-HC-DNA are compared with three other different methods based on cross-utilising hyper-chaotic and DNA sequences (HC-DNA [20]), chaos and DNA encoding (C-DNA [28]), (Cross-utilizing Hyper-Chaotic algorithm (CHC) [29]) to evaluate the performance of the proposed algorithm roundly. Time complexity analysis Appropriate image encryption algorithms should not only protect patients' private information but also meet the actual time requirements. Usually, whether the algorithm can be used in practice depends largely on its running time. Although a complex encryption algorithm has good effect, the long time required is not conducive to p