The quantity of medical image data accessible for analysis is increasing because of advancements in telehealth services. Therefore, efective cryptographic solutions must be developed to prevent data manipulation by unauthorized users in insecure networks. This paper focuses on developing a lightweight symmetric cryptosystem algorithm with decreasing memory and power consumption at high speed for standard and medical images based on 3D intertwining logistic map-cosine (ILM-cosine), which is a powerful chaotic system in contemporary cryptography. The motivation of this paper is to reduce the memory space required for storing program data while minimizing execution time for lower implementation complexity in telehealth applications. Our proposed scheme consists of five main steps: ILM-cosine map key generation with histogram normalization, row rotation, column rotation, and exclusive-OR (XOR) logic operation. Various normal and medical images were used as samples for the simulation. The results showed that cipher images have good visual quality, high information entropy, large key space, and low computational complexity.
To provide information security services, a cryptosystem implements cryptographic techniques and supportIn medical systems, patient data are increasingly stored ing infrastructure. A cipher system is another term used in cloud-based Internet-of-Health (IoHS) systems. There- in cryptosystems. A basic cryptosystem is composed of fore, these devices can be accessed remotely at various several parts, including plaintext, an encryption algofacilities/locations. The data, which included sensitive rithm, an encryption key, a decryption algorithm, and and highly confidential images, were treated as crucial ciphertext. A multitude of security objectives are proinformation. Hence, important criteria, including con- vided by medical image cryptography to guarantee data ifdentiality, validity, and integrity, are required for the privacy, nonalteration, and other concerns. The followtransmission and storage of medical data using the IoHS. ing are some of the objectives of cryptography: Only an
Medical imaging is a valuable tool for providing pa- authorized person is allowed to change the information tients with excellent care, because it can be used for that has been transmitted. No one between the sender both diagnosis and therapy. Medical imaging methods and receiver can change the message sent. are categorized into structural and functional imaging The primary elements of the medical image encryption categories, according to the type of information they of- lifecycle in healthcare are as follows: The first stage is fer about the organ being studied. Magnetic resonance data collection, which is used to submit patient physioimaging (MRI), computed tomography (CT), ultrasound, logical data and share medical information. In the next positron emission tomography (PET), single-photon emis- step, the data must be filtered, classified, and subjected to sion computed tomography (SPECT), magnetic resonance any changes required for use in a relevant study. These angiography (MRA), contrast-enhanced MRI (CT-MRI), data are often compressed using a lossless compression functional MRI (fMRI), magnetic resonance spectroscopy strategy with less processing and a greater compression (MRS), and electrocardiography (ECG) were performed. ratio to minimize the volume of medical data and enhance transmission performance. However, the data 6th International Hybrid Conference On Informatics And Applied Math- gathered may have included sensitive information. Conematics, December 6-7, 2023 Guelma, Algeria sequently, it is critical to create handling, storage, and * Corresponding author. disposal requirements that include security during the s$.behl.kbaocuermek@ouunchive-@bouunmive-rbdoeusm.dezr(dSe.sB.dezlk(aHc.eBmo)u;rekouche); data lifecycle[1]. At this stage, the data are vulnerable to n.messaoudi@univ-boumerdes.dz (N. Messaoudi) a range of assaults, such as distributed/denial-of-service 0000-0003-3516-290X (H. Bourekouche); 0000-0003-0912-3392 attacks, content-based attacks, and attacks on new net(S. Belkacem); 0000-0002-3406-4120 (N. Messaoudi) works. Consequently, by retaining access-level security © 2023 Copyright for this paper by its authors. Use permitted under Creative Commons License
Attribution 4.0 International (CC BY 4.0). and access control with symmetric encryption, the data medical Digital Imaging and Communications DICOM will remain segregated and strictly guarded. In chaos- CT images[4]. Prior to encryption, a median filter was based image encryption, a chaotic system [2] is used used to scramble the rows and columns of the image, and to generate random chaotic sequences that can be used a bitwise XOR operation was performed to generate the as secret keys for the permutation and difusion phases. encrypted image [4].
Permutation is an alteration of the bit order according Ahmed et al.[5] present an innovative image encrypto an algorithm. During the confusion stage, each pixel tion approach for medical imaging. This method uses a must normally be shifted at least once. Following data four-dimensional (4D) hyperchaotic map[5] to construct collection, transformation, and storage in secure storage four substitution boxes (S-boxes). The key benefit of this systems, a data processing analysis is performed to pro- new approach is its sensitivity to threats, which makes vide relevant knowledge that may be used for decryption it extremely secure. The encryption process begins with in a manner similar to encryption. a three-dimensional (3D) Chen map shufling of a plain
When implementing encryption algorithms for tele- image. This was followed by dividing the image into four health applications, lower implementation complexity subimages. The final stage entails replacing the pixel should be guaranteed, which is the motivation of our values in each subimage with values from one of the work, where we aim to reduce the memory space re- four S-boxes. In the first stage, the four subimages are quired for storing program data while minimizing the merged, followed by fusion of the combined image using execution time. Hence, we develop a fast chaos-based a one-dimensional (1D) logistic map[5]. encryption technique that can encrypt medical images Sarosh et al.[6] proposed a quick chaos-based encrypin five steps: generation of a random number by using tion method for medical images. To confuse and disperse the intertwining 3D logistic-cosine map, normalization, medical images. The method uses a logistic map, Chebypixel rotation through which row and column rotation shev map, and piecewise linear chaotic map (PWLCM). is performed, and the XOR-based encryption technique. The image was first circularly shifted, and then, bit-plane The proposed scheme can encrypt a 256 × 256 medi- slicing was performed. A plane is created by performcal image in less than 0.4 seconds and can be used in ing an XOR operation on the most significant bit (MSB) stringent medical applications. and seventh ISB plane MSB plane. The final image was
The remainder of this paper is organized as follows. jumbled using a pseudorandom number (PRN) produced Section 2 introduces the theoretical background of the by the logistic map. The plan is adaptive and computes chaos map used for key- generation. Section 3 reviews image parameters, such as the sum or mean, to establish the related work. Section 4 describes the medical- image the initial conditions of the PWLCM chaotic map. The encryption technique. Section 5 presents the simulation scrambled image was XORed using the key image proresults and security analysis. Section 6 discusses and com- duced by the PWLCM. A Chebyshev map is iterated, and pares our results with those of recent schemes. Finally, a PRN sequence is formed to permute the image pixels Section 7 concludes the study. and produce the final encrypted image[6].
Jain et al.’s [7] novel chaotic image encryption method for medical images guarantees increased chaos and ran2. Related Works domness of the encrypted data, protecting it from cryptanalysis and other statistical attacks. Arnold’s cat map Digital images are multimedia data that contain confiden- and the 2D logistic sine-coupling map (2DLSCM) are tial information in the medical field. The challenge lies in combined into one algorithm. The iterative transformacreating an efective, secure cryptosystem that can safe- tion algorithm, known as Arnold’s cat map, randomly guard shared private images. Thus, several researchers distributes the pixels of the input image. The number of have designed chaos-based symmetric cryptosystem algo- iterations, which is sometimes referred to as the period, rithms for both standard and medical- image encryption. determines the final image. After a certain number of These methods frequently make use of chaos maps, in- iterations, the original image is completely reconstructed. cluding the Lorenz and Chen system, Arnold, logistic Compared to other 2D chaotic maps, 2DLSCM guarantees maps, and cat maps. To assess the state of the art, we greater complexity and ergodicity. selected published research performed mainly from 2018 A Hermite chaotic neural- network-based medical- imto 2023. age encryption algorithm was proposed by Han et al.[8]. First, chaotic sequences of the logistic map are used in the 2.1. Schemes based on chaotic maps medical- image encryption algorithm. Second, a Hermite The hybrid chaotic model proposed by John and chaotic neural network is trained using this chaotic seKumar[3] uses a 2D Lorentz chaotic model coupled with quence. Two key streams created by the trained Hermite a logistic chaotic model for the encryption/decryption of chaotic neural network are subsequently used to encrypt medical images [9].
The authors of [10] provided a cryptosystem with a unique encoding scheme and a lossless compression Nematzadeh et al.[14] presented a hybrid technique based method. Chaos-based DNA cryptography has been used on a coupled lattice map and modified genetic algorithm to enhance the security of medical images. A lossless for the encryption of medical images. The first population discrete Haar wavelet transform was employed to reduce of the modified genetic algorithm was created using a couthe transmission eficiency in terms of both space and pled lattice map. Consequently, the cipher images were time. The binary image created from the compressed of higher quality, and this approach was also more resisimage is then separated into four smaller images. By tant to attacks. The significantly shorter execution time employing a 4D Lornez chaotic map to construct chaotic of the proposed method compared to that of prior evolusequences, the subimage pixels are scrambled. The DNA tionary algorithm-based image encryption techniques is coding instructions were used to create four distinct DNA another significant accomplishment. This was because structures. The XOR technique is used to combine DNA of the method chosen to design the GA. structures, and after DNA decoding, a cipher image is acquired. Based on cryptanalysis, the proposed cryptographic system is secure against diferential, exhaustive, 3. Basic requirement and and statistical attacks. The proposed cryptosystem can definitions be used for telemedicine and e-health applications.
Abdelfatah et al.[11] proposed a medical image encryp- The principles of logistic maps (LMs), intertwining lotion technique based on adaptive deoxyribonucleic acid gistic maps (ILMs), and ILM-cosine, which were used to (DNA) and a novel multi chaotic map (HGL) created by produce keys for the proposed picture encryption scheme, combining Henon, Gaussian, and logistic maps. Using are annotated in this section. adaptive DNA, each image is encrypted with a diferent DNA rule than the other images, making the proposed 3.1. Logistic Map algorithm efective against attackers’ perceptions.
Amdouni et al.[12] discussed the use of chaos and The one-dimensional logistic function provided by equaDNA as encryption methods for digital medical images. tion 1 is a discrete recursive relation of degree two. The The Rossler and Lorenz systems were used to generate a popularity of these maps can be attributed to their ease random key stream. The key and input original images of use. were then encoded using DNA encoding principles. The +1 = (1 − ) (1) scheme was evaluated using National Institute of Standards and Technology (NIST) suite tests. The Zedboard varies in (0, 1], and exhibits chaotic behavior in Development Kit implements the hardware design of the [3.57, 4]. proposed scheme.
Choi et al.[13] proposed a secure and dependable color medical image encryption algorithm based on a nonlinear ⎧⎪+1 = (1 − ) + (2) + 3 ccealtlumlaarp[a1u3t]o.mNaCtoAn, (aNgCrAou) pancdelaluglaernearuatloizmeadt3oDn ccrheaaotteidc ⎨+1 = (1 − ) + (2) + 3 (2) by fusing two nonlinear CAs and a maximum length ⎪⎩+1 = (1 − ) + (2 ) + 3 CA (MLCA), which possesses nonlinearity and expands the key space, is an eficient pseudorandom number gen- This system of equations exhibits chaotic behavior in erator (PRNG)[13]. Pixel values of a basic image may 3.53 < < 3.81, 0 < < 0.022, 0 < < 0.015 be unfeasible. In addition, they employed a generalized [15]. 3D chaotic cat map for efective color medical image encryption shufling. The R, G, and B channels of the 3.3. Intertwining logistic map (ILM) pixels in a color image can be moved using this map. In 2014, Wang and Xu [16] proposed an intertwining The proposed technique conducts a full experimental test relation between diferent LM sequences[ 17], which inthrough in-depth analysis to demonstrate the high secu- dicates that the ILM has more dynamic behavior than rity and dependability of the new color medical image encryption system.
A 3D logistic map with superior chaotic properties compared with a 1D logistic map has recently been investigated. The following equation 2 serves as the definition. the LM[17]. The equations for the ILM sequence are as follows[17]: ⎧⎪+1 = ( (1 − ) + ) ⎨ +1 = ( + (1 + 2+1)) mod 1 mod 1 ⎪⎩+1 = ( ( + 1 + + 1 + ) sin ) mod 1 (3) This system of equations exhibits chaotic behavior for in the range of [0, 4), > 33.5, > 37.9, and > 35.7.
The ILM-cosine expressed by equation 4 is the result of combining the ILM with a cosine function with the aim of improving the ILM output nonlinearity. This system of equations exhibits chaotic behavior when is in the range of [0, 4), > 33.5, > 37.9 , and > 35.7. ⎧+1 = cos (( (1 − ) + ) ⎪ ⎪ ⎪⎨+1 = cos (( + (1 + 2+1)) mod 1 + ) mod 1 + ) ⎪+1 = cos (( ( + 1 + + 1 + ) sin ) ⎪ ⎪⎩+) mod 1
The widespread use of medical image encryption based on chaotic maps has increased in recent years, due to the notable nonlinear features of chaos that make it an appropriate candidate for medical cryptographic applications. In this section, we present a detailed medical image encryption technique. The proposed image encryption scheme based on the ILM-cosine is shown in Figure 1. To create a cryptosystem strong enough to encrypt medical images, the following five crucial procedures are needed:
In this step, we use equation 4 to generate a pseudo- 4.4. Column rotation random bit sequence based on the 3D ILM-cosine chaos sequences. The initial conditions and parameter values are considered keys to the cryptosystem.
(1) = 0.2350, (1) = 0.3500, (1) = 0.7350, = 3.7700, = 33.6, = 39.69, = 36.58.
The steps used to rotate the column are similar to those of row rotation and can be applied as follows: - Applying an ofset value 4, - Choose elements of the chaos sequence starting from the ofset value 4.
The generated values and histogram generation of the 3D ILM-cosine chaotic sequence , , and obtained using equation 4 are depicted in Figure 2a. The resulting chaotic sequence histogram has a nonuniform distribution, which may afect the security of the system. Consequently, we use a normalizing (equalization) technique
The sequence acquired from the row and column rotations is finally subjected to an XOR operation to produce new pixel values that are distinct from the original values. The XOR operation is performed using the following steps. for , , and using equation 5 to further strengthen the security of the resulting histograms by a suficiently large number because the map only generates floating-point values between 1 and -1.
⎧⎪ = ( × 1) ⎨
= ( × 3) ⎪⎩ = ( × 5) mod mod mod 256 (5) where 1, 3 and 5 are large random numbers that (4) are chosen to be equal to or greater than 100,000 for simplicity, while M and N are chosen to be equal to the image dimension (256 × 256). It is clear from Figure 2b that after applying the above constraints, we obtain an equalized histogram for , , and .
The steps used to rotate a gray image of × dimensions are as follows: - Applying an ofset value 2, - Choosing elements of the chaos sequence starting from the ofset value 2, - The chaos value, , obtained using equation5 is used to rotate the row. - Converting the × image to a new 1 × image, - XOR the chaos sequence starting from 6.
In this section, various tests often used to analyze the statistical metrics and security of cryptosystems are employed to evaluate the performance of the proposed scheme. The tests for the performance analysis of the proposed scheme were conducted on a Core (TM) i3-4030U CPU @ 1.90 GHz with 4 GB of RAM.
Databases used In analyzing the proposed solution, all of the standard test images were obtained from the USCSIPIimage database. The medical images used for the analysis arewere retrieved from The Intramural Research Program of the NClinical Center and the National Library of Medicine. The collection in Figure 3 comprises X-ray images (chest X-ray images), sonography images (abdominal sonography images), and MRI images (heart MRI images). These images are .png images with 256 × 256pixel resolution. (a)
An image histogram is used to visually depict the distribution of pixel intensity within an image[18]. The histogram of the encrypted M3 image produced by our scheme is evenly distributed and completely diferent from that of the plain image, as shown in Figure 4. Hence, the proposed approach is more robust to statistical attacks.
The distribution of pixels in cipher images must be completely uniform [19] to ensure safety against any assault. Consequently, the entropy of an n-bit image is n when the pixel distribution is perfectly uniform. After calculating the entropy values using equation 6, it can be observed from Table1 that our scheme is closer to 8, with a mean entropy value of 7.9966, which ensures that the pixel distribution of the cipher images is uniform and provides maximum security.
() = 2− 1 ∑︁ () log2 () =0 (6) () is the probability of a specific symbol , and is the number of bits[7].
By carefully examining the connections between plain and ciphered images, a diferential attack can be used to recover the input image from the encrypted image without the secret key. This is measured using the “Unified Average Changing Intensity (UACI)”, “Number of Pixels Changing Rate (NPCR)”, and “Peak Signal-to-Noise Ratio (PSNR)”[20] given by equations 7-9. The NPCR, UACI, and PSNR of two cipher images, 1, which is encrypted from the original plain image, and 2, which is encrypted from the same image with a single-pixel value change [7]. is referred to as the "gray-level co-occurrence matrix (GLCM)", and (, ) is the number of grayscale values in the matrix. Table 3, shows that the proposed encryption method guarantees the best possible image contrast for the generated cipher images. key space than 1D and 2D chaos; as a result, 3D chaos provides greater security than others[21]. In this work, seven initial conditions (1),(1),(1), , , , . of the chaotic map are used as secret keys for encryption with precision 10− 15. The following six random numbers are used as keys:1, 2, 3,4, 5, and 6 . These are used as keys with a precision of 105. The total key space size is (1015)7 × (105)6 = 10135, which is large enough to resist exhaustive attack.
Images Run time Memory usage In the past section, numerous tests were performed on the M1 0.552356 0.864256 images to assess the security and statistical capabilities M2 0.554510 0.159744 of the proposed image-encryption algorithm. Here, we M3 0.560326 1.626112 compare our scheme with diferent medical algorithms Lena 0.572440 0.872448 in Ref[7], Ref[22], and Ref[23], as tabulated in Table5.
Resistance to statistical attacks: The histograms of the plain image and encrypted image generated by our 5.5. Performance analysis scheme share no similarity. The encrypted image has a more uniform histogram. Additionally, it is clear by comOwing to the vast amount of image data that must be paring the contrast values with those of other encryption processed, performance analysis is crucial for image en- techniques that our encryption scheme performs almost cryption and decryption techniques. It assists in identi- as well as other algorithms. Hence, the proposed techfying potential areas for improvement and optimization, nique was more resistant to statistical assaults. such as reducing useless tasks or memory utilization. To Resistance to ciphertext only attacks: The entropy assess the efectiveness of the proposed algorithm, we of images with 8-bit pixel values should be close to 8. examined its memory requirements and end-to-end run- With a mean entropy value of 7.9970, our encryption time. MATLAB R2023 is the simulation tool and language scheme is more entropy-rich than the aforementioned used. methods. Thus, the proposed technique is more resistant to ciphertext-only assaults. 5.5.1. Run-Time analysis Resistance to diferential attacks: When subjected to diferential analysis, our scheme yielded good results, To assess the efectiveness of the proposed algorithm with a mean score comparable to those of the other for encrypting and decrypting images, we calculated the schemes. Thus, we can conclude that the proposed execution times for various images. Table4shows that the scheme is resistant to diferential assaults. proposed scheme is considerably faster than the other Computational processing analysis: The proposed methods and can encrypt 256× 256 images in an average scheme uses the least amount of memory and encrypts a time of approximately 0.55 seconds. 256 × 256 image in 0.55 seconds, which is the fastest of the other systems. 5.5.2. Memory analysis Consequently, based on several tests, our technique was proven to achieve a reasonable balance between performance and security.
Memory analysis was used to estimate the memory required by the proposed technique for encrypting and decrypting images. We calculate the end-to-end memory usage for diferent images in Figure 4. Since the memory usage of the proposed algorithm depends on the image size and the software/Hardwar performance, our proposed scheme has low memory usage regardless of the PC performance and the simulation tool used.
The key space is the total number of keys that can be used in a cryptographic system. 3D chaos is a more
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