A Secure Medical Image Transmission System Based on 2D Logistic Map and Diffie–Hellman Key Exchange Mechanisms

2.1. Two-Dimensional Logistic Map

The two-dimensional logistic map is a discrete dynamic system with a chaotic behavior including less periodic windows in bifurcation diagrams and a larger range of parameters, which are more suitable for cryptography [10], [11]. It has a perfect chaotic property as a traditional logistic algorithm, and it has more complex behavior than one dimensional chaotic behavior. Mathematically, the two-dimensional logistic map is an example for chaotic map, and it can be discretely defined using Equation (1) as follows [12]:

Where:

The 2D logistic map defined in Equation (1) is more complex than the 1D logistic map, that is, the conventional logistic map is defined in Equation (2), where r is the chaotic behavior control parameter [13].

Fig. 1 shows the 1D logistic map schema, where the horizontal axis is the growth rate which is indicated by the parameter (r) and vertical axis is the population which is indicated by the parameter (x) and the trajectories of every one-dimensional logistics map are shown by the (x) with a fixed (x) as points on Figure.

Fig. 1. The bifurcation schema of the 1D logistic map [13].

In this work, 2D logistic map algorithm was performed to encrypt and decrypt the medical images with high security, which facilitates the process of protecting the private information of medical images.

2.2. Diffie–Hellman Key Exchange Mechanism

The Diffie–Hellman key agreement protocol, also known as an exponential key agreement, is a symmetric key exchange protocol which is widely implemented for encryption process, as shown in Fig. 2. The main objective of the Diffie–Hellman procedure is to make it feasible for two or more parties to build and exchange an identical and hidden session key by exchanging information over a public communications channel [14]. The DH key agreement protocol allows two users to produce a shared and symmetric key over an unsecured network.

Fig. 2. Diffie–Hellman key exchange authentication procedure [15].

According to Fig. 2 both parties, that is, client and server, agree on global elements prime P, and generator G which are both publicly available numbers; for instance, they may post the values on their web sites. They keep their respective private keys (X_A and X_G) secret, use modular division, and calculate respectively their shared (public) keys as Y_A and Y_B mathematically. The shared keys can take any value between 1 and (P – 1). Both parties exchange their shared keys and calculate the common secret keys value to be used in encrypting the image data which are transmitted over network. DHKE depends on a simple property of modular exponentiations. The mechanism of Diffie–Hellman key that exchanges mathematically is described as follows [15]–[17].

Where G, X, A, and P are positive integers. With existing Y_A = G^A mod P and Y_B = G^B mod P, the value of k can be calculated without revealing A or B, which are called secret exponents.

In this work, Diffie–Hellman key exchange mechanism was performed to generate and distribute the shared secret key K between the client and server parts. Then, the Diffie–Hellman encryption key K was defined and coded as a 256-bit integer number. In such a way, the encryption key was made to control the pseudo random sequences from the 2D logistic map algorithm for each round.

2.3. Medical Image Encryption Schemes

Protecting patient confidentiality and medical archives are an authorized requirement. Conventional cryptographic approaches are incapable of dealing with the massive quantity of medical image data and its appropriate statistical attributes. Numerous encryption mechanisms for securing medical privacy based on their content have been reported in the related literature. A modern two-dimensional Sine Logistic modulation map (2D-SLMM) which was derived from the logistic and sine maps was provided Hua et al. [18] with a broader chaotic spectrum than the traditional sine and chaotic logistic maps. In addition, they combined 2D-SLMM with a chaotic magic transform to establish a new image encryption algorithm (CMT). Simulation results and security analysis show that the proposed algorithm was able to protect images with minimal time complexity and a high level of security while also resisting numerous attacks. In Hua et al. [19], the authors addressed a 2D sine chaotification scheme to enhance the complex behavior of current chaotic maps. The authors applied their technique to improve the Henon map and 2D sinus logistics map. A generic medical image encryption system based on a new arrangement of two very powerful concepts, dynamic substitution boxes and chaotic maps, was introduced by Ibrahim et al. [20]. Before and after chaotic substitution, the arrangement of S-box substitution was seen to effectively avoid selected plaintext and cipher text attacks.

A two-dimensional of Sine Chaotification Model (2D-SCM) was recommended by Jo et al. [21]. The proposed technique can not only considerably improve the complexity of 2D chaotic maps but it can also significantly broaden their chaotic ranges. In Liu et al. [22], the authors recommended and implemented an Indistinguishability Under Chosen-Plaintext Attack (IND-CPA) secure CBIR architecture that executed image retrieval on the cloud without the constant interaction of the user. The author addressed a secure CBIR framework based on an Encrypted Difference Histogram (EDH-CBIR) in Liu et al. [23]. In that article, the image owner calculated the RGB component order or disorder difference matrices and encrypted them using value replacement and position scrambling. The encrypted images were subsequently sent to the cloud server, which generated image feature vectors from encrypted difference histograms. To find similar images, image users encrypted the query image in the same way as the image owner did, and the cloud server extracted the query feature vector. To determine the degree of similarity, the Euclidean distance between the query feature vector and the image feature vector was determined.

In Lu et al. [24], the authors reported a secure CBIR framework that enables comparison of similarities between encrypted image features, depending on which the secure image retrieval based on content can be achieved. In the system, they focused on security strategies for image features that make a comparison of similarities between protected features. The authors in Sibahee et al. [25] developed an effective a lightweight system for content-based browsing over an encrypted image dataset using a Locality Sensitive Hashing (LSH) technique. The LSH index increased the system’s expertise and effectiveness, enabling only relevant images to be obtained with a minimum of distance assessments. Vector refining methods were performed for efficient and safe refining of relevant results. The index building process ensured privacy of saved data and trapping doors. In 2017, the author of Gaata and Hantoosh [26] recommended an encrypted CBIR framework with additional improvement for the image retrieval based on features analysis. In this work, the gray level co-occurrence matrix with Haralick features, in combination with color moments, was used to construct the vector feature. In addition, Bloom filter and hash-table for image dataset classification were utilize. A similarity search procedure, based on secure transformation over encrypted cloud images, was presented in Xia et al. [27]. In the system, the authorized image client extracted and encrypted the feature vector with a query image to create the cipher text using the secure transformation method. The cipher text was then sent to the cloud to estimate the similarities of the vectors of the transformed feature.

The authors, in Bhagat and Gite [28], published an article on image retrieval for improved authentication using sparse codewords with cryptography. To prevent some form of attack, the Square Quality Control (SQC) encryption algorithm was utilized to the image. Lima et al. [29] employed a Cosine Number Transform (CNT) medical image encryption framework for the chosen Galois field. Huang et al. [30] implemented an encryption method, which combines chaos and Deoxyribonucleic Acid techniques. To achieve the permutation, substitution, and diffusion needed for encryption, they have performed a scenario of two rounds with six stages. The relatively low encryption speed was the key drawback of their system. The authors, in Hua et al. [31], proposed the Medical Image Encryption: Bitwise XOR (MIE-BX), high-speed scraping, random-pixel input, and pixel adaptive diffusion medical image encryption procedure. Their experimental outcomes indicated that the speed of their encryption method can outperform conventional approaches of encryption, such as Advanced Encryption Standard. However, Chen et al. [32] pointed out a serious vulnerability in MIE-BX to a reset attack known as the reset attack on Pseudo-Random Number Generator (PRNG). In this attack, the adversary restored the PRNG state to produce the same number of sequences each time.

The authors, in Badr et al. [3], introduced the dual authentication mechanism to support an attribute-based encryption (ABE) system that involves multiple parties such as data owners, data users, cloud servers, and authority. The proposed technique provided a safe solution to the problem of sharing significant information such as medical images. In Li et al. [33], a healthcare method was introduced by the authors as a new solution to the secure exchange of electronic health information between various entities in separate clouds. The proposed procedure was based on a revocable key policy and ABE algorithms that allowed clients to share encrypted health information on the basis of the data proprietors’ and patients’ own policy. The research paper in Wu et al. [13] applied the 2D logistic map of complicated basin structures and attractors for image encryption. In cryptography, the presented method implemented the classic permutation-substitution network structure; consequently, it ensures both uncertainty and diffusion properties for a protected cipher. In this work, the medical image encryption and decryption were constructed with the proposed system based on a two-dimensional (2D) chaotic map with Diffie–Hellman key exchange protocols to further enhance the security of the proposed system.

3.1. System Architecture

In the proposed methodology section, the architecture overview is described, as depicted in Fig. 3. In the proposed framework, encryption and decryption techniques were applied as a force for securing medical images from unauthorized access. A content-based query operation was initiated from a client side to retrieve the similar medical images and diagnosis result with respect to a query image. Once the query image was chosen as input, 2D logistic map-based Diffie–Hellman key exchange protocol was applied to perform the encryption process for selected query image. After medical images were encrypted, their owner could upload them to the server for conducting the retrieval and classification tasks.

Fig. 3. Architecture overview of the proposed system operation scenario.

3.2. Encryption and Uploading Stage

First, the authorized users can login using their credentials to login to the proposed system. During this first authentication stage, both credentials are examined by checking the pre-existing dataset. Failure to enter credentials would obstruct the processing of users into additional steps. Now that, a user has registered, and they can start on the client side. On the client side, the query image is selected from a set of test images to carry out the retrieval and diagnosis of medical images. The pseudocode of the encryption procedure using 2D logistic map is shown in Algorithm 1 and the encryption process in the proposed schema involves the following stages:

Algorithm 1: Pseudocode of image encryption

Fig. 4. Medical image encryption using 2D logistic map and Diffie–Hellman key exchange algorithms. original and encrypted medical image: (a) brain tumor; (b) breast mammogram; (c) cecum; (d) chest X-ray; (e) eye fundus; (f) hand X-ray; (g) leukemia; (h) pelvis X-ray; (i) clinical skin; and (j) thyroid images.

3.3. Downloading and Decryption Stage

After the client was authenticated by the server with an approved public key, the encrypted data, including the shared secret keys (K) value and medical query image, had to be downloaded and securely stored to the server. On the server side, the encrypted medical query image was directly decrypted using 2D logistic map algorithm and the same shared secret keys (K) from the key that was used for encryption process. The pseudocode of the decryption procedure using 2D logistic map is shown in Algorithm 2. Then, the decrypted image as shown in Fig. 5 was used as a query image to feed into content-based medical image retrieval (CBMIR) and CAD systems for retrieving and classification process of medical images. Following this, the retrieval and diagnosis results were encrypted and transmitted to the client using same procedure. Finally, the client received the returned encrypted results from the server side and performed the decryption process to get the final retrieval and diagnosis results. The GUI of the client side is shown in Fig. 6.

Algorithm 2: Pseudocode of image decryption

Fig. 5. Medical image decryption using 2D logistic map and Diffie–Hellman key exchange algorithms. encrypted and decrypted medical images: (a) brain tumor; (b) breast mammogram; (c) cecum; (d) chest X-ray; (e) eye fundus; (f) hand X-ray; (g) leukemia; (h) pelvis X-ray; (i) clinical skin; and (j) thyroid images.

Fig. 6. The GUI of the client-side screen.

3.4. Objective Evaluation

Peak Signal-to-Noise Ratio (PSNR) and Mean Square Error (MSE) are two frequently used evaluation indicators. PSNR calculates the ratio between the maximum signal strength and the noise or distortion strength that affects the quality of the representation. In this paper, PSNR is calculated for the recovered (decrypted) image and original host image. The ratio between these two images is calculated in decibels (dB), where I and K denotes the original host image and recovered (decrypted) image. The PSNR is calculated according to the following equation:

where I represent the maximum possible value of the pixel in the image (e.g., for a gray-scale image, the maximum value is 255). MSE calculates the magnitude of average error between the original image and recovered (decrypted) image. The MSE is computed as depicted below:

Where: