Image encryption continues to attract attention of researchers developing new techniques for protecting the confidentiality of image data during both storage and transmission [1]. Image encryption departs from regular text encryption due to the low entropy, high spatial correlation, and large data size [2]. Many cryptographic techniques for realizing the confusion and diffusion goals have been proposed in the literature. In the literature, chaotic maps have been used in cryptography to achieve both goals due to their deterministic behavior that is but highly sensitivity to initial conditions [3]. The uses of chaotic maps in image encryption include histogram equalization [1], pixel scrambling [4], pseudorandom number generation [5], and construction of substitution boxes (S-boxes) [6].

The medical image encryption framework recently proposed in [1] provides a generic framework with demonstrable security features that can be implemented using a wide variety of cryptographic primitives. The framework uses a generic chaotic map component for whitening the histogram of input images and breaking their naturally high spatial correlation. The dynamic S-box component is used for adding an extra layer of confusion and increase the key space beyond the limits of brute force attacks. This framework has several advantages which set it apart from other schemes found in the literature. First, the generic chaotic map is initialized with a seed derived securely from the shared key and a random nonce. This technique deters chosen-plaintext attacks as well as pseudorandom number generator (PRNG) reset attacks. Furthermore, an image-dependent dynamic S-box is applied to both the plain image and the cipher image pixels to protect the chaotic map against cryptanalysis using chosen-plaintext or chosen-ciphertext attacks. The S-box itself is securely controlled by a secret key and a nonce to fend off cryptanalysis attacks through the S-box construction algorithm. In addition to its particular security features, the framework is computationally very efficient. It achieves encryption speeds fit for real-time operation because of the simplicity of its pixel processing pipeline, which employs just an XOR and S-box substitution operations. Although the framework achieves confidentiality, the lack of scrambling operations makes it susceptible to message tampering threats. An adversary may attempt to obstruct the delivery of a portion of the image in transit over a communication channel. This is known as the occlusion attack, which aims to prevent authorized receivers from successful decryption or to render the decrypted image useless [7].

The contribution of this work can be summarized in the following points.

We extend the framework proposed in [1] to include a final scrambling block and visually demonstrate the effectiveness of the extended framework in mitigating the occlusion attack.

The rest of the paper is organized as follows. Section 2 presents some background and reviews relevant literature. The proposed extended medical image encryption framework is described in Section 3. Section 4 evaluates the performance of the proposed framework. Finally, the conclusion and future work are presented in Section 5.

Unlike text data, image data has a large size and high spatial correlation. Since their early use [8] and demonstration of their security features [9], chaotic maps have been employed in many image encryption algorithms [10–13]. Chaotic maps are non-linear and deterministic systems which possess features that are suitable for image encryption. Namely, a chaotic system is sensitive to initial conditions and shows pseudorandom behavior [3]. This means that a slight change in the parameters leads to different output in the chaotic maps [14]. Diverse image encryption techniques have been presented in the literature based on dynamic S-boxes [15,16]. Dynamic S-boxes represent an efficient secret key dependent substitution which increases confusion and serves as nonlinear components that deter linear and differential cryptanalysis [17].

Transmitted or stored images could be subject to different security issues, e.g., modification, eavesdropping, duplication, and noise. In this work, we focus on a type of attack known as the cropping attack or the occlusion attack. In this attack, the adversary attempts to obstruct selected cipher image pixels to stop or invalidate the decryption process. A common defense mechanism against the occlusion attack is pixel scrambling. By randomly and securely shuffling pixel locations, the effect of the occlusion attack can be transformed into speckle noise that affect the decrypted image at random pixel locations. The scrambling process must be reversible to facilitate the recovery of the original pixels during decryption [18].

There are several scrambling techniques in literature. The scrambling techniques varies in methods of scrambling an image under processing [19,20]. The authors in [19] introduced a new image scramble technique. They used a hash value to initiate the value of the piece-wise linear chaotic map (PWLCM) as a key for the global scramble. Then, a local scramble is performed by the Hilbert curve and H-fractal. Finally, they used ciphertext as feedback for enhancing the characteristics of confusion and diffusion. The technique presented in [20] for image scrambling is based on hash table structure and deoxyribonucleic acid (DNA) substitution. It used a closed hash in the structure table with the value of pseudo-random sequence to generate two different sequence keys. The two keys are used in pixel-scrambling of the plain image.

As a traditional method for scrambling some researchers used chaotic maps to scramble a plain image such as [21,22]. In [21], the authors introduced an implementation of a chaotic image encryption system in a transform domain that used Baker map. The scrambling process using The Baker map is performed by splitting the plain image into squares. Then, each square is divided into N rectangles and stretched horizontally to change the positions of the pixels. Also, in [22] the authors presented chaotic image encryption that used Baker map to scramble the plain image. The disadvantage of this method is the same histogram of the plain and scrambled images. Recently, the researchers used other methods for image scrambling such as in [23]. The authors of [23] used the Josephus problem to scramble the pixels of a plain image to new positions to perform the needed confusion for encryption. In [24], the authors designed a 2-dimensional logistic modulated sine coupling logistic chaotic map (LSMCL) to scramble the plain image. The scrambling process is achieved by performing two rounds of permutation. Another image encryption system in [25] utilized a cosine transform-based chaotic system (CTBCS) to produce chaotic maps with highly dynamical behavior to perform efficient scrambling.

In [21] introduced a method for scrambling by chaotic sub-block scrambling (CSBS) based on spiral transformation. The process starts by scanning pixels for a disorder, which is a change in the position of all pixels. In the scanning methods of scrambling process, it is difficult to evade pixels that do not change their positions. To overcome this problem, they used spiral transformations with sub-block scrambling. The authors of [26] designed an encrypt image technique which scrambles a plain image by chaotic coupled sine map (CCSM). The main purpose of using the CCSM is to a degree of freedom to the secure key space. The scrambling process is based on a chaotic sequence which resists the chosen and known-plaintext attacks. The scrambling process was used at the beginning of the encryption system. Their technique showed good performance against the occlusion or data loss attacks.

The proposed framework extends the framework in [1] to include a pixel scrambling phase. In this section, we describe the extended framework and describe the details of the newly added scrambling algorithm.

The proposed framework is generic in the sense that any chaotic map can be invoked to generate the chaotic sequences M and P . However, to illustrate the usability of the framework, we implement it using two specific chaotic maps. For generating the chaotic mask, M , we use Arnold's cat map defined by Eqs. (1) and (2).

(1) xn=(2xn−1+yn−1)mod1

(2) yn=(xn−1+yn−1)mod1

where (x0,y0) is the initial state and (xn,yn) is the state at the n th iteration.

Similar to [1], the initial state of Arnold's cat map (x0,y0) is derived from the initialization vector, IV , using Eq. (3). The chaotic map is first iterated NT=512 times to cancel the transient effect of the initial state thus increasing it key sensitivity.

(3) (x0,y0)=2−53(∑i=053⁡2ibi,∑i=053⁡2ibi+64)

where bi is the i th bit of the initialization vector, IV .

As in [1], the mask bytes ⟨mi⟩i=1L are extracted from the chaotic sequence ⟨(xi,yi)⟩i=1L , where L is the number of image pixels, using Eq. (4)

(4) mi=(224xi+NT)mod256

For generating the scrambling sequence, P , we use Baker map defined by Eqs. (5) and (6).

(5) xn={xn−1p,0≤xn−1<pxn−1−p1−p,p≤xn−1<1

(6) yn={pyn−1,0≤xn−1<p1−(1−p)yn,p≤xn−1<1

where (x0,y0) is the initial state, (xn,yn) is the state at the n th iteration, and p is a parameter.

The initial state of Baker map (x0,y0) is derived from the initialization vector, IV , using the same Eq. (3) and the parameter p is set to 0.6111.

In this following subsection, the proposed scrambling technique is examined under the application of occlusion attack. Then we study the remaining security metrics of the proposed framework.

By adding a scrambling phase to the framework in [1], the proposed framework could successfully mitigate occlusion attacks. This improvement makes the proposed framework applicable to environments where such a threat exists. One potential situation for applying the proposed scheme is when encrypted data is stored in a distributed storage system over multiple servers to reduce the damage caused by a compromised server. A scrambled cipher image generated by the proposed framework can be split into pieces, each of which is stored in a different server. If one of the servers is compromised and the adversary attempts to destroy the image data stored in the system by deleting the portion of the data stored in the compromised server, the proposed framework will successfully mitigate the data loss and partially restore the image data. The level of data loss caused by a compromised server can be limited by increasing the number of servers onto which pieces of the cipher image are stored. The results of this framework show that if a medical cipher image is split into four parts and distributed over four servers, the plain image can be successfully decrypted with correlation 99.8% after applying a median filter. An interesting future research is to study the efficiency of different scrambling techniques within the proposed framework and to compare their respective robustness against the occlusion attack.