# A Novel Selective Encryption Method Based on Skin Lesion Detection

Authors: Dezhi An; Jun Lu; Shengcai Zhang; Yan Li
Journal: Mathematical Problems in Engineering
 (2020)

---

## Abstract

Due to the semitrusted cloud, privacy protection of medical images in medical imaging clouds has become a precondition. For the privacy of patients and the security of medical images in the cloud, this paper proposes a selective encryption based on DNA sequence and chaotic maps for skin lesion image. Initially, we design a transition region-based level set evolution functional which is merged into a variational level set expression with two extra energy functionals, to segment skin lesion image. Once skin lesion detection has been performed, the detected skin lesion pixels are encrypted by employing chaotic systems and DNA sequences. We apply 2D-LASM and 1D-LSS to produce the pseudorandom sequences and use the hash function of the plaintext image to calculate the secret keys of the encryption system. Results demonstrate that the proposed segmentation method is particularly suitable for the detection of skin lesion images with strong noise and complex background. Meanwhile, security analysis also reveals that this selective encryption has a large security key space and high sensitivity to the plaintext image and the secret key.


---

## Body

## 1. Introduction

Medical image processing has developed for many years, and there are more and more powerful tools to help dermatologists identify and classify skin lesions [1–6]. Among all kinds of skin lesions, melanoma is the most aggressive skin cancer and the one leading to the most deaths. However, in the transmission and storage, there are potential threats to the important content of these images, which makes the protection of important content a challenging problem [7–11].To achieve confidentiality, encryption as an effective technology includes full encryption [12–15] and selective encryption [3, 16–20]. Full encryption involves encrypting complete image information, while selective encryption mainly focuses on the encryption of part of the image data. In recent years, selective encryption has been widely studied because of its tradeoff between computational complexity and security. Based on pixels of interest and singular value decomposition, Bhatnagar et al. proposed a selective image encryption scheme [16]. In [17], an edge-based lightweight image encryption scheme is proposed by Zhang et al. which employs chaos-based reversible hidden transform and multiple-order discrete fractional cosine transform. Wen et al. [18] proposed a selective method to encrypt the object of infrared images by using chaotic maps. Furthermore, they protected the salient regions of image by embedding them into a visually meaningful image in the work [19]. Actually, selective encryption is suitable for protecting the important areas of the image, but not the entire image. Most of the existing detection schemes do not have the ability to handle the skin lesions image [20].In recent years, there are many techniques used for skin lesion detection, such as active contour model [21, 22], thresholding [23], fuzzy c-means [24], and neural network [25], and local binary patterns clustering [2]. Rajab et al. [25] introduce the thresholding algorithm and neural network to realize the skin lesion detection. This technique can obtain the efficient result. However, the technique based on neural networks cannot deal with noisy images as the details of the edge were broken. Motivated by these problems, Barcelos et al. [26] posed a detection model for skin lesion image starting from nonlinear diffusion equations. However, in the case of strong noise and complex background, this model has some limitations.So far, various techniques have been proposed for object detection. The level set method is an important segmentation method which has the advantages of allowing variable topological transformation and flexible numerical implementation. However, this method has the problem of contour initialization and reinitialization. To overcome these problems, Li et al. put forward a segmentation model without reinitialization [27] and distance regularized level set evolution (DRLSE) [28]. The two models employ the corresponding deviation penalty energy to force the level set function approach sign distance function and finally eliminate reinitialization. However, these two models need to initialize the contour. Recently, He et al. [29] proposed a weighted region-scalable fitting (WRSF) model which can handle well on medical images with intensity inhomogeneity, but fails to segment these with strong noises. In a partial differential equation (PDE) formulation, two geometric active contour models are, respectively, proposed by Wen et al. [22, 30]. The two models have the ability to segment skin lesion images with blurred boundaries.Inspired by the works of Wen et al. [22, 30], but different from these works, this paper proposes a transition region- (TR-) based energy functional which can compel the level set function to have opposite different inside and outside image target. And then this energy functional is introduced into a variational level set expression with two extra energy functionals. According to the characteristics of significant regions, chaotic systems and DNA are combined to design suitable sensitive encryption algorithms.The main contributions of this paper include the following points:(1)
A novel skin lesion detection-based selective encryption method is proposed. This method consists of the detection process of skin lesion image and selective encryption for privacy protection of skin lesion data.(2)
In the skin lesion detection scheme, we propose a transition region- (TR-) based energy functional which compels this function to have a different sign inside and outside the image target. And the TR-based functional is introduced into a variational level set expression.(3)
In the selective encryption for skin lesion data, we employ chaotic systems and DNA sequence operations. 2D-LASM and 1D-LSS are chosen to generate pseudorandom sequences and determine DNA encoding/decoding rules of the skin lesion region and the key matrix.The structure of this article is described as follows. The DRLSE model and DNA encoding/decoding rules are introduced in Section2. Section 3 describes the proposed skin lesion detection-based selective encryption algorithm which contains skin lesion detection based on TR-based energy functional model and selective encryption algorithm. The experimental results and security analysis are depicted in Section 4. The conclusions are given in Section 5.


## 2. Related Works

### 2.1. The DRLSE Model

Li et al. [27] extended distance regularized level set evolution (DRLSE) and proposed a variational level set model for image segmentation. In a variational framework, this model is formulated about the level set function ϕ as follows:(1)Eϕ=μRpϕ+Eextϕ=μRpϕ+λLgϕ+αAgϕ,=μ∫Ωp∇ϕdx+λ∫Ωg∇Iσ∇Hϕdxdy+α∫Ωg∇IσH−ϕdxdy,where μ>0, λ>0, α∈ℝ are constants, Rpϕ is the level set smooth term, and Eextϕ is a certain external energy term. p is a potential (or energy density) function p:0,∞⟶ℝ, g∇Iσ=1/1+∇Iσ2 is an edge indicator function, and Iσ=Gσ∗I is the convolution of the image I and the Gaussian kernel Gσ with standard deviation σ. The function H is the one-dimensional Heaviside function.The termLgϕ computes the length of the zero level set of ϕ in the conformal metric ds=gCpC′pdp where Cp is a parameterized representation of the zero level set of ϕ. The term Agϕ can be viewed as the weighted area of the region xϕx<0, which forces the zero level set of ϕ to expand or shrink faster during the evolutionary process. Whether the parameter α of Agϕ can be positive or negative depends on the relative position of the object’s initial contour.The level set evolution equation corresponding to equation (1) is obtained by the following equation:(2)∂ϕ∂t=μdivdp∇ϕ∇ϕ+λδϕdivg∇ϕ∇ϕ+αgδϕ,with initial condition ϕx,0=ϕ0x, where dps and ps are, respectively, defined by(3)dps≙p′ss,(4)ps=12π1−cos2πs,ifs≤1,12s−12,ifs≥1.


### 2.2. DNA Encoding/Decoding Rules

A DNA sequence consists of A (adenine), T (thymine), C (cytosine), and G (guanine), where A and T, G, and C are complementary pairs. Further, 0 and 1 are complementary, so the DNA sequence is similar to the binary data. According to the principle of complementary pairing, Table1 shows eight types of encoding rules by the Watson–Crick complement regulation [31–33].Table 1
DNA encoding scheme.
12345678A0000111101100110T1111000010011001C1001100100001111G0110011011110000There introduce algebraic computation operators for DNA sequences to spread DNA computing, such as XOR. On the basis of traditional rule, the XOR operation is manipulated on DNA sequences. There exist 8 types of DNA XOR rules corresponding to 8 types of DNA encoding rules, and Table2 shows DNA XOR under Rule 1.Table 2
DNA XOR rule.
XORATCGAATCGTTAGCCCGATGGCTA


## 2.1. The DRLSE Model

Li et al. [27] extended distance regularized level set evolution (DRLSE) and proposed a variational level set model for image segmentation. In a variational framework, this model is formulated about the level set function ϕ as follows:(1)Eϕ=μRpϕ+Eextϕ=μRpϕ+λLgϕ+αAgϕ,=μ∫Ωp∇ϕdx+λ∫Ωg∇Iσ∇Hϕdxdy+α∫Ωg∇IσH−ϕdxdy,where μ>0, λ>0, α∈ℝ are constants, Rpϕ is the level set smooth term, and Eextϕ is a certain external energy term. p is a potential (or energy density) function p:0,∞⟶ℝ, g∇Iσ=1/1+∇Iσ2 is an edge indicator function, and Iσ=Gσ∗I is the convolution of the image I and the Gaussian kernel Gσ with standard deviation σ. The function H is the one-dimensional Heaviside function.The termLgϕ computes the length of the zero level set of ϕ in the conformal metric ds=gCpC′pdp where Cp is a parameterized representation of the zero level set of ϕ. The term Agϕ can be viewed as the weighted area of the region xϕx<0, which forces the zero level set of ϕ to expand or shrink faster during the evolutionary process. Whether the parameter α of Agϕ can be positive or negative depends on the relative position of the object’s initial contour.The level set evolution equation corresponding to equation (1) is obtained by the following equation:(2)∂ϕ∂t=μdivdp∇ϕ∇ϕ+λδϕdivg∇ϕ∇ϕ+αgδϕ,with initial condition ϕx,0=ϕ0x, where dps and ps are, respectively, defined by(3)dps≙p′ss,(4)ps=12π1−cos2πs,ifs≤1,12s−12,ifs≥1.


## 2.2. DNA Encoding/Decoding Rules

A DNA sequence consists of A (adenine), T (thymine), C (cytosine), and G (guanine), where A and T, G, and C are complementary pairs. Further, 0 and 1 are complementary, so the DNA sequence is similar to the binary data. According to the principle of complementary pairing, Table1 shows eight types of encoding rules by the Watson–Crick complement regulation [31–33].Table 1
DNA encoding scheme.
12345678A0000111101100110T1111000010011001C1001100100001111G0110011011110000There introduce algebraic computation operators for DNA sequences to spread DNA computing, such as XOR. On the basis of traditional rule, the XOR operation is manipulated on DNA sequences. There exist 8 types of DNA XOR rules corresponding to 8 types of DNA encoding rules, and Table2 shows DNA XOR under Rule 1.Table 2
DNA XOR rule.
XORATCGAATCGTTAGCCCGATGGCTA


## 3. Skin Lesion Detection-Based Selective Encryption Algorithm

This paper proposes a secure and privacy-preserving technique to protect patients’ privacy and improve the security of skin lesion images. There have four stages of the proposed technique, as shown in Figure1: TR-based energy functional based on adaptive function, skin lesion detection model, selective encryption based on skin lesion detection, and decryption.Figure 1
The framework of the proposed technique.


### 3.1. Skin Lesion Detection Based on TR-Based Energy Functional Model

Because of the variation of the shape and appearance of the skin lesions, the detection of the edge of the skin lesions is a very important problem. This paper proposes a TR-based energy functional model to segment the skin lesion image.


#### 3.1.1. TR-Based Energy Functional

Introduce an adaptive function via the gray mean of the transition region, which will serve as the weight of the proposed TR-based energy functional.For an imageI:Ω⊂ℝ2⟶ℝ and function ϕ:Ω⊂ℝ2⟶ℝ, we design(5)νx,y=M−Ix,y,where M is mean value of the transition region drawn by LE-TREM algorithms [22, 30]. As shown in the works [22, 30], we observe that the function νx,y has opposite sign inside and outside the transition region. A binary image is displayed in Figure 2(a), and the corresponding 3D plot of νx,y is described in Figure 2(b). From Figure 2(b), we can really reveal that the function νx,y has opposite sign inside and outside the transition region.Figure 2
The 3D plot ofνx,y and its contribution to level set evolution driven by equation (14). (a) The binary image with two disjoint regions separated by a vertical edge. (b) 3D plot of νx,y. (c) 3D plot of the initial level set function ϕ0=0. (d) 3D plot of the level set function after one iteration.
(a)(b)(c)(d)Now we pose a novel energy (TR-based energy) based on the functionνx,y defined by (5). Given a level set function ϕ:Ω⊂ℝ2⟶ℝ, we design this external energy as follows:(6)Eνϕ=∫Ωνx,yg∇IσHε−ϕdxdy,where Hεϕ is the one-dimensional smoothed Heaviside function and g is the edge indicator given by gs=e−s/4.


#### 3.1.2. The Proposed Detection Model

Following the DRLSE model, the energy functionalEνϕ is introduced into a variational level set expression. The energy functional for the proposed model is defined as follows:(7)Eϕ=Evϕ+λEregϕ+μRpϕ,=∫Ωvx,yg∇IσH−ϕdxdy+λ∫Ωg∇Iσδϕ∇ϕdxdy+μ∫Ωp∇ϕdxdy,where the function p is given by (4) and gs=e−s/4 is the edge indicator function, which is different from that used in the DRLSE model.We employ the gradient descent method to minimize energy functional (7) with respect to ϕ and obtain the associated level set evolution equation:(8)∂ϕ∂t=μdivdp∇ϕ∇ϕ+λδϕdivg∇Iσ∇ϕ∇ϕ+νx,yg∇Iσδϕ,where dps is defined by equation (3).


### 3.2. Selective Encryption Based on Skin Lesion Detection

In our encryption method, the proposed TR-based energy functional model can be chosen to detect skin lesion images. Further, the extracted significant region is encrypted by employed chaotic maps and DNA sequences.


#### 3.2.1. Encryption and Decryption Process

Chaotic encryption technology has strong sensitivity. DNA computing has many advantages, such as massive parallelism, huge storage, and ultra-low power consumption. Image encryption method based on DNA encoding integrates biological characteristics, but its encryption principle is closely related to chaotic encryption technology.Step 1.
Construct 1D logistic-sine system (LSS) and 2D logistic-adjusted-sine map (LASM) and by chaotic maps.
Logistic map has high sensitivity and chaotic behavior. The sine map has a similar chaotic behavior with the logistic map. We employ 1D logistic-sine system (LSS) [34] and 2D logistic-adjusted-sine map (2D-LASM) [35] by the logistic and sine maps as seed maps:(9)xn+1=rxn1−xn+4−rsinπx44mod1,(10)yi+1=sinπμzi+3yi1−yi,zi+1=sinπμyi+1+3zi1−zi.
In the LSS system, the parameterr∈0,4, and mod function is the remainder used to return the division of two numbers. In 2D-LASM system, μ∈0,1, and y and z are state variables,y,z∈0,1.Step 2.
Generate the initial values and parameter for 1D-LSS and 2D-LASM.
We employ the SHA 256 hash of the plaintext image to generate a 256-bit external secret key. Then the 256-bit secret keyK is divided into 8-bit blocks ki, so K can also be described as follows:(11)K=k1,k2,…,k32.
Then, the initial values can be produced as follows:(12)x0=x0′+modk1⊕k2⊕k3+k4+∑i=132ki,28256mod1,r0=r0′+modk5⊕k6⊕k7+k8+∑i=132ki,28256mod1,y0=y0′+modk9⊕k10⊕⋯⊕k14+k15⊕k16+∑i=132ki,28256mod1,z0=z0′+modk17⊕k18⊕⋯⊕k22+k23⊕k24+∑i=132ki,28256mod1,μ0=μ0′+modk25⊕k26⊕⋯⊕k30+k31⊕k32+∑i=132ki,28256mod1,where mod is the modular operation, μ0 and r0 are the system parameters, x0, y0,andz0 are initial values, and μ0′,r0′, x0′,y0′, and z0′ are the given values used as secret keys.Step 3.
Perform DNA dynamic encoding process of the significant region.
LetI be an original skin lesion image, and detect the skin lesion region of image I using the proposed method as described in Section 3.1. Design an appropriate rectangle with the size of m×n to cover the skin lesion region.(1)
Convert each pixel in the rectangle block to its binary form, and obtain a binary matrixp of m×8n.(2)
Usex0,r0 produced in Step 1 for 1D-LSS system to iterate (2000+4mn) times, then abandon the former 2000 values, and get chaotic sequences X to perform a matrix U of m×4n.(3)
Generate dynamic encoding mode for every element of the significant region as follows:(13)Ri,j=1,0≤Ui,j<0.125,2,0.125≤Ui,j<0.25,3,0.25≤Ui,j<0.375,4,0.375≤Ui,j<0.5,5,0.5≤Ui,j<0.625,6,0.625≤Ui,j<0.75,7,0.75≤Ui,j<0.875,8,0.875≤Ui,j≤1.(4)
Group every element of the matrixp, then employ the corresponding encoding scheme in equation (13) to encode these elements, and finally form the encoded DNA a matrix p1 of m×4n.Step 4.
Generate the key matrixK.(1)
Useμ0y0,andz0 produced in Step 1 for 2D-LASM map to iterate (2000 + q) times, where q=maxm,4n, and abandon the former 2000 values to avoid the transient effect. Pick up the former m values from Y to construct matrix Y1 of size m×1, and use the former 4n values from Z to produce a matrix Z1 of size 1×4n. Manipulate matrix multiplying operation for Y1 and Z1 to get a matrix V with m×4n.(2)
Employ the matrixV to produce the key matrix K by the following formula:(14)Ki,j=A,0<Vi,j<0.25,T,0.25≤Vi,j<0.5,C,0.5≤Vi,j<0.75,G,0.75≤Vi,j<1.Step 5.
Implement DNA XOR between thep1 and the key matrix K by equation (13):(15)Ci,j=p1i,j⊕Ki,j,where C denote the ciphertext DNA matrix.Step 6.
Decode the matrixC by equation (13) to get the cipher block E.Step 7.
Employ the Arnold transform to make cipher blockE have more secure encryption effect.
Arnold scrambling is an image encryption technology which disturbs the original image by changing the position of image pixels. In our method, Arnold transform is applied to further disturb the pixel of ciphertext imageE, and its definition is represented as follows:(16)xn+1yn+1=1ab1+abxnynmodN,where a and b are positive integers, randomly selected scrambling parameters from the positive integers that affect the output value, and usually 1 is selected. N denotes the order of the image matrix.
The decryption process is the reverse operation of the encryption process.


## 3.1. Skin Lesion Detection Based on TR-Based Energy Functional Model

Because of the variation of the shape and appearance of the skin lesions, the detection of the edge of the skin lesions is a very important problem. This paper proposes a TR-based energy functional model to segment the skin lesion image.


### 3.1.1. TR-Based Energy Functional

Introduce an adaptive function via the gray mean of the transition region, which will serve as the weight of the proposed TR-based energy functional.For an imageI:Ω⊂ℝ2⟶ℝ and function ϕ:Ω⊂ℝ2⟶ℝ, we design(5)νx,y=M−Ix,y,where M is mean value of the transition region drawn by LE-TREM algorithms [22, 30]. As shown in the works [22, 30], we observe that the function νx,y has opposite sign inside and outside the transition region. A binary image is displayed in Figure 2(a), and the corresponding 3D plot of νx,y is described in Figure 2(b). From Figure 2(b), we can really reveal that the function νx,y has opposite sign inside and outside the transition region.Figure 2
The 3D plot ofνx,y and its contribution to level set evolution driven by equation (14). (a) The binary image with two disjoint regions separated by a vertical edge. (b) 3D plot of νx,y. (c) 3D plot of the initial level set function ϕ0=0. (d) 3D plot of the level set function after one iteration.
(a)(b)(c)(d)Now we pose a novel energy (TR-based energy) based on the functionνx,y defined by (5). Given a level set function ϕ:Ω⊂ℝ2⟶ℝ, we design this external energy as follows:(6)Eνϕ=∫Ωνx,yg∇IσHε−ϕdxdy,where Hεϕ is the one-dimensional smoothed Heaviside function and g is the edge indicator given by gs=e−s/4.


### 3.1.2. The Proposed Detection Model

Following the DRLSE model, the energy functionalEνϕ is introduced into a variational level set expression. The energy functional for the proposed model is defined as follows:(7)Eϕ=Evϕ+λEregϕ+μRpϕ,=∫Ωvx,yg∇IσH−ϕdxdy+λ∫Ωg∇Iσδϕ∇ϕdxdy+μ∫Ωp∇ϕdxdy,where the function p is given by (4) and gs=e−s/4 is the edge indicator function, which is different from that used in the DRLSE model.We employ the gradient descent method to minimize energy functional (7) with respect to ϕ and obtain the associated level set evolution equation:(8)∂ϕ∂t=μdivdp∇ϕ∇ϕ+λδϕdivg∇Iσ∇ϕ∇ϕ+νx,yg∇Iσδϕ,where dps is defined by equation (3).


## 3.1.1. TR-Based Energy Functional

Introduce an adaptive function via the gray mean of the transition region, which will serve as the weight of the proposed TR-based energy functional.For an imageI:Ω⊂ℝ2⟶ℝ and function ϕ:Ω⊂ℝ2⟶ℝ, we design(5)νx,y=M−Ix,y,where M is mean value of the transition region drawn by LE-TREM algorithms [22, 30]. As shown in the works [22, 30], we observe that the function νx,y has opposite sign inside and outside the transition region. A binary image is displayed in Figure 2(a), and the corresponding 3D plot of νx,y is described in Figure 2(b). From Figure 2(b), we can really reveal that the function νx,y has opposite sign inside and outside the transition region.Figure 2
The 3D plot ofνx,y and its contribution to level set evolution driven by equation (14). (a) The binary image with two disjoint regions separated by a vertical edge. (b) 3D plot of νx,y. (c) 3D plot of the initial level set function ϕ0=0. (d) 3D plot of the level set function after one iteration.
(a)(b)(c)(d)Now we pose a novel energy (TR-based energy) based on the functionνx,y defined by (5). Given a level set function ϕ:Ω⊂ℝ2⟶ℝ, we design this external energy as follows:(6)Eνϕ=∫Ωνx,yg∇IσHε−ϕdxdy,where Hεϕ is the one-dimensional smoothed Heaviside function and g is the edge indicator given by gs=e−s/4.


## 3.1.2. The Proposed Detection Model

Following the DRLSE model, the energy functionalEνϕ is introduced into a variational level set expression. The energy functional for the proposed model is defined as follows:(7)Eϕ=Evϕ+λEregϕ+μRpϕ,=∫Ωvx,yg∇IσH−ϕdxdy+λ∫Ωg∇Iσδϕ∇ϕdxdy+μ∫Ωp∇ϕdxdy,where the function p is given by (4) and gs=e−s/4 is the edge indicator function, which is different from that used in the DRLSE model.We employ the gradient descent method to minimize energy functional (7) with respect to ϕ and obtain the associated level set evolution equation:(8)∂ϕ∂t=μdivdp∇ϕ∇ϕ+λδϕdivg∇Iσ∇ϕ∇ϕ+νx,yg∇Iσδϕ,where dps is defined by equation (3).


## 3.2. Selective Encryption Based on Skin Lesion Detection

In our encryption method, the proposed TR-based energy functional model can be chosen to detect skin lesion images. Further, the extracted significant region is encrypted by employed chaotic maps and DNA sequences.


### 3.2.1. Encryption and Decryption Process

Chaotic encryption technology has strong sensitivity. DNA computing has many advantages, such as massive parallelism, huge storage, and ultra-low power consumption. Image encryption method based on DNA encoding integrates biological characteristics, but its encryption principle is closely related to chaotic encryption technology.Step 1.
Construct 1D logistic-sine system (LSS) and 2D logistic-adjusted-sine map (LASM) and by chaotic maps.
Logistic map has high sensitivity and chaotic behavior. The sine map has a similar chaotic behavior with the logistic map. We employ 1D logistic-sine system (LSS) [34] and 2D logistic-adjusted-sine map (2D-LASM) [35] by the logistic and sine maps as seed maps:(9)xn+1=rxn1−xn+4−rsinπx44mod1,(10)yi+1=sinπμzi+3yi1−yi,zi+1=sinπμyi+1+3zi1−zi.
In the LSS system, the parameterr∈0,4, and mod function is the remainder used to return the division of two numbers. In 2D-LASM system, μ∈0,1, and y and z are state variables,y,z∈0,1.Step 2.
Generate the initial values and parameter for 1D-LSS and 2D-LASM.
We employ the SHA 256 hash of the plaintext image to generate a 256-bit external secret key. Then the 256-bit secret keyK is divided into 8-bit blocks ki, so K can also be described as follows:(11)K=k1,k2,…,k32.
Then, the initial values can be produced as follows:(12)x0=x0′+modk1⊕k2⊕k3+k4+∑i=132ki,28256mod1,r0=r0′+modk5⊕k6⊕k7+k8+∑i=132ki,28256mod1,y0=y0′+modk9⊕k10⊕⋯⊕k14+k15⊕k16+∑i=132ki,28256mod1,z0=z0′+modk17⊕k18⊕⋯⊕k22+k23⊕k24+∑i=132ki,28256mod1,μ0=μ0′+modk25⊕k26⊕⋯⊕k30+k31⊕k32+∑i=132ki,28256mod1,where mod is the modular operation, μ0 and r0 are the system parameters, x0, y0,andz0 are initial values, and μ0′,r0′, x0′,y0′, and z0′ are the given values used as secret keys.Step 3.
Perform DNA dynamic encoding process of the significant region.
LetI be an original skin lesion image, and detect the skin lesion region of image I using the proposed method as described in Section 3.1. Design an appropriate rectangle with the size of m×n to cover the skin lesion region.(1)
Convert each pixel in the rectangle block to its binary form, and obtain a binary matrixp of m×8n.(2)
Usex0,r0 produced in Step 1 for 1D-LSS system to iterate (2000+4mn) times, then abandon the former 2000 values, and get chaotic sequences X to perform a matrix U of m×4n.(3)
Generate dynamic encoding mode for every element of the significant region as follows:(13)Ri,j=1,0≤Ui,j<0.125,2,0.125≤Ui,j<0.25,3,0.25≤Ui,j<0.375,4,0.375≤Ui,j<0.5,5,0.5≤Ui,j<0.625,6,0.625≤Ui,j<0.75,7,0.75≤Ui,j<0.875,8,0.875≤Ui,j≤1.(4)
Group every element of the matrixp, then employ the corresponding encoding scheme in equation (13) to encode these elements, and finally form the encoded DNA a matrix p1 of m×4n.Step 4.
Generate the key matrixK.(1)
Useμ0y0,andz0 produced in Step 1 for 2D-LASM map to iterate (2000 + q) times, where q=maxm,4n, and abandon the former 2000 values to avoid the transient effect. Pick up the former m values from Y to construct matrix Y1 of size m×1, and use the former 4n values from Z to produce a matrix Z1 of size 1×4n. Manipulate matrix multiplying operation for Y1 and Z1 to get a matrix V with m×4n.(2)
Employ the matrixV to produce the key matrix K by the following formula:(14)Ki,j=A,0<Vi,j<0.25,T,0.25≤Vi,j<0.5,C,0.5≤Vi,j<0.75,G,0.75≤Vi,j<1.Step 5.
Implement DNA XOR between thep1 and the key matrix K by equation (13):(15)Ci,j=p1i,j⊕Ki,j,where C denote the ciphertext DNA matrix.Step 6.
Decode the matrixC by equation (13) to get the cipher block E.Step 7.
Employ the Arnold transform to make cipher blockE have more secure encryption effect.
Arnold scrambling is an image encryption technology which disturbs the original image by changing the position of image pixels. In our method, Arnold transform is applied to further disturb the pixel of ciphertext imageE, and its definition is represented as follows:(16)xn+1yn+1=1ab1+abxnynmodN,where a and b are positive integers, randomly selected scrambling parameters from the positive integers that affect the output value, and usually 1 is selected. N denotes the order of the image matrix.
The decryption process is the reverse operation of the encryption process.


## 3.2.1. Encryption and Decryption Process

Chaotic encryption technology has strong sensitivity. DNA computing has many advantages, such as massive parallelism, huge storage, and ultra-low power consumption. Image encryption method based on DNA encoding integrates biological characteristics, but its encryption principle is closely related to chaotic encryption technology.Step 1.
Construct 1D logistic-sine system (LSS) and 2D logistic-adjusted-sine map (LASM) and by chaotic maps.
Logistic map has high sensitivity and chaotic behavior. The sine map has a similar chaotic behavior with the logistic map. We employ 1D logistic-sine system (LSS) [34] and 2D logistic-adjusted-sine map (2D-LASM) [35] by the logistic and sine maps as seed maps:(9)xn+1=rxn1−xn+4−rsinπx44mod1,(10)yi+1=sinπμzi+3yi1−yi,zi+1=sinπμyi+1+3zi1−zi.
In the LSS system, the parameterr∈0,4, and mod function is the remainder used to return the division of two numbers. In 2D-LASM system, μ∈0,1, and y and z are state variables,y,z∈0,1.Step 2.
Generate the initial values and parameter for 1D-LSS and 2D-LASM.
We employ the SHA 256 hash of the plaintext image to generate a 256-bit external secret key. Then the 256-bit secret keyK is divided into 8-bit blocks ki, so K can also be described as follows:(11)K=k1,k2,…,k32.
Then, the initial values can be produced as follows:(12)x0=x0′+modk1⊕k2⊕k3+k4+∑i=132ki,28256mod1,r0=r0′+modk5⊕k6⊕k7+k8+∑i=132ki,28256mod1,y0=y0′+modk9⊕k10⊕⋯⊕k14+k15⊕k16+∑i=132ki,28256mod1,z0=z0′+modk17⊕k18⊕⋯⊕k22+k23⊕k24+∑i=132ki,28256mod1,μ0=μ0′+modk25⊕k26⊕⋯⊕k30+k31⊕k32+∑i=132ki,28256mod1,where mod is the modular operation, μ0 and r0 are the system parameters, x0, y0,andz0 are initial values, and μ0′,r0′, x0′,y0′, and z0′ are the given values used as secret keys.Step 3.
Perform DNA dynamic encoding process of the significant region.
LetI be an original skin lesion image, and detect the skin lesion region of image I using the proposed method as described in Section 3.1. Design an appropriate rectangle with the size of m×n to cover the skin lesion region.(1)
Convert each pixel in the rectangle block to its binary form, and obtain a binary matrixp of m×8n.(2)
Usex0,r0 produced in Step 1 for 1D-LSS system to iterate (2000+4mn) times, then abandon the former 2000 values, and get chaotic sequences X to perform a matrix U of m×4n.(3)
Generate dynamic encoding mode for every element of the significant region as follows:(13)Ri,j=1,0≤Ui,j<0.125,2,0.125≤Ui,j<0.25,3,0.25≤Ui,j<0.375,4,0.375≤Ui,j<0.5,5,0.5≤Ui,j<0.625,6,0.625≤Ui,j<0.75,7,0.75≤Ui,j<0.875,8,0.875≤Ui,j≤1.(4)
Group every element of the matrixp, then employ the corresponding encoding scheme in equation (13) to encode these elements, and finally form the encoded DNA a matrix p1 of m×4n.Step 4.
Generate the key matrixK.(1)
Useμ0y0,andz0 produced in Step 1 for 2D-LASM map to iterate (2000 + q) times, where q=maxm,4n, and abandon the former 2000 values to avoid the transient effect. Pick up the former m values from Y to construct matrix Y1 of size m×1, and use the former 4n values from Z to produce a matrix Z1 of size 1×4n. Manipulate matrix multiplying operation for Y1 and Z1 to get a matrix V with m×4n.(2)
Employ the matrixV to produce the key matrix K by the following formula:(14)Ki,j=A,0<Vi,j<0.25,T,0.25≤Vi,j<0.5,C,0.5≤Vi,j<0.75,G,0.75≤Vi,j<1.Step 5.
Implement DNA XOR between thep1 and the key matrix K by equation (13):(15)Ci,j=p1i,j⊕Ki,j,where C denote the ciphertext DNA matrix.Step 6.
Decode the matrixC by equation (13) to get the cipher block E.Step 7.
Employ the Arnold transform to make cipher blockE have more secure encryption effect.
Arnold scrambling is an image encryption technology which disturbs the original image by changing the position of image pixels. In our method, Arnold transform is applied to further disturb the pixel of ciphertext imageE, and its definition is represented as follows:(16)xn+1yn+1=1ab1+abxnynmodN,where a and b are positive integers, randomly selected scrambling parameters from the positive integers that affect the output value, and usually 1 is selected. N denotes the order of the image matrix.
The decryption process is the reverse operation of the encryption process.


## 4. Experimental Result and Discussion

In this section, a series of skin lesion images are applied to analyze the performance of the proposed detection. From Table3, the strengths and limitations of different DNA sequence encryption algorithms are summarized and compared. Therefore, the proposed method is superior to other compared encryption schemes in some aspects.Table 3
Summary and comparison with the existing DNA encryption algorithm.
AlgorithmsEncryption typesImage typesAdvantagesLimitations[36]Full encryptionGeneral imageIncreases the strength of encryptionsHigh computational complexity[37]Full encryptionGeneral imageStrong key sensitivity and securityFew experiments to resist security attacks[33]Full encryptionColour light field imageSuitable for colour light field imageComplexity and need high computationProposedSelective encryptionSkin lesion imageSufficient experimental analysis and applied to skin lesion imageIncrease the execution speed


### 4.1. Experimental Results of Skin Lesion Detection

Without loss of generality, we set default parameters:τ=1,Δt=5,μ=0.04,λ=20,c=10, and ε=1 (for δεz). The values of σandα are provided in the following figure. In all the experiments, we simply initialize level set functions to zero function, i.e., ϕ0=0.The following two experiments demonstrate that the diffusion model [26] and our model are applied to extract the lesion areas in several skin lesion images. It is a very important task to extract lesion regions from the background in the field of computer vision. Because of the variation in the shape and appearance of the skin lesions, the detection of the edge of the skin lesions is a very important problem. Other factors such as strong noise and hair, dim edges, or strong asymmetry, or complex texture background also make the segmentation process more difficult.Figure3 describes that the proposed model can handle well for four skin lesion images and is compared with the diffusion model [26] through the detective results and computing times. For a fair comparison, we select the best scale parameter K and the most suitable high threshold tH (given in the caption of Figure 3) for the diffusion method. Our level set evolution starts with ϕ0=0, so there are no initial contours in the top row of Figure 3. It is clearly seen from the bottom that our model (with parameters σ=2.4,2.3,2, α=0.99,0.9,0.78 for the first three images) obtains the satisfactory segmentation results for four images, which are almost the same as the diffusion model visually, but the important improvement of the proposed method is that computation complexity is lower than that in the diffusion method. Iteration umbers and CPU times of the two methods are exhibited in Table 4. It can be surveyed that iteration numbers and CPU times of the proposed method are all less than those of the diffusion model.Figure 3
Comparison of both models. Middle row: diffusion model (K=0.002,0.00025,0.0004,0.0004; tH=0.8,0.55,0.35,0.6). Bottom row: our model.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)Figure 4
Detective results of our model for ten skin lesion images with blurred boundaries and asymmetric areas. The first and third rows: original images; the second and fourth rows: final detective results (left to right: 95, 150, 18, 10, 20 iterations for the second row; 10, 20, 10, 10, 25 iterations for the fourth row).
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)(n)(o)(p)(q)(r)(s)(t)Table 4
Number of iterations and CPU times in seconds of Figure3.
Model(a)(b)(c)(d)Diffusion [26]10020010030069.5195.220.2366.7Ours2520301312.611.16.17.3Figure4 shows detective results of our model for ten skin lesions image with blurry boundaries and/or asymmetric lesions areas, as shown in the first and third rows. It is difficult to extract the lesion areas in such images. Here, we do not show the detective results of the diffusion model [26], as the model cannot achieve satisfactory detective results. It can be observed from the second and fourth rows of Figure 4 that our method (σ=6,6,2.3,2,2, α=0.83,0.81,0.9,0.85,0.99 for images in the first row; and σ=2, α=0.85,0.75,0.95,0.85,0.85 for images in the third row), and for the last two images), stating with a constant function ϕ0=0, accurately extracts the lesion area boundaries.We conclude this section by simply describing about parametersα and σ; for our model, the parameters αandσ are very important for the function νx,y. By experiments, our observations are as follows: for skin lesions images, σ is typically about 2, and α is in the range between 0.75 and 0.99.


### 4.2. Experimental Results of Skin Lesion Region Protection

In this section, we, respectively, exhibit the subjective visual effect and objective data to prove the performance of plaintext encryption. We take four skin lesion images from Figures3 and 4, as examples using the initial values x0,r and x0,y0,z0,μ for the 1D-LSS system and 2D-LASM system. It can be seen from Figure 5 that the proposed method can protect significant regions.Figure 5
The first row: plain images. The second row: final detective results. The third row: cipher images.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)


#### 4.2.1. Key Space Analysis

In the proposed encryption method, the key includes (i) the given initial values and the parameters of 1D LSS and 2D-LASM,μ0′,r0′, x0′,y0′, and z0′, and (ii) the 256-bit external secret key. If the accuracy of the float is 10−16, then μ0′,r0′, x0′,y0′, and z0′ can be any one among 1016 possible values. The whole key space is 1016×1016×1016×1016×1016×2128=1080×2128, which is larger than 2100. Therefore, the proposed encryption method has a large key space to defend against brute force attacks.


#### 4.2.2. Key Sensitivity Analysis

The encryption scheme expects a slight change in the key to result in completely different results. Key sensitivity guarantees the uniqueness of the key. The encryption algorithm contains multiple secret keys, and the value contributed by each key is different in the encryption process. The original clear image can be decrypted only when all the keys are correct.To verify the sensitivity of the encryption algorithm for each key, the key sensitivity is performed by changing just one key in 10−15 position and keeping the rest same. The NPCR of the original target and changed cipher image-blocks for the keys of the proposed algorithm are listed in Table 5. It can be obviously seen from this table that when the key has a trivial change, the encrypted image-blocks have a complete change, and more than 99% pixels are modified compared with Figure 5(i), which implies the proposed scheme is highly key sensitive to all the keys.Table 5
Difference between decrypted image-blocks and target with changed decryption key.
Decryption keyμ0′ + 10−15r0′ + 10−15x0′ + 10−15y0′ + 10−15z0′ + 10−15Comparison with Figure5(i)99.605%99.623%99.615%99.634%99.616%


#### 4.2.3. Histogram of Analysis

Histogram describes the distribution of pixel values in an image. A secure cipher image encryption method should have a uniform histogram [38–41]. Generally speaking, a natural image should follow a regular distribution, while the secure encryption method should force the cipher image to follow a consistent distribution. Figure 6 reveals that our method can effectively prevent significant regions from being attacked by statistical attack opponents.Figure 6
Skin lesion image, cipher image, the corresponding target, and cipher image-block histograms.
(a)(b)(c)(d)Furthermore, the variances of histograms and chi-square test are used to evaluate the uniformity of the pixel value distribution. The variances of histograms and chi-square values can be calculated as follows [42]:(17)varZ=1n2∑i=1n∑j=1n12zi−zj2,(18)χ2=∑i=0255ni−n/2562n/256,where ni is the occurrence frequency of gray level i, n/256 is the expected occurrence frequency of each of gray level, and n is the number of all the pixels. Z=z1,z2,…,z256 is the vector of the histogram values, and ziand zj are the numbers of pixels in which gray values are equal to i and j, respectively.As shown in ref. [42], according to the chi-square distribution table, at 255 degrees of freedom and 0.05 significance level, χ255,0.052=293.2478. With a significance level of 0.05, the chi-square test results are listed in Table 6. The results indicate that the null hypothesis that the distribution is uniform cannot be rejected at 0.05 significance level. In this circumstance, redundancy of the plain images has successfully been concealed and consequently does not provide any clue to apply statistical attacks. Besides, Table 7 lists the comparison of histogram variance among image encryption schemes. From this table, we can observe that the average histogram variance of the proposed method is less than the schemes in ref. [37, 42].Table 6
Chi-square test results of the cipher image-blocks.
Test imagesFigure5(a)Figure5(b)Figure5(c)Figure5(d)χ255,0.052293293293293χ2258272219237ResultsPassPassPassPassTable 7
Comparison of histogram variance among different image encryption schemes.
Test imagesProposed[42][37]Figure5(a)105111341230Figure5(b)98010221010Figure5(c)115412051180Figure5(d)94710201035Average103310951114


#### 4.2.4. Correlation Analysis

We arbitrarily pick up 2,500 pairs of adjacent pixels in three directions which include horizontal, vertical, and diagonal from the skin lesion region of the plain image and the corresponding cipher image. The correlation coefficientsrxy of two adjacent pixels are computed through the following formulas:(19)covx,y=1N∑i=1Nxi−Exyi−Ey,(20)rxy=covx,yDxDy,where x and y are values of the two adjacent pixels in the image. Ex and Dx are given by(21)Ex=1N∑i=1Nxi,(22)Dx=1N∑i=1Nxi−Ex2.Figure7 illustrates the correlations of two horizontally, vertically, and diagonally adjacent pixels in the skin lesion region of plaintext image and its cipher image. Besides, Table 8 describes the correlation coefficients of adjacent pixels of the skin lesion region in the plaintext image and cipher image. We can clearly observe from these results that the correlations between adjacent pixels in each direction of cipher image-block are much lower than the corresponding plaintext blocks.Figure 7
Correlations of horizontally, vertically, and diagonally adjacent pixels: (a–c) skin lesion region; (d–f) the corresponding cipher image-block.
(a)(b)(c)(d)(e)(f)Table 8
Correlation coefficients of adjacent pixels.
DirectionTargetCipher image-blockHorizontal0.8846−0.0105Vertical0.90410.0338Diagonal0.91740.0023


#### 4.2.5. Information Entropy Analysis

Information entropyHm is employed to measure the uniform distribution of pixel grayscale, and its definition is given as follows:(23)Hm=∑i=02N−1pmilog21pmi,where mi denotes the pixel value and the pmi is the probability of mi.If the pixel values are distributed more uniformly, the information entropy is larger. For a gray image in the range of [0, 255], ideally, if all pixel values have an equal probability of occurrence, the upper limit value of image entropyH is 8. From Table 9, we can observe that the entropies of the cipher image-blocks are closed to 8, which have been added to the corresponding plaintexts. Therefore, this reveals that our method can defend the entropy cryptanalysis.Table 9
Information entropy analysis.
Skin lesion imageTargetCipher image-blockFigure5(a)6.97557.8860Figure5(b)7.46717.9939Figure5(c)7.59907.9937Figure5(d)7.53547.9799


#### 4.2.6. Computational and Complexity Analyses

Algorithmic complexity is an important reference standard for algorithm performance. We analyze the computational complexity of the proposed scheme and compare it with ref. [36].For the proposed scheme, the computational complexity has two parts: target extraction and target encryption. In the target extraction process, the main source of time complexity is the numerical solution of level set evolution equation (2). In this paper, we employ a simple explicit finite difference scheme to solve this equation. Its time complexity is Om×n. The encryption process contains the DNA level diffusion part and the Arnold scrambling further disturbs the pixel of cipher image-block. For the DNA level diffusion part, the complexity of the time-consuming includes generating chaotic sequences and DNA encoding and decoding operations. We, respectively, adopt 1D LSS and 2D-LASM to produce the chaotic sequences for the encoded DNA matrix and the key matrix K in the diffusion steps. The time complexity of generating LSS system-based sequence is O8, and the time complexity of generating the 2D-LASM system-based sequence is O2×m×n. So the total time complexity of generating chaotic sequences is O2×m×n. The time complexity of DNA encoding and decoding operation is O4×m×n/8=Om×n/2. The time complexity of Arnold scrambling is no more than Om×n. So the total time complexity of the proposed algorithm is O2×m×n.For ref. [36], there are three stages of encryption steps, that is shuffling, diffusion, and shuffling. The authors employ the complex hyperchaotic system to generate the chaotic sequences for increasing the strength of encryptions and decryptions, whereas low-dimensional chaotic systems are adopted in our algorithm, and the low-dimensional system is easy to implement and can run faster. As mentioned in ref. [36], the time complexity of the algorithm is O4×m×n. Therefore, the time complexity of our algorithm is lower than that of ref. [36].


## 4.1. Experimental Results of Skin Lesion Detection

Without loss of generality, we set default parameters:τ=1,Δt=5,μ=0.04,λ=20,c=10, and ε=1 (for δεz). The values of σandα are provided in the following figure. In all the experiments, we simply initialize level set functions to zero function, i.e., ϕ0=0.The following two experiments demonstrate that the diffusion model [26] and our model are applied to extract the lesion areas in several skin lesion images. It is a very important task to extract lesion regions from the background in the field of computer vision. Because of the variation in the shape and appearance of the skin lesions, the detection of the edge of the skin lesions is a very important problem. Other factors such as strong noise and hair, dim edges, or strong asymmetry, or complex texture background also make the segmentation process more difficult.Figure3 describes that the proposed model can handle well for four skin lesion images and is compared with the diffusion model [26] through the detective results and computing times. For a fair comparison, we select the best scale parameter K and the most suitable high threshold tH (given in the caption of Figure 3) for the diffusion method. Our level set evolution starts with ϕ0=0, so there are no initial contours in the top row of Figure 3. It is clearly seen from the bottom that our model (with parameters σ=2.4,2.3,2, α=0.99,0.9,0.78 for the first three images) obtains the satisfactory segmentation results for four images, which are almost the same as the diffusion model visually, but the important improvement of the proposed method is that computation complexity is lower than that in the diffusion method. Iteration umbers and CPU times of the two methods are exhibited in Table 4. It can be surveyed that iteration numbers and CPU times of the proposed method are all less than those of the diffusion model.Figure 3
Comparison of both models. Middle row: diffusion model (K=0.002,0.00025,0.0004,0.0004; tH=0.8,0.55,0.35,0.6). Bottom row: our model.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)Figure 4
Detective results of our model for ten skin lesion images with blurred boundaries and asymmetric areas. The first and third rows: original images; the second and fourth rows: final detective results (left to right: 95, 150, 18, 10, 20 iterations for the second row; 10, 20, 10, 10, 25 iterations for the fourth row).
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)(m)(n)(o)(p)(q)(r)(s)(t)Table 4
Number of iterations and CPU times in seconds of Figure3.
Model(a)(b)(c)(d)Diffusion [26]10020010030069.5195.220.2366.7Ours2520301312.611.16.17.3Figure4 shows detective results of our model for ten skin lesions image with blurry boundaries and/or asymmetric lesions areas, as shown in the first and third rows. It is difficult to extract the lesion areas in such images. Here, we do not show the detective results of the diffusion model [26], as the model cannot achieve satisfactory detective results. It can be observed from the second and fourth rows of Figure 4 that our method (σ=6,6,2.3,2,2, α=0.83,0.81,0.9,0.85,0.99 for images in the first row; and σ=2, α=0.85,0.75,0.95,0.85,0.85 for images in the third row), and for the last two images), stating with a constant function ϕ0=0, accurately extracts the lesion area boundaries.We conclude this section by simply describing about parametersα and σ; for our model, the parameters αandσ are very important for the function νx,y. By experiments, our observations are as follows: for skin lesions images, σ is typically about 2, and α is in the range between 0.75 and 0.99.


## 4.2. Experimental Results of Skin Lesion Region Protection

In this section, we, respectively, exhibit the subjective visual effect and objective data to prove the performance of plaintext encryption. We take four skin lesion images from Figures3 and 4, as examples using the initial values x0,r and x0,y0,z0,μ for the 1D-LSS system and 2D-LASM system. It can be seen from Figure 5 that the proposed method can protect significant regions.Figure 5
The first row: plain images. The second row: final detective results. The third row: cipher images.
(a)(b)(c)(d)(e)(f)(g)(h)(i)(j)(k)(l)


### 4.2.1. Key Space Analysis

In the proposed encryption method, the key includes (i) the given initial values and the parameters of 1D LSS and 2D-LASM,μ0′,r0′, x0′,y0′, and z0′, and (ii) the 256-bit external secret key. If the accuracy of the float is 10−16, then μ0′,r0′, x0′,y0′, and z0′ can be any one among 1016 possible values. The whole key space is 1016×1016×1016×1016×1016×2128=1080×2128, which is larger than 2100. Therefore, the proposed encryption method has a large key space to defend against brute force attacks.


### 4.2.2. Key Sensitivity Analysis

The encryption scheme expects a slight change in the key to result in completely different results. Key sensitivity guarantees the uniqueness of the key. The encryption algorithm contains multiple secret keys, and the value contributed by each key is different in the encryption process. The original clear image can be decrypted only when all the keys are correct.To verify the sensitivity of the encryption algorithm for each key, the key sensitivity is performed by changing just one key in 10−15 position and keeping the rest same. The NPCR of the original target and changed cipher image-blocks for the keys of the proposed algorithm are listed in Table 5. It can be obviously seen from this table that when the key has a trivial change, the encrypted image-blocks have a complete change, and more than 99% pixels are modified compared with Figure 5(i), which implies the proposed scheme is highly key sensitive to all the keys.Table 5
Difference between decrypted image-blocks and target with changed decryption key.
Decryption keyμ0′ + 10−15r0′ + 10−15x0′ + 10−15y0′ + 10−15z0′ + 10−15Comparison with Figure5(i)99.605%99.623%99.615%99.634%99.616%


### 4.2.3. Histogram of Analysis

Histogram describes the distribution of pixel values in an image. A secure cipher image encryption method should have a uniform histogram [38–41]. Generally speaking, a natural image should follow a regular distribution, while the secure encryption method should force the cipher image to follow a consistent distribution. Figure 6 reveals that our method can effectively prevent significant regions from being attacked by statistical attack opponents.Figure 6
Skin lesion image, cipher image, the corresponding target, and cipher image-block histograms.
(a)(b)(c)(d)Furthermore, the variances of histograms and chi-square test are used to evaluate the uniformity of the pixel value distribution. The variances of histograms and chi-square values can be calculated as follows [42]:(17)varZ=1n2∑i=1n∑j=1n12zi−zj2,(18)χ2=∑i=0255ni−n/2562n/256,where ni is the occurrence frequency of gray level i, n/256 is the expected occurrence frequency of each of gray level, and n is the number of all the pixels. Z=z1,z2,…,z256 is the vector of the histogram values, and ziand zj are the numbers of pixels in which gray values are equal to i and j, respectively.As shown in ref. [42], according to the chi-square distribution table, at 255 degrees of freedom and 0.05 significance level, χ255,0.052=293.2478. With a significance level of 0.05, the chi-square test results are listed in Table 6. The results indicate that the null hypothesis that the distribution is uniform cannot be rejected at 0.05 significance level. In this circumstance, redundancy of the plain images has successfully been concealed and consequently does not provide any clue to apply statistical attacks. Besides, Table 7 lists the comparison of histogram variance among image encryption schemes. From this table, we can observe that the average histogram variance of the proposed method is less than the schemes in ref. [37, 42].Table 6
Chi-square test results of the cipher image-blocks.
Test imagesFigure5(a)Figure5(b)Figure5(c)Figure5(d)χ255,0.052293293293293χ2258272219237ResultsPassPassPassPassTable 7
Comparison of histogram variance among different image encryption schemes.
Test imagesProposed[42][37]Figure5(a)105111341230Figure5(b)98010221010Figure5(c)115412051180Figure5(d)94710201035Average103310951114


### 4.2.4. Correlation Analysis

We arbitrarily pick up 2,500 pairs of adjacent pixels in three directions which include horizontal, vertical, and diagonal from the skin lesion region of the plain image and the corresponding cipher image. The correlation coefficientsrxy of two adjacent pixels are computed through the following formulas:(19)covx,y=1N∑i=1Nxi−Exyi−Ey,(20)rxy=covx,yDxDy,where x and y are values of the two adjacent pixels in the image. Ex and Dx are given by(21)Ex=1N∑i=1Nxi,(22)Dx=1N∑i=1Nxi−Ex2.Figure7 illustrates the correlations of two horizontally, vertically, and diagonally adjacent pixels in the skin lesion region of plaintext image and its cipher image. Besides, Table 8 describes the correlation coefficients of adjacent pixels of the skin lesion region in the plaintext image and cipher image. We can clearly observe from these results that the correlations between adjacent pixels in each direction of cipher image-block are much lower than the corresponding plaintext blocks.Figure 7
Correlations of horizontally, vertically, and diagonally adjacent pixels: (a–c) skin lesion region; (d–f) the corresponding cipher image-block.
(a)(b)(c)(d)(e)(f)Table 8
Correlation coefficients of adjacent pixels.
DirectionTargetCipher image-blockHorizontal0.8846−0.0105Vertical0.90410.0338Diagonal0.91740.0023


### 4.2.5. Information Entropy Analysis

Information entropyHm is employed to measure the uniform distribution of pixel grayscale, and its definition is given as follows:(23)Hm=∑i=02N−1pmilog21pmi,where mi denotes the pixel value and the pmi is the probability of mi.If the pixel values are distributed more uniformly, the information entropy is larger. For a gray image in the range of [0, 255], ideally, if all pixel values have an equal probability of occurrence, the upper limit value of image entropyH is 8. From Table 9, we can observe that the entropies of the cipher image-blocks are closed to 8, which have been added to the corresponding plaintexts. Therefore, this reveals that our method can defend the entropy cryptanalysis.Table 9
Information entropy analysis.
Skin lesion imageTargetCipher image-blockFigure5(a)6.97557.8860Figure5(b)7.46717.9939Figure5(c)7.59907.9937Figure5(d)7.53547.9799


### 4.2.6. Computational and Complexity Analyses

Algorithmic complexity is an important reference standard for algorithm performance. We analyze the computational complexity of the proposed scheme and compare it with ref. [36].For the proposed scheme, the computational complexity has two parts: target extraction and target encryption. In the target extraction process, the main source of time complexity is the numerical solution of level set evolution equation (2). In this paper, we employ a simple explicit finite difference scheme to solve this equation. Its time complexity is Om×n. The encryption process contains the DNA level diffusion part and the Arnold scrambling further disturbs the pixel of cipher image-block. For the DNA level diffusion part, the complexity of the time-consuming includes generating chaotic sequences and DNA encoding and decoding operations. We, respectively, adopt 1D LSS and 2D-LASM to produce the chaotic sequences for the encoded DNA matrix and the key matrix K in the diffusion steps. The time complexity of generating LSS system-based sequence is O8, and the time complexity of generating the 2D-LASM system-based sequence is O2×m×n. So the total time complexity of generating chaotic sequences is O2×m×n. The time complexity of DNA encoding and decoding operation is O4×m×n/8=Om×n/2. The time complexity of Arnold scrambling is no more than Om×n. So the total time complexity of the proposed algorithm is O2×m×n.For ref. [36], there are three stages of encryption steps, that is shuffling, diffusion, and shuffling. The authors employ the complex hyperchaotic system to generate the chaotic sequences for increasing the strength of encryptions and decryptions, whereas low-dimensional chaotic systems are adopted in our algorithm, and the low-dimensional system is easy to implement and can run faster. As mentioned in ref. [36], the time complexity of the algorithm is O4×m×n. Therefore, the time complexity of our algorithm is lower than that of ref. [36].


## 4.2.1. Key Space Analysis

In the proposed encryption method, the key includes (i) the given initial values and the parameters of 1D LSS and 2D-LASM,μ0′,r0′, x0′,y0′, and z0′, and (ii) the 256-bit external secret key. If the accuracy of the float is 10−16, then μ0′,r0′, x0′,y0′, and z0′ can be any one among 1016 possible values. The whole key space is 1016×1016×1016×1016×1016×2128=1080×2128, which is larger than 2100. Therefore, the proposed encryption method has a large key space to defend against brute force attacks.


## 4.2.2. Key Sensitivity Analysis

The encryption scheme expects a slight change in the key to result in completely different results. Key sensitivity guarantees the uniqueness of the key. The encryption algorithm contains multiple secret keys, and the value contributed by each key is different in the encryption process. The original clear image can be decrypted only when all the keys are correct.To verify the sensitivity of the encryption algorithm for each key, the key sensitivity is performed by changing just one key in 10−15 position and keeping the rest same. The NPCR of the original target and changed cipher image-blocks for the keys of the proposed algorithm are listed in Table 5. It can be obviously seen from this table that when the key has a trivial change, the encrypted image-blocks have a complete change, and more than 99% pixels are modified compared with Figure 5(i), which implies the proposed scheme is highly key sensitive to all the keys.Table 5
Difference between decrypted image-blocks and target with changed decryption key.
Decryption keyμ0′ + 10−15r0′ + 10−15x0′ + 10−15y0′ + 10−15z0′ + 10−15Comparison with Figure5(i)99.605%99.623%99.615%99.634%99.616%


## 4.2.3. Histogram of Analysis

Histogram describes the distribution of pixel values in an image. A secure cipher image encryption method should have a uniform histogram [38–41]. Generally speaking, a natural image should follow a regular distribution, while the secure encryption method should force the cipher image to follow a consistent distribution. Figure 6 reveals that our method can effectively prevent significant regions from being attacked by statistical attack opponents.Figure 6
Skin lesion image, cipher image, the corresponding target, and cipher image-block histograms.
(a)(b)(c)(d)Furthermore, the variances of histograms and chi-square test are used to evaluate the uniformity of the pixel value distribution. The variances of histograms and chi-square values can be calculated as follows [42]:(17)varZ=1n2∑i=1n∑j=1n12zi−zj2,(18)χ2=∑i=0255ni−n/2562n/256,where ni is the occurrence frequency of gray level i, n/256 is the expected occurrence frequency of each of gray level, and n is the number of all the pixels. Z=z1,z2,…,z256 is the vector of the histogram values, and ziand zj are the numbers of pixels in which gray values are equal to i and j, respectively.As shown in ref. [42], according to the chi-square distribution table, at 255 degrees of freedom and 0.05 significance level, χ255,0.052=293.2478. With a significance level of 0.05, the chi-square test results are listed in Table 6. The results indicate that the null hypothesis that the distribution is uniform cannot be rejected at 0.05 significance level. In this circumstance, redundancy of the plain images has successfully been concealed and consequently does not provide any clue to apply statistical attacks. Besides, Table 7 lists the comparison of histogram variance among image encryption schemes. From this table, we can observe that the average histogram variance of the proposed method is less than the schemes in ref. [37, 42].Table 6
Chi-square test results of the cipher image-blocks.
Test imagesFigure5(a)Figure5(b)Figure5(c)Figure5(d)χ255,0.052293293293293χ2258272219237ResultsPassPassPassPassTable 7
Comparison of histogram variance among different image encryption schemes.
Test imagesProposed[42][37]Figure5(a)105111341230Figure5(b)98010221010Figure5(c)115412051180Figure5(d)94710201035Average103310951114


## 4.2.4. Correlation Analysis

We arbitrarily pick up 2,500 pairs of adjacent pixels in three directions which include horizontal, vertical, and diagonal from the skin lesion region of the plain image and the corresponding cipher image. The correlation coefficientsrxy of two adjacent pixels are computed through the following formulas:(19)covx,y=1N∑i=1Nxi−Exyi−Ey,(20)rxy=covx,yDxDy,where x and y are values of the two adjacent pixels in the image. Ex and Dx are given by(21)Ex=1N∑i=1Nxi,(22)Dx=1N∑i=1Nxi−Ex2.Figure7 illustrates the correlations of two horizontally, vertically, and diagonally adjacent pixels in the skin lesion region of plaintext image and its cipher image. Besides, Table 8 describes the correlation coefficients of adjacent pixels of the skin lesion region in the plaintext image and cipher image. We can clearly observe from these results that the correlations between adjacent pixels in each direction of cipher image-block are much lower than the corresponding plaintext blocks.Figure 7
Correlations of horizontally, vertically, and diagonally adjacent pixels: (a–c) skin lesion region; (d–f) the corresponding cipher image-block.
(a)(b)(c)(d)(e)(f)Table 8
Correlation coefficients of adjacent pixels.
DirectionTargetCipher image-blockHorizontal0.8846−0.0105Vertical0.90410.0338Diagonal0.91740.0023


## 4.2.5. Information Entropy Analysis

Information entropyHm is employed to measure the uniform distribution of pixel grayscale, and its definition is given as follows:(23)Hm=∑i=02N−1pmilog21pmi,where mi denotes the pixel value and the pmi is the probability of mi.If the pixel values are distributed more uniformly, the information entropy is larger. For a gray image in the range of [0, 255], ideally, if all pixel values have an equal probability of occurrence, the upper limit value of image entropyH is 8. From Table 9, we can observe that the entropies of the cipher image-blocks are closed to 8, which have been added to the corresponding plaintexts. Therefore, this reveals that our method can defend the entropy cryptanalysis.Table 9
Information entropy analysis.
Skin lesion imageTargetCipher image-blockFigure5(a)6.97557.8860Figure5(b)7.46717.9939Figure5(c)7.59907.9937Figure5(d)7.53547.9799


## 4.2.6. Computational and Complexity Analyses

Algorithmic complexity is an important reference standard for algorithm performance. We analyze the computational complexity of the proposed scheme and compare it with ref. [36].For the proposed scheme, the computational complexity has two parts: target extraction and target encryption. In the target extraction process, the main source of time complexity is the numerical solution of level set evolution equation (2). In this paper, we employ a simple explicit finite difference scheme to solve this equation. Its time complexity is Om×n. The encryption process contains the DNA level diffusion part and the Arnold scrambling further disturbs the pixel of cipher image-block. For the DNA level diffusion part, the complexity of the time-consuming includes generating chaotic sequences and DNA encoding and decoding operations. We, respectively, adopt 1D LSS and 2D-LASM to produce the chaotic sequences for the encoded DNA matrix and the key matrix K in the diffusion steps. The time complexity of generating LSS system-based sequence is O8, and the time complexity of generating the 2D-LASM system-based sequence is O2×m×n. So the total time complexity of generating chaotic sequences is O2×m×n. The time complexity of DNA encoding and decoding operation is O4×m×n/8=Om×n/2. The time complexity of Arnold scrambling is no more than Om×n. So the total time complexity of the proposed algorithm is O2×m×n.For ref. [36], there are three stages of encryption steps, that is shuffling, diffusion, and shuffling. The authors employ the complex hyperchaotic system to generate the chaotic sequences for increasing the strength of encryptions and decryptions, whereas low-dimensional chaotic systems are adopted in our algorithm, and the low-dimensional system is easy to implement and can run faster. As mentioned in ref. [36], the time complexity of the algorithm is O4×m×n. Therefore, the time complexity of our algorithm is lower than that of ref. [36].


## 5. Conclusion

A novel approach for skin lesion detection and privacy protection is presented in this paper. Firstly, a transition region-based level set evolution method is proposed to detect skin lesion image. This idea of the proposed method is to construct the energy functional that compels the level set function to have a different sign inside and outside the image target. Then this functional is introduced into a variational level set expression with the other two functionals. Then, once skin lesion detection has been performed, the detected skin lesion pixels are encrypted by utilizing DNA sequences and chaotic systems. We employ 2D-LASM and 1D-LSS to make the pseudorandom sequences and use the 256-bit hash value of the plaintext image to generate the initial values and system parameters. Different from these existing encryption algorithms based on DNA computing, the DNA encoding/decoding rules of the skin lesion region and the key matrix are generated by the skin lesion region, and this may increase resilience to statistical attacks. Experimental results of skin lesions detection show that the proposed method is particularly suitable for the detection of skin lesion images with strong noise and complex background. Meanwhile, security analyses reveal that our selective encryption method has a good encryption effect.



---

*Source: 7982192-2020-09-28.xml*