1 Introduction

The wireless network of the body area is one of most significant emerging health-care technologies. Via it we will keep track of the patient’s wellbeing without affecting his daily life. With regard to WBAN, transmission of patient information must be protected without sacrificing the privacy and confidentiality of the data. Due to any change in data, incorrect diagnosis and treatment can result. The wireless body area network faces many challenges such as memory constraint, computing, usability and scalability [14].

DNA cryptography offers many benefits which make it a promising technology for WBAN [2, 17] First, it has a large parallelism that helps improve the speed of computing. Second, it has wide capacity to store DNA molecules and low energy consumption. So, DNA coding is a modern uninterrupted data technology and provides high protection in WBAN over conventional coding such as DES and AES [11, 16]. And for medical images, several scientists have reported that DNA coding is an effective technique for secure transmission of a medical images [3]. Chaotic encryption technology has characteristics such as vulnerability to initial conditions, pseudo-randomness and non-periodicity, making it commonly used for image encryption [8, 22]. Because of the benefits of DNA coding and the chaotic method, researchers use these two approaches in image cryptosystems to create very effective and stable structures that are difficult to penetrate or crack [4, 6, 20].

1.1 Our involvement

In the proposed scheme adaptive DNA coding is used with a modern one-dimensional (HGL) chaotic mapping system that has more features than the traditional chaotic system (Henon map, Gaussian map, logistic map, …) like larger variable range, wide randomization and several chaotic series. So, the chaotic series generated by (HGL) is hard to prophesy. At first, the medical image input is hashed using SHA-256 hash function to obtain the initial chaotic map (HGL) value and get the chaotic series. At second, the image is crossover and adaptive DNA coding is applied on image and chaotic map to get two DNA matrix. Finally, the two DNA matrix is xored using Xor operation to get a new DNA matrix and DNA decoding rules is implemented to obtain cipher image. The results of simulation and the security analysis show that, the algorithm has been shown to exhibit strong encryption effects and can effectively withstand any type of attack. This article is divided as follow. Section 1 describes the proposed scheme’s preliminaries. Section 2 discusses the suggested scheme for encryption. Section 3 illustrate experimental and simulation tools. Section 4 display security analysis and result. The conclusions are given in Section 5.

2 Preliminaries

2.1 DNA operation

DNA (Deoxyribonucleic acid) is a nucleic acid that holds living organisms’ genetic information. In one DNA sequence, there are four distinct nucleic acid bases: adenine -A, thymine -T, cytosine -C, guanine-G, where complementary pairs are C and G, T and A. We can get 24 encoding schemes if 4 bases A, T, C, G are encoded to 00,11,10,01. Due to the complementary connection between DNA bases, eight types of coding groups comply with the basic complementary rule as shown in Table 1, and there are eight types of XOR operation for each DNA base as well. in Table 2, The XOR operation for DNA rule5 [1].

Table 1 DNA encoding & decoding rules
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Table 2 The XOR operation for DNA sequence
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2.2 Chaotic map

Chaotic maps are extremely sensitive dynamic systems to initial conditions and the parameters of control. These characteristics can be regarded as similar to the required cryptographic structures. The cryptography schemes based on Chaos utilizing boundary conditions as a key to cryptography. The chaotic map as Logistic map, Gaussian map and Henon map are illustrated as the follows, which are simple and standard dynamic equation of complicated chaotic pattern [19, 24].

$$\begin{array}{*{20}c}\text{Logistic\ map}: {x}_{n+1}=r \ {x}_{n}(1-{x}_{n})\\ \text{Gaussian\ map}: {x}_{n+1}=exp\left(-\alpha {x}_{n}^{2}\right)+\beta\\ \text{One-dimension\ decomposition\ henon\ map}:{x}_{n+1}=1-a {x}_{n}^{2}+b{ x}_{n-1}.\end{array}$$

3 The proposed scheme for encryption

3.1 Overview of proposed algorithm

3.1.1 The suggested multi-chaotic map system (HGL)

The logistic and Gaussian map are merged in this scheme with Henon map as shown in Fig. 1 To obtain a modern one-dimensional chaotic map with a unique design and more variables, parameters and unpredictable attitude. The suggested (HGL) Map’s Mathematical structure is defined in Eq. (1).

$${\text{z}}_{\text{n}+1}=1-\text{a} \ \text{exp}{\left(-{\upalpha } \ {\text{z}}_{\text{n}}^{2}\right)}^{2}+\text{b}\left(\text{r} \ {\text{z}}_{\text{n}-1}\right(1-{\text{z}}_{\text{n}-1}\left)\right)$$
(1)

Where \({z}_{n}\) ,\({\text{z}}_{\text{n}-1}\)is initial value and a, b, \({\upalpha }\) ,r is the parameter of the chaotic system.

Fig. 1
figure 1

Proposed (HGl) chaotic map

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3.1.2 Statistical analysis for (HGL) chaotic system

The randomness of the suggested HGL chaotic map is checked using the NIST test feature consisting of 16 statistical measures. Such measures determine whether or not the sequence generated is random. For such measures, the basic reliance is on the likelihood value (p-value). The value p is compared to the meaning level α which represents the boundary between the region of rejection and non-rejection. The significant level in NIST equals 0.01. It implies that the series is not a random series and deny for p-value less than 0.01 and for p-value more than 0.01, This ensures that the series is random and approved. Table 3 shows the results of the series created by the proposed chaotic map. As a consequence, the suggested sequence of chaotic HST map are totally random and ideal to be used.

Table 3 suggested HGL map randomness tests
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3.2 Key generation

For this scheme, the hash function of SHA-256 is applied on the input image to obtain 256-bit of secret key K. In that every single bit alteration in the image would produce a totally different hash value. As in Eq. (2), the secret key K is divided into 8-bit blocks, and the primary values are extracted from Eqs. (3), (4). Since the initial values given are Z0 ' and Z1′.

$$K\:=\:k_1,\;k_2,\;k_3,\;{\dots},\;k_{32}$$
(2)
$$Z0=\;\lbrack Z0^\prime +\;\lbrack(k1\:+\:k2\:+\:k3+{\dots}+k16)\;/256\rbrack\rbrack\;Mod1$$
(3)
$$Z1=\;\lbrack Z1^\prime +\;\lbrack(k17\:+\:k18\:+\:k19+ {\dots} +k32)/256\rbrack\rbrack\;Mod1$$
(4)

3.3 Encryption algorithm

  • Step1: image I is hashed to get the initial value of (Henon –Gaussian- Logistic map) according to Section (3.1).

  • Step2: calculate the value of \({\text{H}}_{\text{i}}\)and\({\text{p}}_{\text{i}}\)for plain image by using Eqs. (5), (6). Which is used to determine the DNA rule number used for coding. With it, each image is encoded by a different DNA rule than the other images and then a new image V (m, n) is produced using the crossover technique.

    $$ H_i=value\;of\;pixel\;in\;position\;\lbrack1\:\times\:3\rbrack\;+\;value\;of\;pixel\;in\;position\;\lbrack M\;\times \;(N-3)\rbrack$$
    (5)
    $$p_i=\;\lbrack Hi\;Mod\;8\rbrack\:+\:1$$
    (6)

  • Step 3: V (m, n) matrix is converted into a binary series by representing each pixel in 8 bits and then coding for the DNA encoding rules according to\({ \text{p}}_{\text{i}}\)for getting\({\text{V}}_{\text{d}\text{n}\text{a}}\)

  • Step 4: create an array of chaotic series W using the suggested chaotic map (HGL) of length (m x n) with parameter and initial value a, b, α, r, Z0, Z1

  • Step 5: Similar to step 2, \({\text{H}}_{\text{c}}\)and \({\text{p}}_{\text{c}}\)for chaotic are calculated and then encode the chaotic array W with DNA encoding rules according to\({\text{p}}_{\text{c}}\) for getting\({ \text{W}}_{\text{d}\text{n}\text{a}}\)

  • Step 6: By using XOR operation in Table 2, \({\text{V}}_{\text{d}\text{n}\text{a}}\)is xor with \({ \text{W}}_{\text{d}\text{n}\text{a}}\) and the outcome is decoding with the selected DNA rule 5 to have the encrypt image Q (m, n)

3.4 Decryption algorithm

  • Step1: The encrypt image is encoded according to the selected DNA rule 5 that was used in the encryption algorithm to obtain \({\text{Q}}_{\text{d}\text{n}\text{a}}\).

  • Step2: Repeat steps 4, 5 as with the encryption algorithm.

  • Step3: Based on the XOR process for DNA in Table 2, \({\text{Q}}_{\text{d}\text{n}\text{a}}\)is xor with\({ \text{W}}_{\text{d}\text{n}\text{a}}\) to get\({ \text{V}}_{\text{d}\text{n}\text{a}}\).

  • Step4: calculate \({\text{p}}_{\text{i}}\)from given\({\text{H}}_{\text{i}}\) according to Eq. (6) and then decoding\({ \text{V}}_{\text{d}\text{n}\text{a}}\) with DNA rule according to\({ \text{p}}_{\text{i}}\) and obtain V.

  • Step5: Inverse crossover to get the plain image I (Figs. 2 and 3).

Fig. 2
figure 2

Block diagram of encryption algorithm

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Fig. 3
figure 3

Block diagram of decryption algorithm

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4 Simulation result and discussion

4.1 Tools

The proposed encryption and decryption scheme are executed on a personal computer using Wolfram (Mathematica11.3) and (MATLAB R2016a) software with Intel ®, core TMi7-8550u, CPU@1.80GH and 8 GB laptop running windows 10. The proposed scheme was conducted on multiple medical images like (MRI, X-Ray, CT, Ultrasound, ECG) images and Lena image with size of 256 × 256 and 512 × 512. Figure 4 display samples of the images tested for encryption and decryption with chaotic control parameter and initial value a = 1.4, b = 0.3, r = 0.399, \({\upalpha }=4.9,\) Z0′= 0.1, Z1′ = 0.15.

Fig. 4
figure 4

(l, m, c, x, u, e) are the plain, encrypted and decoded images of (Lena, MRI, CT, X-ray, ultrasound, ECG) images

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4.2 Security analysis and performance tests

4.2.1 Key space analysis

The key space must be wide enough for a successful encryption scheme to stand up to the brute force attack. In this scheme the key is the control parameter (a, b, \({\upalpha }\), r), the initial values (Z0′, Z1′), The value of added pixel of image (\({\text{H}}_{\text{i}}\)) and 256 bits for hash value. If computational precision of number equal 10 − 15. The total key space will be equal 2128 × 10 105 ≈ 3.4028 × 10 143 .This is greater than the permissible space for the key (2256) for realistic symmetrical AES encryption [15]. So, it’s large enough to withstand attack by brute force.

4.2.2 Key sensitivity analysis

Key Sensitivity ensures which only the right key could decode the encrypted image and any effort to decode it for other keys will failure. To evaluate key sensitivity, various key combinations are used to decrypt encrypted images by changing the initial values (Z0′, Z1′) of henon-Gaussian-logistic chaotic map just slightly. As show in Fig. 5, The decryption process by slight change in Z0′and Z1′ does not offer any characteristics of the plain image.

Fig. 5
figure 5

Key sensitivity test. (a) original image. (b) cipher image. (c) decrypt with Z0′ change. (d) decrypt with Z1′ change

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4.2.3 Information entropy analysis

The entropy of the information shall be considered to determine the quantity of randomness in the image. The maximum value of the information entropy for an ideal grayscale image is 8 by Eq. (7). Where m, P (mi) refers to the source of the information and the likelihood of the mi sign. Table 4 demonstrates the entropy results [5].

$$H(m)=\sum\nolimits _{i=0}^{{2}^{N}-1}P\left({m}_{i}\right){{log}}_{2}\frac{1}{p\left({m}_{i}\right)}$$
(7)
Table 4 Entropy of tested images
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4.2.4 The histogram analysis

The image histogram shows the spread of pixel value inside the image. against the different intensity levels. The histogram of the encoding image must be uniform enough to be an effective image encoding system. Shows in Fig. 6, the histograms of original and cipher images. The histogram of the images is evidently very different and the histogram of the cipher image is standardized, that allows it to face the statistical assault.

4.2.5 Correlation analysis

This informs how much the relationship is between the similar pixels of the original and the encoded image. Cryptography algorithms should increase the connection between the adjacent pixels in the cipher image. Correlation coefficients for our structure are calculated by Eq. (8) utilizing randomly 4000 pairs of adjacent pixels from both the plain and encrypted image, and the results are shown in Table 6.

$$\begin{array}{*{20}c}{R}_{xy} =\frac{cov\left(x,y\right)}{\sqrt{D\left(x\right)}\sqrt{D\left(y\right) }}, & Cov(x,y) = \frac{1}{N}{\sum }_{i=1}^{N}({x}_{i}-E\left(x\right))({y}_{i}-E(y))\\ E\left(x\right)=\frac{1}{N}\sum _{i=1}^{N}{x}_{i}, & D\left(x\right)= \frac{1}{N}\sum _{i=1}^{N}{({x}_{i}-E\left(x\right))}^{2}\end{array}$$
(8)

The results show that in the original image the correlation coefficients are near to 1while the coefficients of the cipher image are around 0. So that signifies how our scheme has assisted in removing the relationship in the image between neighboring pixels, which enables to avoid statistical attacks as shown in Fig. 6 and Table 5.

Fig. 6
figure 6figure 6

Correlation of two neighboring pixels

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Table 5 Correlation coefficients of two neighbouring pixels in the plain and cipher-images
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4.2.6 Differential attack analysis

The sensitivity of an encrypted image to the few changes in the original image is one way of measuring. The two variables used are NPCR and UACI, which are determined using the Eq. (9). Overall, the NPCR and UACI values ​​should be approximate 99.6093% and 33.4635% respectively. In this scheme one pixel in the plain image was modified and both NPCR and UACI are calculated and from the results showing in Table 6, we notice that NPCR > 99.6% and UACI > 33.3% which make it able to overcome differential attacks [5].

$$\begin{array}{*{20}c}\begin{array}{*{20}c}NPCR=\frac1{M\times N}(\sum_{i,j}D\left(i,j\right))\times100\%, & UACI=\frac1{M\times N}\left(\sum\nolimits_{i,j}\left|\frac{c_1\left(i,j\right)-c_2\left(i,j\right)}{255}\right|\right)\times100\%\end{array}\\ D\left(i,j\right)=\left\{\begin{array}{*{20}c}0 &{c}_{1}\left(i,j\right)={c}_{2}(i,j)\\ 1 &{c}_{1}(i,j)\ne {c}_{2}(i,j)\end{array}\right.\end{array}$$
(9)
Table 6 The UACI & NPCR of tested images
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4.2.7 Peak signal to noise analysis

The PSNR is used in the evaluation of image quality, arithmetically described by the mean square error (MSE) as in the Eq. (10). Table 7 shows the value of MSE and PSNR values using the proposed scheme. Results indicate that the PSNR values between both the encoded and the plain images are low and that the MSE values between both the encoded and the plain images are big. Which indicates that this scheme has a strong performance and greater safety.

$$\begin{array}{*{20}c}PSNR =20 \ {{log}}_{10}(MaxI/\sqrt{MSE}) \\ MSE =\frac{1}{M\times N}\sum _{i=0}^{M-1}\sum _{i=0}^{N-1}{({G}_{0}\left(i,j\right)-{G}_{1}\left(i,j\right))}^{2}\end{array}$$
(10)
Table 7 The MSE and PSNR of images
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4.2.8 Noise added analysis

During transmission over a noisy channel, the encrypted image is exposed to noise. The efficiency of the scheme is determined by the noise resistance and the reliable receiver’s capability to identify the image after decoding. By adding Gaussian noise with variance (0.01, 0.1) and pepper and salt noise with density (0.05, 0.5) to the encrypted image, the proposed scheme is checked and then decrypted with appropriate key. Figure 7 displays the encrypted and decoded images.

Fig. 7
figure 7

(a), (b) encrypted and decoded image with Gaussian noise variation (0.01,0.1) and (c), (d) encrypted and decoded image with salt and pepper density (0.05,0.5) respectively

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4.2.9 Complexity

The computational complexity in this scheme shall be determined as the following, for an image with size M x N the time complexity is O(M x N). The algorithm generates a random number with size of M x N using a chaotic map so the complexity for chaotic series is O(M x N), then the complexity time for encoding image and chaotic series to DNA is O(4 x M x N) and the complexity time for DNA XOR operation is O(4 x M x N) also the time of decoding DNA sequence is O(8 x M x N) so the total complexity of the algorithm is nearly equal O(8 x M x N). The computational complexity of the algorithm will also be reduced when the algorithm is run in parallel mode.

4.3 Comparison results with others

The performance of the proposed image coding scheme is compared with other approaches using Entropy, UACI, and NPCR tests and the results demonstrate the fact that our algorithm provides better performance in terms of protection compared to the results obtained by other algorithms.

As shown in Table 8; The entropy of the proposed Lena image is greater than the entropy in the other references and this proves that the proposed algorithm is robust enough and capable of countering statistical attacks.

Table 8 Comparison of Lena entropy with other schemes
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Table 9 indicates that, relative to the other references, the UACI and NPCR values of the proposed Lena image are good enough and capable of overcoming differential attacks.

Table 9 Comparison of UACI and NPCR of Lena’s image with other schemes
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Table 10 shows that; Medical images tested with the proposed algorithm have good Entropy, UACI and NPCR values compared to other references making them able to withstand statistical and differential attacks.

Table 10 Comparison of entropy, UACI and NPCR of tested medical images with other schemes
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5 Conclusion

This paper proposes a medical image encryption scheme using Adaptive DNA and new multi chaotic map (HGL). by using Adaptive DNA each image is encrypted with DNA rule different to other images That makes the algorithm proposed effective against attackers ' perceptions. Whereas a new multi-chaotic map was created by combining Henon, Gaussian and Logistic map (HGL) that produce more chaotic pseudo-random series. the security analysis and experimental Simulation Result show that this algorithm has high entropy value, low correlation, low PSNR value and uniform histogram, high level of security, large key space make it capable of resisting all kinds of attacks.