In the medical sector, the digital image is multimedia data that contain secret information. However, designing an efficient secure cryptosystem to protect the confidential images in sharing is a challenge. In this work, we propose an improved chaos-based cryptosystem to encrypt and decrypt rapidly secret medical images. A complex chaos-based PRNG is suggested to generate a high-quality key that presents high randomness behaviour, high entropy, and high complexity. An improved architecture is proposed to encrypt the secret image that is based on permutation, substitution, and diffusion properties. In the first step, the image’s pixels are randomly permuted through a matrix generated using the PRNG. Next, pixel’s bits are permuted using an internal condition. After that, the pixels are substituted using two different
In the medical sector, the digital image is multimedia data that contain secret information. However, designing an effective cryptosystem to protect medical image content is a challenge. Using public or shared digital networks, images are vulnerable to potentially more destructive attacks such as replay or human-based attacks, brute-force, and statistical attack. The need for effective cryptographic solutions for medical image requires the development of an improved algorithm and implementation. To protect the image against new generations of attacks, encryption solutions should guarantee the confidentiality of the image. Confidentiality is achieved by encryption to make data unintelligible and unusable even if the data is lost or hacked. Among encryption schemes, symmetric encryption is the best cryptographic solution that permits the confidentiality of large volume data. In this innovative idea, chaos is an effective axis of modern cryptography challenging existing traditional symmetric encryption systems like the Advanced Encryption System (AES) [
After this innovative idea was investigated, many researchers turned to design chaos-based symmetric cryptosystem algorithms for ordinary and medical image encryption. This is using different types of chaotic models such as the Lorenz and Chen system, skew tent map, and logistic map [
The challenge is that traditionally, key generation, encryption, authentication, and integrity have been complex and computationally costly to execute while keeping in mind the issue related to the security level. All mentioned image cryptosystems have many weaknesses. It is sequential, too long in design and calculation, which greatly increases the execution time. In this work, we propose an improved chaos-based symmetric cryptosystem for fast image encryption and decryption. The goal is to achieve high-level security and high performance with low computational complexity and reasonable resources. Our contribution is as follows: Design of improved chaos-based PRNG with the goal to enlarge the key space, increase the entropy, randomness, and complexity, and avoid the key’s sequence relationship and determinism. This permits the generating of high-quality key streams with high randomness behaviour, unpredictability, and complexity. Design of fast and secure encryption and decryption architecture based on permutation, substitution, and diffusion properties. This permits enhancing the randomness and decreasing the correlation. The goal is to achieve a high-level performance with low computational cost and with reasonable resources. Undertake in-depth experimental measurements for medical images with different type, content, and size to evaluate the strength of the proposed cryptosystem against the new generation of attacks. Undertake an evaluation study of the performance of the execution and compare the result with other recent works.
This paper is planned in four parts as follows: in Section
The symmetric cryptographic scheme is the best solution to encrypt and decrypt large volume data. The proposed cryptosystem algorithm is a symmetric scheme based on confusion and diffusion properties. To generate a high-quality key, a complex chaos-based PRNG is suggested. The general view of the proposed cryptosystem is depicted in Figure
General view of the proposed cryptosystem.
PRNGs are used to generate key useful for encryption. The proposed PRNG is a chaos-based key generator. A complex PRNG architecture is designed with the goal to increase the key complexity, entropy, randomness, sensitivity, and key space and to avoid determinism, correlation, and key dependence.
The proposed PRNG is illustrated in Figure
General view of the proposed PRNG.
After random values generation by the chaotic design, the convertor block is used that permits modulating the generated values into 32-bit numbers (equation (
The used chaotic systems are the Henon map, 2D logistic map in a complex set, and the Baker map. Their mathematical models are described in equations (
The Henon map has a state of two variables (
The 2D logistic map in a complex set has a state of two variables (
The Baker map has a state of two variables (
A symmetric scheme is adopted for image encryption. The cryptosystem uses the Secure Hash Algorithm (SHA-256) to generate a unique 256-bit hash value fully related to the secret image I as follows:
The image’s hash value is considered as the initial secret key of the cryptosystem that is named Step 1: read a medical image I with any size Step 2: bits permutation of pixels. The image’s pixels are permuted by cycling right shift or cycling left shift according to the pixel’s position parity. Figure If the position of the pixel is pair, then the pixel’s bits are permuted by cycling right shift of 2 bits:
General architecture of the image encryption algorithm.
Process of pixel bits permutation.
Step 3: random permutation of the pixel’s position. Here, a permutation matrix (PM) of size If the position of the pixel is impair, then the pixel’s bits are permuted by cycling left shift of 2 bits:
Step 4: image’s pixels substitution using two different
Generation of the PM matrix.
Process of random permutation of pixels.
Process of generation of
Afterward, an internal condition is used for block’s pixel permutation that permits utilizing the If the position of the permuted pixel is pair, then the pixel is substituted by the state of the If the position of the permuted pixel is impair, then the pixel is substituted by the state of the
The
Each pixel of the image block is substituted by the state of the table which corresponds to the intersection of
Step 5: pixels XOR diffusion with a key stream. Thus, The PRNG is iterated again for
Step 6: repeat all last steps
After the encryption step, the encrypted image can be stored or transmitted to a well-defined destination using an insecure network (diffusion step). At the reception, the image must be processed by the decryption system to find the plain image. The decryption system is an inverse algorithm of the encryption algorithm. In the substitution step, inverse
Inverse
In this section, a thorough assessment of the proposed cryptosystem is detailed. Several indicators are used, which are the most used in the image cryptography community. Using the proposed cryptosystem, we can perform
Standard Lena, peppers, and baboon images used for the test. (a) Colour Lena.jpg (512 × 512 × 3). (b) Peppers.jpg (512 × 512 × 3). (c) Colour baboon.jpg (512 × 512 × 3).
Eight different medical images selected for the test: (a) 3D medical scanner ankle (1080 × 1920 x 3); (b) 3D X-ray chest image (3816 × 2832 × 3); (c) 3D ultrasound baby (625 × 410 × 3); (d) 1D ultrasound (1200 × 700 × 1); (e) 3D CT-scan chest image (800 × 600 × 3); (f) 1D MRI (456 × 456 × 1); (g) 1D endoscopy (634 × 549 × 1); (h) 3D radiography foot (2400 × 2956 × 3).
Here, we make objective measurements of the encrypted image quality where the original image is the reference. Peak signal-to-noise ratio (PSNR) and structural similarity index measure (SSIM) are used for that [
PSNR and SSIM values of the encrypted image.
Image | PSNR | SSIM |
---|---|---|
Lena | 7.6051 | 0.0059 |
Peppers | 6.1244 | 0.0080 |
Baboon | 7.0725 | 0.0061 |
3D ultrasound | 7.5974 | 0.0064 |
1D ultrasound | 7.1465 | 0.0072 |
3D scanner | 6.1943 | 0.0040 |
3D radiography foot | 6.4712 | 0.0063 |
3D X-ray | 6.9839 | 0.0065 |
3D CT-scan | 7.4483 | 0.0072 |
1D RMI | 6.7421 | 0.0054 |
1D endoscopy | 7.3805 | 0.0075 |
From Table
The statistical analysis of the plain and encrypted image includes the analysis of histogram, entropy, two-dimensional normalized correlation (NC), and the correlation coefficient (
The image histogram is a two-dimensional statistical curve showing the distribution of gray scales according to their values. Figure
Histogram of the original images and their corresponding encrypted images.
As seen in Figure 10.4, Figure 10.8, Figure 10.12, Figure 10.16, Figure 10.20, Figure 10.24, Figure 10.28, Figure 10.32, Figure 10.36, Figure 10.40, and Figure 10.44, we note that the histogram of the resultant encrypted image is uniformly distributed and dissimilar compared to the histogram of the original image in Figure 10.2, Figure 10.6, Figure 10.10, Figure 10.14, Figure 10.18, Figure 10.22, Figure 10.26, Figure 10.30, Figure 10.34, Figure 10.38, and Figure 10.42 which contains large spikes. Therefore, the original image’s pixels and the encrypted image’s pixels are completely different.
The 2D NC is a measure of the degree of reliability between two images. After encrypting the original images, the NC is computed between the original image and its corresponding encrypted image. From Table
NC results of encrypted images.
Image | NC | ||
---|---|---|---|
Red | Blue | Green | |
Lena | −0.0041 | −0.0024 | −0.00065 |
Peppers | −0.0025 | −0.00018 | −0.00079 |
Baboon | −0.0027 | −0.0028 | −0.00063 |
3D ultrasound | 0.00003 | −0.00021 | −0.00029 |
3D ankle | −0.00009 | 0.00003 | −0.00024 |
3D | −0.00041 | −0.00042 | −0.0015 |
3D radiography | −0.0039 | −0.00367 | −0.0043 |
3D CT-scan | −0.0028 | −0.00056 | −0.00073 |
1D ultrasound | −0.0047 | ||
MRI | −0.0036 | ||
Endoscopy | −0.00042 |
Shannon entropy is a measure of the degree of randomness associated with an image. It is defined as follows:
The global Shannon entropy is measured by applying equation (
Global and local Shannon entropy values of encrypted images.
Image | Local Shannon entropy | Global Shannon entropy | ||||
---|---|---|---|---|---|---|
Red | Blue | Green | Red | Blue | Green | |
Lena | 7.9548 | 7.9546 | 7.9542 | 7.9998 | 7.9998 | 7.9997 |
Peppers | 7.9546 | 7.9549 | 7.9544 | 7.9998 | 7.9997 | 7.9997 |
Baboon | 7.9554 | 7.9557 | 7.9553 | 7.9998 | 7.9998 | 7.9998 |
3D ultrasound | 7.9557 | 7.9552 | 7.9548 | 8.0000 | 8.0000 | 8.0000 |
3D ankle | 7.9563 | 7.9559 | 7.9559 | 8.0000 | 8.0000 | 8.0000 |
3D X-ray | 7.9568 | 7.9563 | 7.9564 | 8.0000 | 8.0000 | 8.0000 |
3D radiography | 7.9562 | 7.9563 | 7.9560 | 8.0000 | 8.0000 | 8.0000 |
3D CT-scan | 7.9567 | 7.9567 | 7.9565 | 8.0000 | 8.0000 | 8.0000 |
1D ultrasound | 7.9556 | 8.0000 | ||||
MRI | 7.9553 | 7.99998 | ||||
Endoscopy | 7.9549 | 7.99998 |
Analysing the results, the encrypted image’s global entropy value is highly close to the ideal value 8 and the mean of local entropy is very important. This indicates that the pixels of the encrypted image are random. As a consequence, the proposed system is safe against entropy and statistical attacks. Table
Comparative study of entropy values.
Image | Ordinary image | Medical image | ||
---|---|---|---|---|
Entropy | Global | Local | Global | Local |
Reference [ | — | — | 7.99950 | 7.90300 |
Reference [ | — | — | 7.99930 | — |
Reference [ | — | — | 7.99954 | — |
Reference [ | 7.99930 | — | — | — |
Reference [ | 7.98910 | — | — | — |
Reference [ | 7.99932 | — | — | — |
Reference [ | 7.98830 | — | — | — |
Reference [ | 7.99930 | — | — | — |
Reference [ | 7.99720 | — | — | — |
Reference [ | — | — | 7.99740 | — |
Proposed algorithm | 7.99985 | 7.95486 | 7.99998 | 7.95627 |
The
Table
Image | Direction | Original image | Encrypted image | ||||
---|---|---|---|---|---|---|---|
Red | Blue | Green | Red | Blue | Green | ||
Lena | H | 0.9588 | 0.9358 | 0.9160 | −0.0196 | −0.0145 | −0.0546 |
V | 0.9818 | 0.9665 | 0.9522 | −0.0162 | −0.0184 | −0.0082 | |
D | 0.9900 | 0.9810 | 0.9737 | −0.0078 | −0.0012 | −0.0049 | |
Peppers | H | 0.9617 | 0.9658 | 0.9443 | −0.0136 | −0.0070 | −0.0014 |
V | 0.9814 | 0.9789 | 0.9671 | −0.0288 | −0.0054 | 0.0046 | |
D | 0.9666 | 0.9655 | 0.9455 | −0.0310 | −0.0294 | 0.0084 | |
Baboon | H | 0.8656 | 0.9291 | 0.8399 | 0.0053 | 0.0063 | −0.0040 |
V | 0.7897 | 0.8848 | 0.7629 | 0.0020 | 0.0076 | 0.0098 | |
D | 0.8855 | 0.9309 | 0.8619 | 0.0077 | 0.0049 | −0.0075 | |
3D ultrasound baby | H | 0.8989 | 0.9008 | 0.8360 | −0.0022 | −0.0024 | −0.0020 |
V | 0.9720 | 0.9723 | 0.9559 | −0.0056 | −0.0090 | −0.0013 | |
D | 0.9789 | 0.9815 | 0.9662 | −0.0019 | −0.0082 | −0.0002 | |
3D scanner ankle | H | 0.9981 | 0.9983 | 0.9963 | −0.0073 | −0.0187 | −0.0100 |
V | 0.9975 | 0.9984 | 0.9956 | −0.0319 | −0.0259 | −0.0061 | |
D | 0.9993 | 0.9992 | 0.9984 | −0.0024 | −0.0051 | −0.0179 | |
3D radiography | H | 0.9993 | 0.9994 | 0.9994 | −0.0022 | −0.0018 | −0.0007 |
V | 0.9989 | 0.9916 | 0.9945 | −0.0029 | −0.0036 | −0.0032 | |
D | 0.9946 | 0.9944 | 0.9901 | −0.0015 | −0.0019 | −0.0002 | |
3D X-ray | H | 0.9981 | 0.9971 | 0.9955 | −0.0241 | −0.0051 | −0.0164 |
V | 0.9995 | 0.9990 | 0.9986 | −0.0071 | −0.0034 | −0.0180 | |
D | 0.9995 | 0.9990 | 0.9987 | −0.0043 | −0.0108 | −0.0336 | |
3D CT-scan | H | 0.9946 | 0.9944 | 0.9901 | −0.0018 | −0.0066 | −0.0011 |
V | 0.9946 | 0.9944 | 0.9891 | −0.0012 | −0.0033 | −0.0039 | |
D | 0.9944 | 0.9941 | 0.9897 | −0.0046 | −0.0018 | −0.0026 | |
1D ultrasound | H | 0.9865 | −0.00012 | ||||
V | 0.9843 | −0.00084 | |||||
D | 0.9839 | −0.00069 | |||||
MRI | H | 0.9144 | −0.0022 | ||||
V | 0.9346 | −0.0041 | |||||
D | 0.99422 | −0.0019 | |||||
Endoscopy | H | 0.9882 | −0.0260 | ||||
V | 0.9869 | −0.0022 | |||||
D | 0.9847 | −0.0047 |
Distribution of 3000 pairs of randomly selected adjacent pixels of the original Lena image in the horizontal, vertical, and diagonal directions.
Distribution of 3000 pairs of randomly selected adjacent pixels of the encrypted Lena image in the horizontal, vertical, and diagonal directions.
Distribution of 3000 pairs of randomly selected adjacent pixels of the medical encrypted ankle image in the horizontal, vertical, and diagonal directions.
Distribution of 3000 pairs of randomly selected adjacent pixels of the medical original ankle image in the horizontal, vertical, and diagonal directions.
Using digital networks for transmission, image is vulnerable to several types of noise and loss. However, having any noise or loss in the encrypted image can result in difficulty to recover the clear image using the decryption algorithm. Noise and loss refer to random errors in pixels values of the image acquired during image transmission. A good cryptosystem algorithm should recover the plain image when the encrypted image was affected by any treatment. In this part, we evaluate the robustness of the proposed cryptosystem against Gaussian white noise and “salt and pepper” data loss. Firstly, we produce an encrypted image using the encryption system. Then, we attack it with an attack which results in a modified encrypted image. Afterward, we try decrypting the modified encrypted image by the decryption system. Finally, we evaluate the decrypted image using the NC, PSNR, and SSIM tools where the original image is the reference [
Salt and pepper noise is added to an image by the addition of both random on and off pixels, i.e., random bright with a pixel value of 255 and random dark with 0 pixel value, all over the image. Table
PSNR, SSIM, and NC results between the original and the corresponding decrypted image under different intensities of salt and pepper noise.
Image | Data loss | Salt and pepper | ||||||
---|---|---|---|---|---|---|---|---|
Intensity | 0.009 | 0.01 | 0.05 | 0.09 | 0.1 | 0.5 | ||
Lena | PSNR | 39.51 | 37.96 | 35.68 | 32.66 | 29.89 | 28.67 | 26.61 |
SSIM | 0.982 | 0.969 | 0.967 | 0.856 | 0.765 | 0.748 | 0.479 | |
NC | 0.988 | 0.980 | 0.979 | 0.899 | 0.828 | 0.814 | 0.557 | |
Peppers | PSNR | 39.08 | 37.58 | 35.02 | 31.11 | 29.54 | 28.05 | 26.09 |
SSIM | 0.983 | 0.969 | 0.967 | 0.857 | 0.771 | 0.751 | 0.489 | |
NC | 0.990 | 0.982 | 0.980 | 0.906 | 0.840 | 0.826 | 0.564 | |
Baboon | PSNR | 39.81 | 38.20 | 36.93 | 32.81 | 30.27 | 28.83 | 26.82 |
SSIM | 0.977 | 0.959 | 0.957 | 0.821 | 0.722 | 0.701 | 0.458 | |
NC | 0.992 | 0.987 | 0.986 | 0.931 | 0.878 | 0.867 | 0.521 | |
3D ultrasound baby | PSNR | 40.92 | 38.40 | 37.98 | 35.90 | 31.34 | 29.89 | 26.92 |
SSIM | 0.936 | 0.902 | 0.894 | 0.713 | 0.623 | 0.604 | 0.420 | |
NC | 0.994 | 0.991 | 0.990 | 0.949 | 0.907 | 0.897 | 0.496 | |
3D scanner ankle | PSNR | 40.26 | 37.69 | 36.21 | 35.17 | 31.65 | 29.21 | 25.20 |
SSIM | 0.986 | 0.937 | 0.917 | 0.856 | 0.782 | 0.571 | 0.437 | |
NC | 0.994 | 0.990 | 0.989 | 0.945 | 0.904 | 0.894 | 0.501 | |
3D radiography | PSNR | 41.21 | 38.85 | 37.32 | 35.79 | 32.63 | 29.85 | 25.81 |
SSIM | 0.981 | 0.916 | 0.896 | 0.805 | 0.663 | 0.549 | 0.425 | |
NC | 0.994 | 0.990 | 0.989 | 0.946 | 0.905 | 0.893 | 0.487 | |
3D X-ray | PSNR | 40.26 | 38.47 | 36.96 | 34.98 | 31.75 | 28.72 | 25.34 |
SSIM | 0.985 | 0.979 | 0.968 | 0.871 | 0.782 | 0.766 | 0.421 | |
NC | 0.976 | 0.963 | 0.945 | 0.883 | 0.769 | 0.747 | 0.453 | |
3D CT-scan | PSNR | 40.64 | 38.35 | 36.45 | 34.66 | 30.74 | 27.76 | 25.17 |
SSIM | 0.979 | 0.973 | 0.841 | 0.795 | 0.632 | 0.473 | 0.437 | |
NC | 0.979 | 0.968 | 0.946 | 0.891 | 0.787 | 0.761 | 0.507 | |
1D ultrasound | PSNR | 39.54 | 37.26 | 36.08 | 32.17 | 28.95 | 27.21 | 25.14 |
SSIM | 0.987 | 0.942 | 0.909 | 0.867 | 0.831 | 0.782 | 0.587 | |
NC | 0.993 | 0.989 | 0.953 | 0.851 | 0.704 | 0.694 | 0.501 | |
MRI | PSNR | 39.75 | 37.81 | 35.52 | 31.62 | 29.98 | 27.83 | 24.92 |
SSIM | 0.991 | 0.975 | 0.860 | 0.713 | 0.689 | 0.626 | 0.516 | |
NC | 0.995 | 0.983 | 0.974 | 0.898 | 0.826 | 0.711 | 0.501 | |
Endoscopy | PSNR | 39.67 | 38.14 | 37.32 | 35.23 | 31.07 | 29.17 | 25.72 |
SSIM | 0.984 | 0.924 | 0.887 | 0.812 | 0.674 | 0.589 | 0.477 | |
NC | 0.995 | 0.987 | 0.982 | 0.943 | 0.910 | 0.879 | 0.513 |
Result decrypted chest X-ray image under different intensities of salt and pepper data loss.
Table
PSNR, SSIM, and NC results between the original and the corresponding decrypted image under different variance of Gaussian white noise.
Image | Noise | Gaussian white | ||||||
---|---|---|---|---|---|---|---|---|
Variance | 0.005 | 0.009 | 0.01 | 0.05 | 0.09 | 0.1 | 0.5 | |
Lena | PSNR | 38.90 | 37.81 | 35.61 | 33.19 | 29.11 | 28.23 | 23.61 |
SSIM | 0.906 | 0.837 | 0.824 | 0.725 | 0.658 | 0.548 | 0.409 | |
NC | 0.947 | 0.893 | 0.781 | 0.719 | 0.695 | 0.663 | 0.465 | |
Peppers | PSNR | 38.75 | 12.72 | 12.54 | 10.21 | 9.56 | 9.45 | 8.17 |
SSIM | 0.932 | 0.882 | 0.832 | 0.754 | 0.622 | 0.541 | 0.415 | |
NC | 0.954 | 0.889 | 0.847 | 0.783 | 0.637 | 0.515 | 0.457 | |
Baboon | PSNR | 39.19 | 38.15 | 36.07 | 33.83 | 29.75 | 28.54 | 23.77 |
SSIM | 0.922 | 0.876 | 0.763 | 0.604 | 0.571 | 0.530 | 0.405 | |
NC | 0.983 | 0.891 | 0.800 | 0.751 | 0.540 | 0.508 | 0.443 | |
3D ultrasound baby | PSNR | 39.43 | 38.53 | 36.10 | 33.71 | 29.02 | 28.90 | 23.82 |
SSIM | 0.971 | 0.877 | 0.849 | 0.732 | 0.650 | 0.635 | 0.412 | |
NC | 0.982 | 0.925 | 0.872 | 0.747 | 0.636 | 0.622 | 0.397 | |
3D scanner ankle | PSNR | 39.72 | 38.13 | 37.81 | 32.76 | 29.15 | 27.42 | 23.85 |
SSIM | 0.981 | 0.893 | 0.867 | 0.759 | 0.673 | 0.648 | 0.415 | |
NC | 0.996 | 0.953 | 0.891 | 0.756 | 0.647 | 0.631 | 0.421 | |
3D chest radiography | PSNR | 39.86 | 38.57 | 36.22 | 33.72 | 29.33 | 28.94 | 24.03 |
SSIM | 0.981 | 0.895 | 0.862 | 0.743 | 0.659 | 0.643 | 0.425 | |
NC | 0.993 | 0.936 | 0.895 | 0.786 | 0.671 | 0.655 | 0.443 | |
3D X-ray | PSNR | 39.59 | 38.42 | 36.86 | 33.61 | 29.22 | 28.47 | 23.69 |
SSIM | 0.982 | 0.879 | 0.850 | 0.737 | 0.656 | 0.641 | 0.419 | |
NC | 0.989 | 0.981 | 0.864 | 0.791 | 0.677 | 0.669 | 0.453 | |
3D CT-scan | PSNR | 38.78 | 38.05 | 35.91 | 33.11 | 29.23 | 28.15 | 23.39 |
SSIM | 0.975 | 0.853 | 0.824 | 0.718 | 0.629 | 0.631 | 0.402 | |
NC | 0.982 | 0.968 | 0.837 | 0.745 | 0.653 | 0.646 | 0.420 | |
1D ultrasound | PSNR | 39.14 | 38.42 | 35.98 | 33.47 | 28.87 | 27.97 | 23.52 |
SSIM | 0.972 | 0.846 | 0.815 | 0.698 | 0.609 | 0.522 | 0.389 | |
NC | 0.980 | 0.959 | 0.828 | 0.719 | 0.627 | 0.569 | 0.390 | |
MRI | PSNR | 38.72 | 37.85 | 35.21 | 32.71 | 28.18 | 27.46 | 23.31 |
SSIM | 0.973 | 0.851 | 0.809 | 0.692 | 0.589 | 0.519 | 0.382 | |
NC | 0.986 | 0.965 | 0.829 | 0.714 | 0.631 | 0.573 | 0.387 | |
Endoscopy | PSNR | 38.68 | 37.87 | 35.25 | 32.68 | 28.12 | 27.37 | 23.22 |
SSIM | 0.975 | 0.846 | 0.811 | 0.697 | 0.585 | 0.5116 | 0.379 | |
NC | 0.984 | 0.960 | 0.826 | 0.705 | 0.629 | 0.569 | 0.386 |
Result decrypted chest X-ray image under different variances of Gaussian white noise.
Following the obtained results, the proposed algorithm proves its performance to a certain extent. This is due to the main feature that our algorithm does not allow any propagation error.
In the proposed algorithm, the diffusion process is performed by the XOR operation. Thus, it is very essential to evaluate its robustness against the chosen-plaintext attack. This type of attack uses the encrypted image with arbitrary plaintext data to crack the cryptosystem algorithm. According to reference [
Chosen-plaintext analysis. (a)
In general, an attacker uses whole black or whole white images to find out the possible patterns in the cryptosystem algorithm. However, the whole white and whole black images of 512 × 512 × 3 size are encrypted by the proposed algorithm. Figure
(a) Clear white image. (b) Clear black image. (c) Encrypted white image. (d) Encrypted black image.
Entropy value of encrypted black and white images.
Tool | Entropy | Correlation coefficient | |||
---|---|---|---|---|---|
Global | Local | H | V | D | |
Plain black image | 0 | 0 | — | — | — |
Encrypted black image | 7.9998 | 7.9574 | −0.0023 | −0.0042 | −0.00354 |
Plain white image | 0 | 0 | — | — | — |
Encrypted white image | 7.9998 | 7.9574 | −0.0035 | −0.0029 | −0.00173 |
The analysis of the key includes the key space, key sensitivity, and randomness analysis test to evaluate the strength of the cryptosystem against brute-force and differential hackers.
The key space of a safety encryption scheme should be very large to resist the brute-force attack. The designed PRNG has six outputs each with 32-bit length. Thus, there is a 23×64 = 2192 possible key. Following reference [
Comparative study of key space.
Work | Key space |
---|---|
Reference [ | 2150 |
Reference [ | 1042 |
Reference [ | 3.4 × 1038 |
Proposed algorithm | 2192 |
The PRNG should be sensitive to a small change in the initial key
Therefore, we encrypt the same Lena image using the
Key sensitivity test applied at the encryption phase.
Simulation results of the NPCR and UACI test.
Image | NPCR (%) | UACI (%) | ||||
---|---|---|---|---|---|---|
Red | Blue | Green | Red | Blue | Green | |
Lena | 99.68109 | 99.69172 | 99.68452 | 33.83002 | 34.03204 | 33.69463 |
Peppers | 99.75642 | 99.70531 | 99.69347 | 33.68726 | 33.59820 | 33.65629 |
Baboon | 99.74926 | 99.69642 | 99.70562 | 34.03204 | 33.64322 | 33.58726 |
3D ultrasound | 99.87215 | 99.81436 | 99.75443 | 33.65629 | 33.70929 | 33.66517 |
3D scanner | 99.89427 | 99.83960 | 99.89441 | 34.07125 | 34.08311 | 34.19787 |
3D radiography | 99.89853 | 99.88799 | 99.89711 | 34.09614 | 34.09556 | 34.08134 |
3D X-ray | 99.87732 | 99.89493 | 99.89467 | 34.09847 | 34.09597 | 34.09613 |
3D CT-scan | 99.79369 | 99.65950 | 99.76318 | 33.80594 | 33.89826 | 33.89117 |
1D ultrasound | 99.84620 | 33.82922 | ||||
1D brain | 99.75471 | 33.79463 | ||||
1D endoscopy | 99.79556 | 33.89125 |
Like the aforementioned results, NPCR and UACI percentages are important. In addition, the NC coefficient is very weak; i.e., the images are dissimilar. We conclude that the proposed cryptosystem is highly sensitive to a one-bit change in the given initial key.
Key sensitivity test applied at the decryption phase.
The NC value between the original and the image in Figure
The analysis of the randomness of a key stream can be achieved using the NIST 800-22 test. The test is useful to test random and pseudorandom number generators to determine whether or not a PRNG is appropriate for data encryption [
The test results of a sequence of 262400 bytes generated by the proposed PRNG-CTR are shown in Table
Simulation results of the NIST 800-22 test for the proposed PRNG.
Statistical | Status | |
---|---|---|
Status frequency | 0.4372742 | Pass |
Block frequency ( | 0.4372742 | Pass |
Forward CUSUM | 0.4372742 | Pass |
Reverse CUSUM | 0.4372742 | Pass |
Runs | 0.4372742 | Pass |
Long runs of ones | 0.4372742 | Pass |
Binary matrix rank | 0.4372742 | Pass |
Spectral DFT | 0. 8755390 | Pass |
Nonoverlapping template ( | 0.7070707 | Pass |
Overlapping template ( | 0.5449921 | Pass |
Universal | 0.0713232 | Pass |
Approximate entropy ( | 0.0125474 | Pass |
Random excursions ( | 0.9030558 | Pass |
Random excursions variant ( | 0.3974291 | Pass |
Linear complexity ( | 0.1922722 | Pass |
In real-time image processing, the execution time is a major constraint. In a software implementation, the speed of execution mainly depends on CPU performance. The proposed algorithm is implemented using the Matlab R2017a software running on a personal computer with CPU Intel Core i7-3770 3.4 GHz frequency. We can use the approximate equations (
The proposed cryptosystem executes four processes in each encryption round: pixel’s bit permutation, random permutation of pixel's position,
Performance of the proposed encryption algorithm.
Process | Key generation | Random permutation | XOR diffusion | |
---|---|---|---|---|
Time (s) | 0.0192 | 0.2426 | 0.1880 | 0.0378 |
Total time (s) | 0.4876 | |||
Speed (Mb/s) | 12.9 |
Comparative study of encryption algorithm speed.
Work | Permutation | Substitution | Diffusion | |
---|---|---|---|---|
Reference [ | √ | — | √ | 0.2 |
Reference [ | — | √ | √ | 9.6 |
Reference [ | — | — | √ | 3.4 |
Reference [ | — | — | √ | 13.52 |
Reference [ | √ | — | √ | 2.4 |
Proposed algorithm | √ | √ | √ | 12.9 |
In the proposed algorithm, the permutation, substitution, and diffusion are not complex that can be done with reasonable resources and low computational cost. In addition, they are independent that can be performed in parallel execution. This reduces significantly the execution time. The proposed scheme provides high-level security with high performance and reasonable resources.
In this work, we have proposed an improved chaos-based symmetric cryptosystem for medical image encryption and decryption. The SHA-256 is used to generate a 256-bit key of the cryptosystem. A complex chaos-based PRNG is designed to generate a high-quality encryption key. The generated key presents high randomness behaviour, high entropy, and high complexity. Improved architecture based on confusion and diffusion property is proposed for image encryption. The image undergoes a processing cycle of four operations in order to produce the encrypted image: random permutation of the position of pixels, position permutation of pixel’s bits,
The data used to support the findings of this study are included within the article.
The authors declare that they have no conflicts of interest.