Multiple medical image encryption algorithm based on permutation and diffusion synchronous update

Abstract

The application provides a multi-medical image encryption algorithm based on synchronous update of permutation and diffusion, and the improved tent-logical cross hybrid coupled mapping lattice has better chaotic characteristics than the original cross coupled mapping lattice; in the image encryption algorithm, a bijective function is used to construct M-box and N-box to perform permutation on a single medical image, then the single medical image is horizontally spliced into a large image, the image is divided into eight bit planes, the synchronous update algorithm of permutation and diffusion is performed on the eight bit planes respectively, and finally, the encrypted medical image is obtained; the application has the characteristics of high security and high efficiency.

Description

Technical Field

[0001] This invention relates to the field of information processing and data encryption technology, specifically to a multi-image encryption algorithm based on scrambling and diffusion synchronous updates. Background Technology

[0002] With the continuous advancement of information science and technology, the transmission and storage of data are no longer secure. As a carrier of massive amounts of data, images should be given more attention in terms of security protection. In the medical system, medical images play a vital role, enabling doctors not only to accurately assess patients' conditions, but also to discuss treatment plans more intuitively.

[0003] However, these medical images contain highly sensitive information, and unauthorized access or use may violate patient privacy and potentially lead to serious medical accidents; therefore, addressing the security issues of medical images is an urgent need.

[0004] In view of the above, this application provides a multi-image encryption algorithm based on scrambling and diffusion synchronous updates to solve the above problems. Summary of the Invention

[0005] To address the above issues and overcome the shortcomings of existing technologies, this invention provides a multi-image medical image encryption algorithm based on simultaneous scrambling and diffusion updates. This invention constructs a novel tent-logic cross-coupled mapping lattice chaotic system. This chaotic system has a larger range and superior dynamic characteristics compared to the original cross-coupled mapping lattice. To ensure the security of the encryption algorithm, a bijective function is first used to scramble individual medical images. Then, the scrambled medical images are horizontally stitched together into a large image. Finally, a bit-level simultaneous scrambling and diffusion algorithm is applied to the large image. Therefore, when the pixel value of a single plaintext medical image changes, it will affect the changes in all medical images, effectively countering various attacks.

[0006] The encryption algorithm for multiple medical images based on scrambling and diffusion synchronous updates is characterized by first constructing an improved tent-logic cross-coupled mapping lattice chaotic system according to the cross-coupled mapping lattice; then using a bijective function to scramble the modified single medical image, and horizontally stitching the scrambled images into a large image.

[0007] The key and initial value of the chaotic system are obtained using the Hash-512 algorithm, and the chaotic sequence is obtained by iteratively improving the tent-logic cross-hybrid coupled mapping lattice chaotic system.

[0008] A bit-level scrambling and diffusion synchronous update algorithm is applied to the scrambled image to finally obtain the encrypted image.

[0009] The beneficial effects of the above technical solution are as follows:

[0010] (1) Based on the original chaotic system, this invention modifies some parameters to make it a more complex chaotic system, giving it more complex dynamic characteristics, better ergodicity and randomness, and making it more suitable for application in encryption algorithms.

[0011] (2) This invention also proposes a bit-level scrambling and diffusion synchronous update algorithm, which can effectively encrypt medical images. Using this algorithm, medical images can be stored and transmitted efficiently and securely.

[0012] (3) Considering that doctors often need multiple images for diagnosis, this invention proposes an algorithm that can encrypt multiple medical images at the same time, which greatly improves the efficiency of doctors' diagnosis. Attached Figure Description

[0013] Figure 1 This is a flowchart illustrating the encryption process of the present invention.

[0014] Figure 2 This is a schematic diagram of the bit-level simultaneous scrambling and diffusion algorithm of the present invention;

[0015] Figure 3 This is a schematic diagram of four medical images horizontally stitched together to form a larger image according to the present invention;

[0016] Figure 4 This is a schematic diagram of the encrypted image of the large image of the present invention;

[0017] Figure 5 This is a schematic diagram of histogram analysis of large images in this invention;

[0018] Figure 6 This is a schematic diagram of histogram analysis of the encrypted image of the present invention; Detailed Implementation

[0019] The foregoing and other technical contents, features and effects of the present invention will be clearly presented in the following detailed description of the embodiments with reference to the accompanying drawings. The structural contents mentioned in the following embodiments are all based on the accompanying drawings.

[0020] Chaos theory is not only one of the most commonly used methods in the field of image encryption, but also one of the most effective. Chaos theory has the characteristics of pseudo-randomness, unpredictability, and high sensitivity to initial conditions and parameters, making it particularly suitable for image encryption. In recent years, with the emergence of cross-coupled mapping lattice chaotic systems, more and more people have proposed innovations in this area. This invention modifies some parameters of the original chaotic system to make it a more complex chaotic system, giving it more complex dynamic characteristics, better ergodicity and randomness, and making it more suitable for application in encryption algorithms.

[0021] By utilizing the characteristic of bijective functions to calculate coordinate positions as values, we can generate replacement boxes to achieve image scrambling. However, this linear scrambling is vulnerable to brute-force attacks. Therefore, this invention also proposes a bit-level scrambling and diffusion synchronous update algorithm, which can effectively encrypt medical images. This algorithm can be used to efficiently and securely store and transmit medical images. Considering that doctors often need multiple images for diagnosis, this invention proposes an algorithm that can encrypt multiple medical images simultaneously, greatly improving the efficiency of doctors' diagnoses.

[0022] The specific steps are as follows:

[0023] I. Constructing a tent-logic cross-coupled mapping lattice

[0024] Based on the cross-coupled mapping lattice chaotic system shown in Equation (1), the tent-logic cross-hybrid coupled mapping lattice chaotic system is constructed as shown in Equation (2).

[0025]

[0026]

[0027] Formula (1) is a commonly used cross-coupled mapping lattice chaotic system, but its randomness and ergodicity are not good enough; Formula (2) is an improved tent-logic cross-coupled mapping lattice, which changes the parameter e in Formula 1 to the more random tent-logic mapping and adds some new parameters, making the chaotic characteristics of Formula 2 better;

[0028]

[0029] The first formula is the tent-logic chaotic system, which will be used to replace the parameter e in formula (1) to make the parameter randomness of formula (2) better; the second formula is the generation method of parameters p and q on the top, and their values ​​are fixed in the range of 1 to L, where L is the number of grids, and the formula below is the generation method of matrix A, where a, b, c, and d are random Fibonacci numbers. These two formulas can make p and q more random.

[0030] Here, n represents time, k represents the number of cells, k∈[1,L], and L is the number of cells. The cells with indices k+1 and k-1 are the adjacent cells of the k-th cell, and their boundary conditions are defined as follows:

[0031]

[0032] This is a logical mapping.

[0033] II. Key Generation

[0034] Step 1: Horizontally stitch the original medical images into a large image P.

[0035] Step 2: Use the hash-512 algorithm on image P to obtain the hexadecimal number h.

[0036] Step 3: Convert h into a binary sequence h1.

[0037] Step 4: Use the function K(i) = bin2dec(h1(i:i+8)) / (2^16) to obtain K(i).

[0038] Step 5: Use formula (3) to obtain the key (i), where i ranges from 1 to L+3, and L is the number of cells.

[0039] key(i)=mod(K(i)+K(2*i)+K(3*i)+K(4*i),1) (3)

[0040] Step 6: Use formula (4) to pair the subkey Assign values ​​to μ, r, and θ0.

[0041]

[0042] III. Image Encryption

[0043] Preprocessing stage: Standardizing the size of medical images

[0044] Suppose a certain medical image W has a size of M×N. Since the size of each medical image may be different, we will select the largest medical image as the standard and fill the remaining medical images with this size M′×N′.

[0045] Phase 1: Scrambling of single medical images

[0046] Step 1: Create a 3D matrix G with dimensions M′×N′×T to perform a scrambling operation on the plaintext image, where T is the number of scrambling rounds.

[0047] Step 2: In order to perform multi-round scrambling, we initialize matrix G with initial values, where W can be understood as a two-dimensional matrix and G can be understood as a three-dimensional matrix composed of multiple two-dimensional matrices. We fill the first layer of G with the values ​​of W.

[0048] G(:,:,1)=W (5)

[0049] W can be understood as a two-dimensional matrix, and G can be understood as a three-dimensional matrix, which is composed of multiple two-dimensional matrices. The values ​​of W are filled into the first layer of G.

[0050] Step 3: We need to use a bijective function to create two boxes, M-box and N-box, with sizes M′ and N′ respectively. The formula for the bijective function is:

[0051]

[0052] m and n represent the x-coordinate and y-coordinate of the coordinate system, respectively.

[0053] The specific creation process of M-box and N-box is shown in Algorithm 1:

[0054] Algorithm 1: M-box and N-box generation algorithm

[0055]

[0056] Step 4: Perform multiple rounds of scrambling using M-box and N-box. M-box is used to scramble rows, and N-box is used to scramble columns.

[0057] G(i′,j′,t+1)=G(M-box(i′,t),N-box(j′,t),t) (7)

[0058] Where i′=1,2,…,M′,j′=1,2,…,N′,t=1,2,…,T-1.

[0059] Step 5: After T-1 rounds of scrambling, we can obtain the final scrambled image.

[0060] P′=G(:,:,T) (8)

[0061] Second stage: Bit-level scrambling and diffusion synchronous update algorithm for large images

[0062] Step 1: Horizontally stitch together w scrambled medical images into a large image P″, with a size of M×w×N.

[0063] Step 2: Iterative tent-logic cross-coupling mapping lattice chaotic system Next, discard the results of the first s1 calculations to obtain a result of size . The matrix.

[0064] Step 3: Obtain two chaotic sequences x(i) of length M×w×N = {x1, x2, ..., xn}. M×w×N} and y(i)={y1,y2,...,y M×w×N}

[0065] Step 4: Use formulas (9) and (10) to process the chaotic sequences x and y respectively.

[0066] X(i) = mod(floor(x(i)) × 10 15 ,M×w×N) (9)

[0067] Y(i) = mod(floor(y(i)) × 10 15 ,256) (10)

[0068] Floor(x) gives the smallest integer greater than or equal to x, and mod() represents the modulo operation.

[0069] Step 5: Sort the X sequence and derive the index matrix V. Therefore, V has a size of M×w×N, where all values ​​are between 1 and M×w×N and are unique.

[0070] Step 6: Divide the chaotic sequence Y(i) and the large image P″ into 8 bit planes, and perform scrambling and diffusion synchronous update algorithms on these 8 bit planes respectively. Finally, merge the obtained 8 bit planes to obtain the ciphertext image. The algorithm calculation is as follows:

[0071]

[0072] Where C{k}(0)=0, This represents a bit-level XOR operation.

[0073] During the scrambling and diffusion synchronization update process, the i-th binary value of the k-th bit plane is related to the V(i)-th binary value of the k-th bit plane of the original image, the V(i)-th binary value of the k-th bit plane of the chaotic sequence Y(i), and the previously encrypted binary value of that plane. Therefore, the position and pixel value of the original image can be modified simultaneously.

[0074] Step 7: Divide image C into w final encrypted images.

[0075] C(i)=reshape(C,M,wN),1≤i≤w (12)

[0076] As attached Figure 3 As shown, this invention selects four medical images of different sizes, fills them all with a size of 512×512, and uses the encryption algorithm of this invention to obtain the attached image. Figure 4 The encrypted image shown clearly demonstrates that no useful information can be obtained from it, effectively protecting medical images and the individual's privacy.

[0077] Histograms can characterize the distribution of pixel values, as shown in the attached figure. Figure 5 The image shown is a histogram of four medical images. Figure 5 The horizontal axis represents the pixel value, which is fixed between 0 and 255, and the vertical axis represents the number of pixels with that value.

[0078] Clearly, the distribution of plaintext pixel values ​​is extremely irregular. If an attacker understands this pattern, they could very likely brute-force their way to the plaintext image; as shown in the attached image. Figure 6 The image shown is a histogram of four medical images obtained after applying the encryption algorithm of this invention, where the horizontal and vertical coordinates are... Figure 5 The consistent pixel values ​​indicate that the ciphertext image effectively covers the pixel distribution pattern of the plaintext image.

[0079] IV. Image Decryption

[0080] Step 1: Horizontally stitch the obtained encrypted images into a large image.

[0081] Step 2: Obtain sequence Y(i) and V according to steps 2-5 of the second stage of encryption.

[0082] Step 3: The decrypted large matrix image can be obtained by using the reverse process of the scrambling and diffusion synchronous update algorithm.

[0083]

[0084] Where C{k}(0)=0, This represents a bit-level XOR operation.

[0085] Step 4: Divide the large image into w smaller images according to formula (14).

[0086] D(i)=reshape(D,M,wN),1≤i≤w (14)

[0087] Step 5: Use M-box and N-box to reverse scramble the w images.

[0088] The above description is only for illustrating the present invention and should be understood as not being limited to the above embodiments. Various modifications that conform to the spirit of the present invention are within the protection scope of the present invention.

Claims

1. A multi-image encryption algorithm based on simultaneous scrambling and diffusion updates, characterized in that, First, based on the cross-coupled mapping lattice, an improved tent-logic cross-hybrid coupled mapping lattice chaotic system is constructed; The adjusted single medical image is scrambled using a bijective function, and the scrambled images are horizontally stitched together to form a large image. The key and initial value of the chaotic system are obtained using the Hash-512 algorithm, and the chaotic sequence is obtained by iteratively improving the tent-logic cross-hybrid coupled mapping lattice chaotic system. The improved tent-logic cross-hybrid coupled mapping lattice chaotic system has the following equations: Wherein, formula (1) is the existing cross-coupled mapping lattice chaotic system, and formula (2) is the improved tent-logic cross-hybrid coupled mapping lattice chaotic system, wherein: The first formula is for a tent-logic chaotic system, which will replace the parameter e in formula (1) to improve the randomness of the parameters in formula (2); the second formula has the generation method for parameters p and q on the top and the generation method for matrix A on the bottom, where a, b, c, and d are random Fibonacci sequences, n represents time, and θ n Let θ0 represent the value of the subkey at time n, r represent one of the subkey elements, and i represent the number of cells. Let i represent the state value of the i-th lattice at time n, where i ∈ [1, L] and L is the number of lattices. The lattices with indices i+1 and i-1 are the adjacent lattices of the i-th lattice, and their boundary conditions are defined as follows: For logical mapping, μ represents one of the subkey elements; The scrambled image is then subjected to a bit-level scrambling and diffusion synchronous update algorithm using the chaotic sequence, resulting in an encrypted image.

2. The multi-image medical image encryption algorithm based on scrambling and diffusion synchronous updates according to claim 1, characterized in that, The key generation process is as follows: First, the original medical images are horizontally stitched together to form a large image P. Then, the Hash-512 algorithm is used on image P to obtain a hexadecimal number h, and h is converted into a binary sequence h1. K(j) is obtained by using the function K(j)=bin2dec(h1(j:j+8)) / (2^16), and the key key(j) is obtained by using formula (3), where j ranges from 1 to L+3 and L is the number of cells; key(j)=mod(K(j)+K(2×j)+K(3×j)+K(4×j),1) (3) Use formula (4) to pair the subkey Assign values ​​to μ, r, and θ0; 3. The multi-image medical image encryption algorithm based on scrambling and diffusion synchronous updates according to claim 1, characterized in that, Two boxes, M-box and N-box, are generated using a bijective function, and each original medical image is scrambled using these two boxes respectively. Then, the scrambled images are horizontally stitched together to form a large image I, and I is divided into 8 bit planes. Bit-level scrambling and diffusion synchronous update algorithms are then applied to these 8 bit planes to obtain the encrypted large image. Finally, the encrypted large image is horizontally sliced ​​into individual medical images.

4. The multi-image medical image encryption algorithm based on scrambling and diffusion synchronous updates according to claim 3, characterized in that, The scrambling steps for each original medical image are as follows: Suppose a certain medical image is M×N in size. Since the size of each medical image may be different, we will select the largest medical image as the standard and fill the remaining medical images with this size M′×N′. Step 1: Create a 3D matrix G with dimensions M′×N′×T to perform a scrambling operation on the plaintext image, where T is the number of scrambling rounds; Step 2: In order to perform multi-round scrambling, initialize matrix G with initial values, where W is a two-dimensional matrix and G is a three-dimensional matrix composed of multiple two-dimensional matrices. Fill the first layer of G with the values ​​of W. G(:,:,1)=W (5) Step 3: Use a bijective function to create two boxes, M-box and N-box, with sizes M′ and N′ respectively. The formula for the bijective function is: x′ and y′ represent the horizontal and vertical coordinates, respectively; Step 4: Perform multiple rounds of scrambling using M-box and N-box, where M-box is used to scramble rows and N-box is used to scramble columns; G(i′,j′,t+1)=G(M-box(i′,t),N-box(j′,t),t) (7) Where i′=1,2,…,M′,j′=1,2,…,N′,t=1,2,…,T-1; Step 5: After T-1 rounds of scrambling, the final scrambled image is obtained; P′=G(:,:,T) (8).

5. The multi-image medical image encryption algorithm based on scrambling and diffusion synchronous updates according to claim 4, characterized in that, The steps for scrambling and spreading synchronously updating the large image are as follows: Step 1: Horizontally stitch together w scrambled medical images into a single large image P″, with a size of M′×w×N′; Step 2: Iterative tent-logic cross-coupling mapping lattice chaotic system Next, discard the results of the first s1 calculations to obtain a result of size . Matrix; Step 3: Obtain two chaotic sequences x = {x1, x2, ..., xN'} of length M′×w×N′. M′×w×N′ } and y = {y1, y2, ..., y M′×w×N′ }; Step 4: Use formulas (9) and (10) to process the chaotic sequences x and y respectively; X(k)=mod(floor(x(k)×10 15 ),M′×w×N′) (9) Y(k)=mod(floor(y(k)×10 15 ),256) (10) Floor(num) gives the smallest integer greater than or equal to num, and mod() represents the modulo operation; Step 5: Sort the X sequence and derive the index matrix V. Therefore, the size of V is M′×w×N′, where all values ​​are between 1 and M′×w×N′ and are unique. Step 6: Divide the chaotic sequence Y(k) and the large image P″ into 8 bit planes, and perform scrambling and diffusion synchronous update algorithms on these 8 bit planes respectively. Finally, merge the obtained 8 bit planes to obtain the ciphertext image. The algorithm calculation is as follows: Where C{u}(0)=0, This represents a bit-level XOR operation; Step 7: Divide image C into w final encrypted images; C(ω)=reshape(C,M′,wN′),1≤ω≤w (12).

6. The multi-image medical image encryption algorithm based on scrambling and diffusion synchronous updates according to claim 1, characterized in that, The image decryption process includes the following: First, the encrypted medical images are horizontally stitched together to form a large image, and then the eight bit planes of the large image are decrypted using the inverse algorithm of scrambling and diffusion synchronous update. The large image is then segmented, and each segment is then inversely scrambled to obtain the original image.

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