Fast image encryption method based on chaos and pseudo wavelet transform

Abstract

A fast image encryption method based on chaos and pseudo wavelet transform belongs to the field of information encryption. As an important information carrier, images occupy a very important position in various fields. With the increasing image clarity and data volume, the encryption efficiency of images becomes crucial. In order to ensure the real-time and reliability of image encryption, inspired by image wavelet transform, the present invention proposes an image encryption method based on chaos and pseudo wavelet transform. First, the original image is inversely transformed by wavelet transform and divided into four sub-bands; secondly, the low-frequency sub-band components are locally scrambled and XOR diffusion is performed using a chaotic system; finally, the matrix is ​​reconstructed by inverse pseudo wavelet transform to obtain an encrypted image. Experimental results and algorithm analysis show that this method only needs to process part of the data in the original image to achieve a good encryption effect, and avoids the problem of precision loss in traditional frequency domain transform, with good encryption effect and high security.

Description

Technical Field

[0001] The invention relates to an information encryption technology, in particular to a fast image encryption method based on chaos and pseudo wavelet transformation. Background Art

[0002] As an important information carrier, images play a very important role in various fields. Images contain a lot of sensitive information. Designing secure image encryption technology to ensure the security of data transmission and storage has become a hot topic in network security.

[0003] In today's fast-paced life, time is becoming more and more precious. With the increasing demand for image clarity, as well as the continuous improvement of image resolution and sensor technology, the amount of image data is increasing. Therefore, the encryption efficiency of image encryption algorithms is an important issue that researchers must consider.

[0004] Inspired by the local processing idea in frequency domain image processing, and in order to restore the image without distortion, a fast image encryption method based on chaos and pseudo wavelet transform is proposed. This method processes the image locally in the time domain space, reduces the amount of computational data, and improves encryption efficiency. Summary of the invention

[0005] The purpose of the present invention is to propose a fast image encryption method based on chaos and pseudo wavelet transform in view of the low encryption efficiency of the existing time domain image encryption method and the problem of decryption distortion in the frequency domain image encryption method.

[0006] Technical solution of the present invention: To achieve the above-mentioned purpose of the invention, the technical solution adopted is a fast image encryption method based on chaos and pseudo wavelet transform. The encryption steps of the method are described in detail as follows:

[0007] Step 1: Image preprocessing: Let the original image be I, whose size is m×n, and both m and n are required to be even numbers; if m or n is an odd number, I is padded with zeros to add a row or a column.

[0008] Step 2: Pseudo wavelet transform: Perform pseudo wavelet transform on I to obtain low-frequency subband I1 and high-frequency subbands P2, P3, P4, all of which are (m / 2)×(n / 2).

[0009] Step 3: Chaotic sequence generation: Randomly select the initial values ​​x0∈(0,1), y0∈(0,1) of the two-dimensional Henon map, and iterate mn / 4 times according to formula (1) to obtain two chaotic sequences X and Y;

[0010]

[0011] Where i = 0, 1, ..., mn / 4-1, X i∈(0,1), Y i ∈(0,1), control parameters a=1.4 and b=0.3;

[0012] Step 4: Sort the chaotic sequence: Sort X and we get:

[0013] S1=sort(X), (2)

[0014] Among them, sort(·) is an ascending sorting function, and S1 is the index value sequence;

[0015] Step 5: Integerization of chaotic sequence: Integerization of Y,

[0016] S2=mod(floor(Y×10 14 ),256), (3)

[0017] Among them, mod(·) and floor(·) are modulo operation and integer operation functions respectively, and S2 is an integer chaotic sequence;

[0018] Step 6: Local image scrambling: Use S1 to scramble I1 to get the scrambled subband R1.

[0019] R1(j)=I1(s(j)), (4)

[0020] Where j = 1, 2, ..., mn / 4, s(i)∈S1;

[0021] Step 7: Local diffusion of the image: Use S2 to perform the diffusion operation shown in formula (5) on R1 to obtain the diffused subband R2.

[0022] R2=S2⊕R1, (5)

[0023] Among them, ⊕ is the exclusive OR operation;

[0024] Step 8: Inverse pseudo wavelet transform: Perform inverse pseudo wavelet transform on R2, P2, P3, P4 to obtain the encrypted image J.

[0025] Furthermore, in step 2, the pseudo wavelet transform refers to the time domain sampling and rearrangement operation of I, and the process is similar to the discrete wavelet transform of I. The specific operation is: each pixel point in I with odd row and column coordinates and its adjacent pixel points at the right, bottom and diagonal positions are sampled and saved into four matrices I1, I2, I3 and I4 with a size of (m / 2)×(n / 2) according to formula (6).

[0026]

[0027] Where k = 1, 2, ..., m / 2, t = 1, 2, ..., n / 2; then, calculate:

[0028]

[0029] Furthermore, in step 8, the inverse pseudo wavelet transform refers to the inverse process of the pseudo wavelet transform, and the specific operation is: calculating:

[0030] Then, R2, I2, I3 and I4 are combined into an m×n matrix J according to formula (9), which is the image after inverse pseudo wavelet transformation;

[0031]

[0032] Among them, k = 1, 2,…, m / 2, t = 1, 2,…, n / 2.

[0033] Beneficial effects: In view of the problems of low encryption efficiency and image distortion in frequency domain encryption in current image encryption methods, this invention proposes a fast image encryption method based on chaos and pseudo wavelet transform. The main contributions are as follows: (1) The proposed method only processes local data, which reduces the amount of encrypted data and improves encryption efficiency; (2) Compared with traditional frequency domain wavelet transform, the proposed algorithm is simple to operate and solves the problem of precision loss in frequency domain transform, which has better encryption effect; (3) Experimental results and method analysis show that the new method has good encryption effect, strong security and high efficiency, and can realize real-time encryption and network transmission of images. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 :Flowchart of fast image encryption based on chaos and pseudo wavelet transform;

[0035] Figure 2 : original image;

[0036] Figure 3 : Schematic diagram of pseudo wavelet transform process;

[0037] Figure 4 : Encrypted image. DETAILED DESCRIPTION

[0038] The embodiments of the present invention are further described in detail below with reference to specific drawings and examples.

[0039] Figure 1 It is a flowchart of fast image encryption based on chaos and pseudo wavelet transform.

[0040] The programming software used is Matlab R2020. An arbitrary grayscale encrypted image is selected, such as Figure 2As shown, the proposed fast image encryption method based on chaos and pseudo wavelet transform is adopted, and the encryption process is described in detail as follows.

[0041] Step 1: Read the original image I to be encrypted, whose size is 512×512, and no zero padding operation is required;

[0042] Step 2: Pseudo wavelet transform: Perform pseudo wavelet transform on I to obtain low-frequency subband I1 and high-frequency subbands P2, P3, and P4, all of which have a size of 256×256. Figure 3 It is a schematic diagram of pseudo wavelet transform of 8×8 matrix;

[0043] Step 3: Chaotic sequence generation: Select the initial values ​​of the two-dimensional Henon map x0 = 0.5137, y0 = 0.3144, and iterate 256 × 256 times according to formula (1) to obtain two chaotic sequences X and Y with a length of 65536;

[0044] Step 4: Chaotic sequence sorting: Sort the chaotic sequence X according to formula (2) to get the sorted index matrix S1: Step 5: Chaotic sequence integerization: Integerize the chaotic sequence Y according to formula (3) to get the integer sequence S2:

[0045] Step 6: Local image scrambling: According to the index matrix S1, scramble the subband I1 according to formula (4), and get R1:

[0046] Step 7: Local diffusion of the image: Use the integer sequence S2 to perform an XOR operation on R1 according to formula (5) to obtain R2:

[0047] Step 8: Inverse pseudo wavelet transform: Perform inverse pseudo wavelet transform on R2, P2, P3, P4 to obtain the encrypted image J, as shown in Figure 4 shown.

Claims

1. A fast image encryption method based on chaos and pseudo wavelet transform, characterized in that: The encryption process includes the following steps: Step 1: Image preprocessing: Let the original image be I, whose size is m×n, and both m and n are required to be even numbers; if m or n is an odd number, then I is padded with zeros to add a row or a column; Step 2: Pseudo wavelet transform: Pseudo wavelet transform refers to the time domain sampling and rearrangement operation of I. The process is similar to the discrete wavelet transform of I. The specific operation is: each pixel point with odd row and column coordinates in I and its adjacent pixels to the right, bottom and diagonal positions are sampled and saved into four matrices I1, I2, I3 and I4 with a size of (m / 2) × (n / 2) according to formula (1). Where k = 1, 2, ..., m / 2, t = 1, 2, ..., n / 2; then, calculate: By performing pseudo wavelet transform on I, we can obtain low-frequency subband I1 and high-frequency subbands P2, P3, and P4, all of which have the size of (m / 2)× (n / 2)； Step 3: Chaotic sequence generation: Randomly select the initial values ​​x0∈(0,1), y0∈(0,1) of the two-dimensional Henon map, and iterate mn / 4 times according to formula (3) to obtain two chaotic sequences X and Y; Where i = 0, 1, ..., mn / 4-1, X i ∈(0,1), Y i ∈(0,1), control parameters a=1.4 and b=0.3; Step 4: Sort the chaotic sequence: Sort X and we get: S1=sort(X), (4) Among them, sort(·) is the ascending sorting function, and S1 is the index value sequence; Step 5: Integerization of chaotic sequence: Integerization of Y, S2=mod(floor(Y×10 14 ), 256), (5) Among them, mod(·) and floor(·) are modulo operation and integer operation functions respectively, and S2 is an integer chaotic sequence; Step 6: Local image scrambling: Use S1 to scramble I1 to get the scrambled subband R1. R1(j) = I1(s(j)), (6) Where j = 1, 2, ..., mn / 4, s(i)∈S1; Step 7: Local diffusion of the image: Use S2 to perform the diffusion operation shown in formula (7) on R1 to obtain the diffused subband R2. in, is an XOR operation; Step 8: Inverse pseudo wavelet transform: Inverse pseudo wavelet transform refers to the inverse process of pseudo wavelet transform. The specific operation is: Calculation: Then, R2, I2, I3 and I4 are combined into an m×n matrix J according to formula (9), which is the image after inverse pseudo wavelet transformation. Among them, k = 1, 2, ..., m / 2, t = 1, 2, ..., n / 2; by performing inverse pseudo wavelet transform on R2, P2, P3, P4, the encrypted image J can be obtained.

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