CN114553483B - Novel image encryption method based on Ruckedge and compressed sensing - Google Patents

Novel image encryption method based on Ruckedge and compressed sensing Download PDF

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CN114553483B
CN114553483B CN202210052828.6A CN202210052828A CN114553483B CN 114553483 B CN114553483 B CN 114553483B CN 202210052828 A CN202210052828 A CN 202210052828A CN 114553483 B CN114553483 B CN 114553483B
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CN114553483A (en
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曹国栋
杨宇光
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Beijing University of Technology
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    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
    • H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L63/00—Network architectures or network communication protocols for network security
    • H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
    • H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
    • H04L63/0478—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload applying multiple layers of encryption, e.g. nested tunnels or encrypting the content with a first key and then with at least a second key
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/06—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols the encryption apparatus using shift registers or memories for block-wise or stream coding, e.g. DES systems or RC4; Hash functions; Pseudorandom sequence generators
    • H04L9/0643—Hash functions, e.g. MD5, SHA, HMAC or f9 MAC
    • H—ELECTRICITY
    • H04—ELECTRIC COMMUNICATION TECHNIQUE
    • H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
    • H04L9/00—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols
    • H04L9/08—Key distribution or management, e.g. generation, sharing or updating, of cryptographic keys or passwords
    • H04L9/0861—Generation of secret information including derivation or calculation of cryptographic keys or passwords
    • H04L9/0869—Generation of secret information including derivation or calculation of cryptographic keys or passwords involving random numbers or seeds

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Abstract

The invention discloses a novel image encryption method based on Ruckridge and compressed sensing. The original image is preprocessed, i.e. the image is transformed into a sparse coefficient matrix using a discrete wavelet transform. And generating a random measurement matrix by using the one-dimensional chaotic system, and measuring the sparse matrix by using the random measurement matrix. And quantizing the value of the obtained matrix to the interval of [0-255], thereby obtaining an intermediate image. Performing hash operation on the intermediate image to obtain a function value, generating an initial value of the Ruckedge chaotic system by the function value and the hash function value together, generating four random matrixes by using the Ruckedge chaotic system, and performing block scrambling on the intermediate image according to the random matrixes. Finally, a diffusion algorithm is used for disturbing the pixel positions of the image, so that a secret image is obtained. The invention can better resist the known plaintext attack and select the plaintext attack.

Description

Novel image encryption method based on Ruckedge and compressed sensing
Technical Field
The invention relates to the field of information security, in particular to the field of image encryption, and discloses a novel image encryption technology based on the combination of Ruckedge and compressed sensing.
Background
Among the vast information transmission carriers in the internet age, images are one of the most popular forms of multimedia. However, due to the openness of the internet and the scarcity of bandwidth resources, security and transmission efficiency of images are also of great concern. Therefore, it is important to encrypt and compress the image during transmission. The image encryption technology can protect the image information from leakage and tampering, and the image compression can effectively reduce the redundant information of the image, thereby reducing the storage space of the image and improving the transmission efficiency of the image in a network. Since compressed sensing techniques (Compressive Sensing, CS) can be used to simultaneously compress and encrypt images, many compressed sensing-based image encryption techniques have been proposed.
CS technology is a process of generating a low-dimensional signal from a high-dimensional sparse signal by random sampling. The principle of encrypting an image using CS theory is to input a plaintext image as a signal, a measurement matrix as an encryption key, and a ciphertext image as a low-dimensional signal. The academy has demonstrated the security and robustness of CS-based encryption algorithms and indicated that CS-based encryption is computationally secure. However, CS is essentially a linear measurement and compression when processing images, and is vulnerable to known plaintext attacks and selective plaintext attacks, and in order to better ensure the security of image transmission, CS and some image encryption algorithms are usually used in combination. CS-based image encryption algorithms essentially encrypt the intermediate image when the image is encrypted twice, but these algorithms do not correlate the intermediate image with a key.
To solve these problems, we propose herein a new image encryption algorithm based on ruckedge and CS. In order to solve the security problem of the linear measurement of CS, a Ruckedge chaotic system is used for carrying out secondary encryption on the intermediate ciphertext image. In order to strengthen the association of the algorithm and the plaintext, a plaintext image association key stream is used, the algorithm respectively calculates hash values of the plaintext image and the intermediate image by using a SHA-256 hash function before and after compressive sensing is applied to the plaintext image, and the hash values of the plaintext image and the intermediate image are used for jointly generating the key stream of the encryption system. And for the scrambling stage, a block permutation algorithm strongly associated with the plaintext is provided, and for the diffusion stage, an addition modulo operation associated with the plaintext is selected. The correlation of the plaintext, the ciphertext and the key stream is enhanced, the capability of bearing the attack of selecting the plaintext and the attack of the known plaintext is greatly improved, and the security of an image encryption algorithm is improved.
Disclosure of Invention
The invention provides a novel image encryption algorithm based on Ruckridge and compressed sensing, which uses a compressed sensing technology to quickly compress an image in order to improve the image encryption speed, and the compressed sensing technology can encrypt the image at the same time when the image is compressed, so that the advantages greatly improve the image encryption speed. When the traditional compressed sensing technology is used for image encryption, a random measurement matrix is used as a secret key, so that the secret key is too large and bulky. Because of the superior iteration speed of the low-dimensional chaotic system, the invention can use the Logistic chaotic system to generate the random measurement matrix, thus the initial value of the chaotic system can be used as a key for transmission, the whole random measurement matrix is not used as the key, the key transmission bandwidth is greatly reduced, and the transmission cost of images in the Internet is effectively reduced.
The Ruckedge chaotic system is a mathematical model established based on practical application, is a typical nonlinear power system, is sensitive to initial values, has a complex nonlinear motion track in chaotic images, and proves excellent chaotic characteristics. Because the compressed sensing technology is linear in nature and easy to crack, in order to improve the security level of the secret image, the method can use the Ruckedge chaotic system to control the ciphertext image to carry out secondary encryption.
The secondary encryption of the image is essentially the encryption of the intermediate image, however most existing algorithms only relate to the plaintext image when the plaintext is associated with the key, thereby ignoring the intermediate image. Therefore, the bright point plaintext image and the intermediate image generated in the algorithm process are combined, the hash function values of the bright point plaintext image and the intermediate image are jointly used as the initial value of the Ruckedge chaotic system, and a block scrambling algorithm related to plaintext is provided, so that the relevance of the plaintext is increased, namely the plaintext image has a little change, and the final ciphertext image is greatly changed. Therefore, the invention can better resist the known plaintext attack and select the plaintext attack.
The block scrambling algorithm of plaintext association proposed by the invention is as follows:
step 1: given an m×n matrix a, dividing the matrix a into two blocks from the vertical direction to obtain two matrices B and C with sizes of m×n/2, where m=m, n=n/2.
Step 2: given any one pixel coordinate point (i, j) in matrix B, i epsilon [1, N/2 ]]The sum of the ith row (excluding B (i, j)) in matrix B is calculated and denoted as H i . Calculate the sum of the j-th column (excluding B (i, j)) in matrix B, denoted as L j . The values of i 'and j' are calculated according to the following equation:
wherein the matrices D and E are given random matrices. After calculating the new coordinates, the values of the matrix B (i, j) and the matrix C (i ', j').
Step 3: and traversing the matrix B in a left-to-right and top-to-bottom scanning mode, and sequentially and circularly executing the step 2 to realize scrambling from the matrix B to the matrix C.
Step 4: and (3) performing position exchange on the matrix B and the matrix C, scrambling the matrix B from the matrix C, giving two new random matrices F, J to replace D and E, and repeating the steps (2) and (3).
Step 5: and recombining the matrix B with the size of MxN/2 and the matrix C into a new matrix I with the size of MxN, wherein the new matrix I is the new image after scrambling.
The invention is realized by the following technical scheme: an image encryption method based on Ruckedge and compressed sensing comprises the following steps:
A. image encryption stage
a) And in the compressed sensing stage, the image is compressed and encrypted for the first time.
i. The plaintext image is transformed into the wavelet domain using a two-dimensional discrete wavelet transform technique (DWT).
Scrambling the transformed image using the zig-zag technique.
Generating a random measurement matrix using a one-dimensional chaotic system.
And (3) measuring the image obtained in the step (ii) by using the generated random measurement matrix.
And v. obtaining an intermediate image.
b) And a secondary encryption stage, performing secondary encryption processing on the intermediate image generated in the step a).
i. Four random sequences are generated using the ruckedge chaotic system.
Four random matrices are generated using two of the random sequences.
Dividing the intermediate image into two blocks of equal size.
A plaintext-associative permutation algorithm controlled by a random matrix is used separately for each block.
And v. reorganizing the scrambled two blocks into an image and further encrypting the image by using a diffusion algorithm.
B. Image decryption stage
a) One-time decryption
i. Random sequences are generated using a ruckedge chaotic system.
Transformation is performed using the inverse of the diffusion algorithm.
Four random matrices are generated using the random sequences.
And fifthly, carrying out inverse scrambling by combining a scrambling algorithm associated with the random matrix and the plaintext.
b) Secondary decryption
i. A random measurement matrix is generated using a one-dimensional chaotic system.
Reconstructing the intermediate image by combining the random measurement matrix and a compressed sensing reconstruction algorithm.
And obtaining a plaintext image by using the Zigzag inverse transformation.
Drawings
The foregoing and other objects, features, and advantages of the invention will be apparent from the following more particular description of exemplary embodiments of the invention, as illustrated in the accompanying drawings.
The algorithm provided by the invention has two stages: an encryption stage and a decryption stage.
Fig. 1 shows an encryption flow chart of the algorithm based on the ruckridge and the compressed sensing technology.
Fig. 2 shows a corresponding decryption flow chart of the algorithm.
Detailed Description
The objects, technical solutions and advantages of the present invention will become more apparent by describing the present invention in more detail with reference to the accompanying drawings. It should be understood that the specific embodiments described herein are for purposes of illustration only and are not intended to limit the scope of the invention.
Referring to fig. 1, shown in fig. 1 is a flowchart of an encryption phase based on the ruckridge and compressed perceived image encryption technique.
As is apparent from fig. 1, the algorithm has approximately the following flow:
(1) Firstly, an original image is subjected to operation by applying a hash function, and an initial value of the one-dimensional chaotic system is generated.
(2) The original image is then preprocessed, i.e. the image is transformed into a sparse coefficient matrix using a discrete wavelet transform. Because the measurement of a two-dimensional matrix by using compressed sensing is basically performed on a one-dimensional vector, but because the sparsity of a sparse matrix is aimed at the whole matrix instead of a single column vector, the problem of 0 aggregation of the single column vector is caused, and finally, the compressed sensing measurement effect is poor. In order to solve the problem of 0 aggregation of the coefficient matrix, the coefficient matrix is disturbed by using the Zigzag technology, and finally the original image is transformed into a sparse matrix which can meet the technical requirements of compressed sensing.
(3) And generating a random measurement matrix by using the one-dimensional chaotic system, and measuring the sparse matrix by using the random measurement matrix. And quantizing the value of the obtained matrix to the interval of [0-255], thereby obtaining an intermediate image.
(4) Performing hash operation on the intermediate image to obtain a function value, generating an initial value of the Ruckedge chaotic system by the function value and the hash function value in the step (1), generating four random matrixes by using the Ruckedge chaotic system, and performing block scrambling on the intermediate image according to the random matrixes.
(5) Finally, a diffusion algorithm is used for disturbing the pixel positions of the image, so that a secret image is obtained.
The following details the specific steps of the encryption stage based on the ruckedge and compressed sensing image encryption technology according to the present invention with reference to fig. 1:
step 1: let the input image be P and the size be mxn.
Step 2: calculating SHA-256 hash function value of the image P to obtain a sequence K= { K 1 ,k 2 ,...,k 32 And obtaining an initial value lx of the Logistic chaotic system by using the following formula 0 。
Wherein lxt is a specified value.
Step 3: and transforming the image P into a discrete wavelet domain to obtain a coefficient matrix P1, wherein the matrix size is consistent with that of the original image.
Step 4: and using Zigzag scrambling to the coefficient matrix P1 to obtain P2.
Step 5: using Logistic chaotic system and initial value lx thereof 0 The initial parameters of step d=10, generating a chaotic sequence S of 100+m×n length. First, discard the first 100 values for better randomness, and second, range the size to [0,1 ]]The sequence S of (2) is transformed to [ -1,1 using the following formula]Finally, the S is reshaped in a column-first manner into a random measurement matrix Φ of size M rows and N columns, where n=n, m=cr×m, CR being the compression ratio.
S i ＝1-S i ×2,i∈[1,M×N]
Step 6: p2 is measured using Φ to obtain a measurement matrix P3, which has a size of mxn.
Step 7: p3 is quantized to the [0-255] range using the following equation, yielding an intermediate image P4, where min and max are the minimum and maximum values of P3, respectively.
Step 8: calculating the SHA-256 function value of the intermediate image P4 to obtain a sequence K ', and obtaining K ' by using the following formula from the K and the K ' calculated in the step 2.
Step 9: and (3) calculating an initial value cx of the Ruckedge chaotic system by using the following method in combination with the sequence K' generated in the step (8) 0 、cy 0 、cz 0 And generating 4 chaotic sequences h1, h2, h3 and h4 with the length of 1000+M multiplied by N, and discarding the first 1000 items of values in order to avoid transient effects, wherein cxt, cyt, czt is a specified value.
Step 10: splitting a random sequence h1 with the length of MxN into two random sequences with the length of MxN/2, remodelling the random sequences into two random matrices D, E with the length of M rows and N/2 columns in a column priority mode, splitting h2 into two random matrices F, J with the length of M rows and N/2 columns, and carrying out scrambling operation on P4 by using the four random matrices and the scrambling algorithm to obtain P5.
Step 11: and respectively using h3 and h4 as forward diffusion and reverse diffusion chaotic sequences of a diffusion algorithm, and further disturbing the image by using the diffusion algorithm of the following formula on P5 to obtain P6, namely a final secret image C.
Wherein P is a given plaintext image to be diffused, S is a given chaotic sequence guiding diffusion, and C is a diffused ciphertext image. The two formulas are forward diffusion algorithm and reverse diffusion algorithm, respectively.
Fig. 2 shows the decryption steps of the algorithm of the present invention, and it can be seen that the decryption algorithm generally comprises the following steps: the method comprises the steps of obtaining an initial value of a Ruckedge chaotic system by using a secret key, further obtaining a chaotic sequence, then carrying out inverse diffusion and inverse scrambling on a secret image through the guidance of the chaotic sequence to obtain an intermediate image, carrying out inverse quantization on the intermediate image, then using a one-dimensional chaotic system to generate a random measurement matrix, using the matrix and a compressed sensing reconstruction algorithm to restore the image, and finally obtaining a plaintext image by using Zigzag inverse transformation and discrete wavelet inverse transformation respectively.
The following details the decryption phase in conjunction with fig. 2:
step 1: the read secret image C is denoted as P6, and has a size of mxn.
Step 2: and generating chaotic sequences h1, h2, h3 and h4 with the length of 1000+M multiplied by N according to the received secret key by using a Ruckedge chaotic system, and discarding the first 1000 items.
Step 3: the reduction operation of diffusion was performed on P6 using the h3 and h4 sequences using the following formula to give P5.
Wherein C is a given ciphertext image to be decrypted, S is a given chaotic sequence guiding diffusion, and P is a plaintext image. The two formulas are a forward diffusion reduction algorithm and a reverse diffusion reduction algorithm, respectively.
Step 4: four random matrices D, E, F, J are generated using the h1 and h2 sequences and P5 is reduced back to P4 using a scrambling algorithm that is substantially the same as the scrambling algorithm set forth above, except that the order of the operations is changed.
Step 5: the image P4 is inversely quantized using the following formula to obtain P3.
Step 6: and generating a chaotic sequence with the length of 100+M multiplied by N by using a Logistic chaotic system, modeling the chaotic sequence into a random measurement matrix phi of M rows and N columns, and reconstructing P3 by using phi and a reconstruction algorithm to obtain P2.
Step 7: and carrying out Zigzag inverse transformation on the P2 to obtain P1.
Step 8: the plaintext image P is obtained by applying an inverse discrete wavelet transform to P1.

Claims (1)

1. A novel image encryption method based on Ruckedge and compressed sensing is characterized in that: the implementation steps of the method are as follows:
(1) Firstly, carrying out operation on an original image by applying a hash function to generate an initial value of a one-dimensional chaotic system;
(2) Preprocessing the original image, namely transforming the image into a sparse coefficient matrix by using discrete wavelet transformation; disturbing the coefficient matrix by using a Zigzag technology, and finally transforming the original image into a sparse matrix capable of meeting the compressed sensing technical requirement;
(3) Generating a random measurement matrix by using a one-dimensional chaotic system, and measuring a sparse matrix by using the random measurement matrix; quantizing the value of the obtained matrix to a [0-255] interval, thereby obtaining an intermediate image;
(4) Performing hash operation on the intermediate image to obtain a function value, jointly generating an initial value of the Ruckedge chaotic system by the function value and the hash function value in the step (1), generating four random matrixes by using the Ruckedge chaotic system, and performing block scrambling on the intermediate image according to the random matrixes;
(5) Finally, disturbing pixel positions of the image by using a diffusion algorithm to obtain a secret image;
the block scrambling process of plaintext association is as follows:
step 1: giving an M multiplied by N matrix A, dividing the matrix A into two blocks from the vertical direction to obtain two matrixes B and C with the size of M multiplied by N/2, wherein m=M, n=N/2;
step 2: given any one pixel coordinate point (i, j) in matrix B, i epsilon [1, N/2 ]]Calculating the sum of the ith row in the matrix B, removing B (i, j), and marking as Hi; calculate the sum of the j-th columns in matrix B, remove B (i, j), denoted L j The method comprises the steps of carrying out a first treatment on the surface of the The values of i 'and j' are calculated according to the following equation:
wherein, the matrices D and E are given random matrices; after calculating new coordinates, exchanging the values of matrix B (i, j) and matrix C (i ', j');
step 3: traversing the matrix B in a left-to-right and top-to-bottom scanning mode, and sequentially and circularly executing the step 2 to realize scrambling from the matrix B to the matrix C;
step 4: the positions of the matrix B and the matrix C are exchanged, the matrix C is scrambled to the matrix B, two new random matrixes F, J are given to replace D and E, and the step 2 and the step 3 are repeated;
step 5: recombining the matrix B with the size of MxN/2 and the matrix C into a new matrix I with the size of MxN, wherein the new matrix I is a new image after scrambling;
in the course of the image encryption phase,
a) A compressed sensing stage, wherein the image is compressed and encrypted for the first time;
i. transforming the plaintext image into the wavelet domain using a two-dimensional Discrete Wavelet Transform (DWT);
scrambling the transformed image using a zig-zag technique;
generating a random measurement matrix by using a one-dimensional chaotic system;
measuring the image obtained in the step ii by using the generated random measurement matrix;
v. obtaining an intermediate image;
b) A secondary encryption stage, which is to perform secondary encryption processing on the intermediate image generated in the step a);
i. four random sequences are generated by using a Ruckedge chaotic system;
generating four random matrices using two of the random sequences;
dividing the intermediate image into two blocks of the same size;
a plaintext correlation permutation algorithm controlled by a random matrix is used for each block respectively;
v, reorganizing the two scrambled blocks into an image, and encrypting by using a diffusion algorithm;
in the course of the image decryption stage,
decrypting for the first time;
generating a random sequence by using a Ruckedge chaotic system;
transforming using the inverse of the diffusion algorithm;
generating four random matrices using a random sequence;
performing inverse scrambling by combining a scrambling algorithm associated with a random matrix and a plaintext;
secondary decryption;
generating a random measurement matrix by using a one-dimensional chaotic system;
reconstructing the intermediate image by combining a random measurement matrix and a compressed sensing reconstruction algorithm;
the plaintext image is obtained using the inverse zig-zag transformation.
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