CN110719170B - Bit-level image encryption method based on compressed sensing and optimized coupling mapping grid - Google Patents

Bit-level image encryption method based on compressed sensing and optimized coupling mapping grid Download PDF

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CN110719170B
CN110719170B CN201910812409.6A CN201910812409A CN110719170B CN 110719170 B CN110719170 B CN 110719170B CN 201910812409 A CN201910812409 A CN 201910812409A CN 110719170 B CN110719170 B CN 110719170B
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image
sequence
bit position
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value
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CN110719170A (en
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沈骞
刘文波
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Nanjing University of Aeronautics and Astronautics
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    • 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
    • H04L9/14—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using a plurality of keys or algorithms
    • 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
    • H04L9/0618—Block ciphers, i.e. encrypting groups of characters of a plain text message using fixed encryption transformation
    • H04L9/0631—Substitution permutation network [SPN], i.e. cipher composed of a number of stages or rounds each involving linear and nonlinear transformations, e.g. AES algorithms

Abstract

The invention discloses a bit-level image encryption method based on compressed sensing and optimized coupling mapping grid, which comprises the steps of substituting Logistic mapping with optimized parameter value range into a bidirectional coupling mapping grid model to construct an OCML system; subsequently, generating a required encryption sequence using the OCML based on the key information; secondly, constructing a high-low two-stage measurement matrix by using the generated encryption sequence to measure the main information and the secondary information of the image respectively; then, the two-stage measurement values are respectively quantized to avoid that the data space occupied by the ciphertext image is larger than the space occupied by the plaintext image information; and finally, scrambling and replacing the quantized image information, and combining the quantized image information into a final ciphertext image according to the weight. The invention takes the OCML system as a chaotic signal generator, takes the CS as a tool for compressing and encrypting the image information, and carries out encryption operation on the image information at a bit level, thereby realizing a new image encryption method. The method is simple and easy to implement, and has excellent safety performance.

Description

Bit-level image encryption method based on compressed sensing and optimized coupling mapping grid
Technical Field
The invention relates to the field of image encryption, in particular to a bit-level image encryption method.
Background
In image encryption applications, in order to improve the operation efficiency of the encryption process, compression encryption is usually selected on image data in a transform domain. The Compressed Sensing (CS) technology ensures that the image data is compressed while being acquired, which is beneficial to improving the efficiency of the encryption process. Whereas in CS-based image encryption methods, a pseudo-random sequence generator is typically used to construct the measurement matrix. The variable sequence generated by the chaotic system has the characteristics of randomness determination, extreme sensitivity and boundedness to the initial state and the like, and is very suitable to be used as a sequence generator. However, most of the current chaotic systems have the problems of small parameter value range or periodic window and the like, and the practical application value is limited.
In recent years, to further improve security, bit-level image encryption schemes have been developed. Most of the existing bit-level image encryption methods are operated by decomposing image element values into a plurality of gray-scale images according to bits, and the efficiency is low.
Disclosure of Invention
The purpose of the invention is as follows: aiming at the defects of the existing chaotic system and the bit-level image encryption scheme, the invention provides an Optimized Coupled Map Lattice (OCML) with larger parameter value range and no period window, and designs a bit-level image encryption method with higher efficiency by combining the CS technology.
The technical scheme is as follows: in order to achieve the purpose, the technical scheme adopted by the invention is as follows:
a bit-level image encryption method based on compressed sensing and optimized coupling mapping grids comprises the following steps:
(1) building an OCML system by substituting Logistic mapping with optimized parameter value range into a bidirectional coupling mapping lattice model;
(2) extracting parameter values and initial value information required by the operation of the OCML system from the key to generate four groups of different encryption sequences S1、S2、S3And S4；
(3) Dividing all element values in an image into high bit position information x by bit positionhAnd low bit position information xlBased on the encryption sequence S, respectively1And S2Constructing matrix phi in form of circulant matrixhAnd philAs the above two-level information xhAnd xlThe measurement matrix of (2);
(4) using a measurement matrix phihAnd philHigh bit position information x for respective imageshAnd low bit position information xlMeasuring to obtain corresponding measured value yhAnd yl；
(5) Measured value yhAnd ylRespectively quantizing to obtain quantized information Q of high bit position measurement valuehAnd quantization information Q of low bit position measurement valuesl；
(6) Using an encryption sequence S3And S4For the quantized value QhAnd QlAnd carrying out scrambling and replacing operation, and recombining the data obtained after operation into a final ciphertext image C according to the weight.
Wherein, the Logistic mapping iterative equation for parameter value range optimization in the step 1 is as follows:
xn+1＝sin((f+500)·π·xn·(1-xn))·cos((f+500)·π·xn·(1-xn))·2
wherein f, xnAnd xn+1Respectively representing the value of the n-th element and the value of the n + 1-th element of the system parameter and the iterative sequence of the system state variables.
The bidirectional coupling mapping grid model is as follows:
xn+1(i)＝(1-ε)·y(xn(i))+ε/2·(y(xn(i-1))+y(xn(i+1)))
wherein ε is the coupling coefficient; n represents the index number of the state variable iteration sequence; i denotes a lattice number, and i ═ 1, 2. L represents the number of lattices of the model; and the function y (-) represents a Logistic mapping iterative equation with the optimized parameter value range.
High bit position information x of the imagehAnd low bit position information xlRespectively refer to the high-order part and the low-order part in the image element value expressed in the form of binary sequence, and the construction method is as follows: representing the image by 8-bit gray scale map, the ith row and jth column element value P in the plaintext image Pi,jData in binary form
Figure BDA0002185423430000021
Wherein the high bit position information is a four-bit binary number
Figure BDA0002185423430000022
The data is composed of low bit position information of four-bit binary number
Figure BDA0002185423430000023
Composed data, high bit position information in all element values are arranged in sequence to form vector xhThe low bit position information is ordered to form a vector xl。
The structure of the cyclic matrix is as follows:
Figure BDA0002185423430000024
where m is the number of rows of the measurement matrix and the number of columns n of the measurement matrixThe ratio is the compression ratio in the measurement process; constant coefficient
Figure BDA0002185423430000031
Is a normalized scale factor and is used for realizing the column normalization of the matrix; a is1、a2、…、anAn encrypted sequence value iteratively generated for an OCML system.
The measurement value is the product of the measurement matrix and the vectorized image information, i.e. the measurement value yh＝Φh·xhMeasured value yl＝Φl·xl。
The high bit position measurement yhQuantized value Q ofhAnd low bit position measurement ylQuantized value Q oflAre sequences of 4-bit binary numbers, and the quantization process is performed in a uniform quantization manner.
The scrambling operation is to use an encryption sequence S with a length of 2m3Sequence numbers in size to Q of length mhAnd QlReordering to obtain sequence Qrc hAnd Qrc lWhere m is the number of rows in the measurement matrix.
The replacement operation is to use an encryption sequence S of length 2m4For sequence Qrc hAnd Qrc lExecuting XOR operation to obtain ciphertext information ChAnd ClThe operation process is
Figure BDA0002185423430000032
And
Figure BDA0002185423430000033
the combination process is that C ═ Ch·24+ClAnd C is the final ciphertext image.
Has the advantages that: compared with the prior art, the invention has the following beneficial effects:
1. compared with a traditional chaotic system model, the OCML based on the optimized Logistic mapping has better chaotic performance. Specifically, the method has a higher Lyapunov index value and a larger parameter value range, and no periodic window exists in the whole parameter value interval, so that the stability of the chaos performance of the iterative sequence is improved.
2. The CS and OCML-based bit-level image encryption method respectively acquires the main information and the secondary information of an image by using a high-low two-level measurement matrix, places the main information of the image in a high-bit position part of a ciphertext image, and places the secondary information of the image in a low-bit position part of the ciphertext image. Compared with the existing bit-level image encryption method, the method provided by the invention obviously simplifies the operation steps, so that the running expense of an encryption system is smaller and the efficiency is higher.
Drawings
FIG. 1 is a flow chart of an image encryption method according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of Kolmogorov-Sinai entropy density of OCML in accordance with an embodiment of the present invention;
FIG. 3 is a schematic diagram of the Kolmogorov-Sinai entropy breadth of OCML in accordance with an embodiment of the present invention;
FIG. 4 is a block diagram of a bit-level image encryption system according to an embodiment of the present invention;
FIG. 5 is a schematic illustration of key sensitivity in an encryption process according to an embodiment of the invention;
FIG. 6 is a schematic illustration of key sensitivity during decryption according to an embodiment of the invention;
FIG. 7 is a statistical histogram of an image Lena before and after being encrypted by an encryption system according to an embodiment of the present invention;
FIG. 8 is a schematic diagram illustrating the correlation between adjacent pixels before and after an image Lena passes through an encryption system according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings.
The invention takes CS and OCML as the basis, designs a high-low two-level hierarchical bit-level encryption scheme, and referring to FIG. 1, the image encryption method comprises the following steps:
step 1, substituting the Logistic mapping with the Optimized parameter value range into a bidirectional Coupled mapping Lattice model to obtain a novel multidimensional chaotic system, which is called an Optimized Coupled Mapping Lattice (OCML) system.
The Logistic mapping iterative equation for optimizing the value range of the parameter value is as follows:
xn+1＝sin((f+500)·π·xn·(1-xn))·cos((f+500)·π·xn·(1-xn))·2
wherein, f, xnAnd xn+1Respectively representing the nth element value and the (n +1) th element value of the system parameter and the system state variable iteration sequence, wherein the value ranges of the nth element value and the (n +1) th element value are (0,0.8), (0,1) and (0, 1);
the two-way coupling mapping trellis model is xn+1(i)＝(1-ε)·y(xn(i))+ε/2·(y(xn(i-1))+y(xn(i +1))), wherein epsilon is a coupling coefficient, and the value range is (0, 1); n represents the index number of the state variable iteration sequence; i denotes a lattice number, and i ═ 1, 2. L represents the number of lattices of the model; and the function y (-) represents a Logistic mapping iterative equation with the optimized parameter value range.
And 2, extracting information such as parameter values, initial values and the like required by the operation of the OCML system from the key so as to generate a chaotic encryption sequence.
Specifically, by substituting information such as system parameter values, state variable iteration initial values, lattice numbers, coupling parameters and the like extracted from the key into the OCML system, a discrete value sequence with a required length can be generated in an iterative manner, and the sequence is a chaotic sequence which has the characteristics of determining randomness, boundedness, traversability and the like and can be used for encryption.
Step 3, because the number of elements required for constructing the circular measurement matrix is small, and the performance of the circular measurement matrix is equivalent to that of a Gaussian measurement matrix, the CS-based encryption algorithm usually uses an encryption sequence to construct the measurement matrix in the circular matrix form. The structure of the cyclic matrix is as follows:
Figure BDA0002185423430000051
wherein m is the row number of the measurement matrix, and the ratio of the row number of the measurement matrix to the column number n of the measurement matrix is the compression ratio in the measurement process; constant coefficient
Figure BDA0002185423430000052
Is a normalized scale factor and is used for realizing the column normalization of the matrix; a is1、a2、am-1、…、amAn encryption sequence is iteratively generated for the OCML system.
The chaotic performance of the OCML system is evaluated by using the common KS (Kolmogorov-Sinai) entropy density and KS entropy breadth. The concrete formula is as follows:
Figure BDA0002185423430000053
hu＝L+/L
wherein L represents the number of cells of the coupling map lattice model, λ+(i) Denotes a positive Lyapunov exponent value, L, under the trellis index i+Denotes the Lyapunov exponent value as the number of positive lattices. According to the definition, the corresponding KS entropy density h and KS entropy breadth hu in the proposed model can be calculated according to the Lyapunov index, and a curved surface graph is drawn according to different coupling coefficients epsilon and parameter values f. As can be seen from fig. 2 and 3, the OCML system does not have a period window in all parameter value intervals and lattice sequence number ranges, and can stably operate in a chaotic state, so that the iterative sequence value thereof can be directly used for generating an encryption sequence. In addition, the value range of the parameter value f of the OCML reaches (0,0.8), and the experimental result also proves the beneficial effect of the technical scheme of the invention.
The bit-level image encryption method provided by the invention divides the plaintext image information into high bit position information xhAnd low bit position information xlTwo-stage measurement is carried out respectively, so that the information such as parameter values and initial values required by an OCML system for constructing two-stage measurement matrixes needs to be extracted from the secret key so as to generate two groups of different encryption sequences S1And S2And then constructed based on the circulant matrix structureMeasurement matrix phihAnd phil。
Step 4, using the measurement matrix phihFor high bit position information xh(main information of image) to obtain a measured value yh(ii) a Using a measurement matrix philFor low bit position information xl(secondary information of image) to obtain a measured value yl。
The high bit position information xhAnd low bit position information xlRespectively, to the high and low portions of a digital image element value represented in binary sequence form. Since images of different forms can be regarded as superposition combination of 8-bit gray level images, without loss of generality, all images are assumed to be of the size
Figure BDA0002185423430000061
The 8-bit gray level map means that the pixel points in the horizontal axis and the vertical axis of the image are all pixels
Figure BDA0002185423430000062
The root number is n, so that the whole image has n pixel points, and the sequence xhAnd xlIs also n, which requires the number of columns of the measurement matrix to be n. Thus, the value P of the ith row and jth column element in the plaintext image P can be obtainedi,jData viewed as binary form
Figure BDA0002185423430000063
Wherein the high-bit position information is data composed of 4-bit binary number
Figure BDA0002185423430000064
The low-bit position information is data composed of 4-bit binary number
Figure BDA0002185423430000065
Arranging high bit position information in all element values of a plaintext image in sequence to form a vector xhThe low bit position information is ordered to form a vector xl. The measurement process is a product operation of the measurement matrix and the vectorized image information, i.e. yh＝Φh·xh、yl＝Φl·xl。
Step 5, in order to avoid adding extra data volume during information transmission, the measurement result needs to be quantized. In particular, the high bit position measurement yhQuantized value Q ofhAnd low bit position measurement ylQuantized value Q oflAre all 4-bit binary numbers, and the quantization process is performed in a uniform quantization manner.
And 6, scrambling and replacing the quantized values by using the two encrypted sequences, and recombining the data obtained after operation into a final ciphertext image according to the weight.
Scrambling: using an encryption sequence S of length 2m3Sequence of ordered series numbers to a sequence of quantized values Q of length mhAnd QlRe-ordering to obtain the scrambled sequence Qrc hAnd Qrc l；
And (3) replacing: using an encryption sequence S of length 2m4For Q with length of mhAnd QlCarrying out XOR operation to obtain a replaced sequence ChAnd ClThe operation formula is
Figure BDA0002185423430000066
And
Figure BDA0002185423430000067
combining: sequence C with length of mhAnd ClRecombining into an 8-bit binary number sequence in a combination mode of C ═ Ch·24+ClAnd C is the final ciphertext image.
In one embodiment, using image encryption in a wireless sensor network as an application background, a block diagram of an encryption system is shown in fig. 4. Since different forms of images can be regarded as the superposition combination of 8-bit gray-scale images, and without loss of generality, an 8-bit gray-scale digital image with the size of 256 × 256 is taken as an example, and the whole encryption operation process is as follows.
Step a: slave cipherExtracting information such as parameter values and initial values required by the operation of the OCML system from the key, and substituting the information into the OCML1, the OCML2, the OCML3 and the OCML4 to generate a corresponding chaotic encryption sequence S1、S2、S3And S4. Wherein S is1And S2Length n, S3And S4The length is 2 m;
step b: based on the encryption sequence S according to the compression ratio set during the compressed sensing measurement1And S2Constructing a matrix phi in the form of a circulant matrixhAnd philRespectively as plaintext image high bit position information xhAnd low bit position information xlThe measurement matrix of (2). The specific scheme is as follows:
Figure BDA0002185423430000071
Figure BDA0002185423430000072
wherein m is the number of rows of the measurement matrix; constant coefficient
Figure BDA0002185423430000073
Is a normalized scale factor;
step c: using the measurement matrix phi separatelyhAnd philFor information xhAnd xlMeasuring to obtain corresponding measured value yhAnd ylThe calculation process is yh＝Φh·xh、yl＝Φl·xl；
Step d: measured value yhAnd ylRespectively quantizing the signals to 4-bit binary numbers to obtain quantized high-order information sequences QhAnd a low order information sequence Ql；
Step e: calculating to obtain a sequence S with the length of 2m3The serial numbers arranged according to the size, and the pair of Q with the length of mhAnd QlReordering to obtain sequence Qrc hAnd Qrc l；
Step f: using a sequence S of length 2m4For sequences Q with length of mrc hAnd Qrc lCarrying out XOR operation to obtain a replaced sequence ChAnd ClThe operation formula is
Figure BDA0002185423430000074
And
Figure BDA0002185423430000075
step g: sequence C with length of mhAnd ClRecombining into an 8-bit binary number sequence in a combination mode of C ═ Ch·24+ClAnd C is the final ciphertext image.
As shown in fig. 4, the above steps a to g are the complete encryption process in the front-end sensing node. The resulting ciphertext image C may be affected by noise or other interference as it passes through the transmission channel, with the ciphertext image C' representing the data received by the end user.
As shown in fig. 4, the end user decrypts the received ciphertext image information C 'to obtain a reconstructed image x', which is an estimation of scene information (plaintext image) acquired by the front-end sensing node. The entire decryption process can be viewed as the inverse operation of the encryption process. First, ciphertext image information C ' is decomposed into higher-order information C ' by weight 'hAnd low bit information C'l(ii) a Which are then separately subjected to inverse substitution, inverse scrambling and inverse quantization operations to derive an estimate y 'of the compressed perceptual measurement'hAnd y'l(ii) a Then, an estimate x 'of the plaintext image high bit position information is reconstructed from the measured values based on a compressed perceptual reconstruction algorithm (e.g., orthogonal matching pursuit)'hAnd estimate x 'of low bit position information'lAnd finally x ' to x ' by weight 'h·24+x'lThe method of (1) recombines the high and low bit position information into a reconstructed image x', which is an estimate of the scene information (plaintext image x).
In order to evaluate the security performance of the encryption method proposed by the present inventionThe size of its key space is analyzed. According to the definition of the OCML model, a mapping parameter f, a coupling parameter epsilon and an iteration initial value x are needed0Number of cells L and number of cells LindexAnd the value of the variable is equal. Assuming that the data precision is 16bits, according to the structure diagram of the encryption system shown in fig. 4, the whole encryption method needs a key stream with a length exceeding 256bits, i.e. the system satisfies 2 bits in the information security theory112Key space requirements. Of course, according to actual conditions and requirements, the size of the key space can be dynamically adjusted by limiting certain parameters to be constant or improving data accuracy during use.
In order to evaluate the key sensitivity of the encryption method proposed by the present invention, the image Lena is analyzed as an example. In the encryption process, a key sequence K is assumed1And K2Generation of the scrambling sequence S only at the control OCML33Are slightly different, resulting in a de-read mapping initial value x0There is a deviation of 0.001. Fig. 5 and 6 illustrate an image Lena as an example, and respectively prove that slight deviations of the key during encryption and decryption will cause significant differences in the encryption and decryption results. Fig. 5(a) is an image Lena original; FIG. 5(b) shows an image Lena with a key K1A ciphertext image is obtained after the ciphertext image is encrypted by an encryption system; FIG. 5(c) shows an image Lena with a key K2And (4) obtaining a ciphertext image after encryption by an encryption system. Wherein the secret key K2And K1In contrast, there is only a slight difference in the portion that controls OCML3 to generate the scrambling sequence, resulting in an iterative initial value x for the solution read0There is a deviation of 0.001; FIG. 5(d) shows an image Lena with a key K1And K2And respectively obtaining a pixel difference distribution diagram between the ciphertext images after being encrypted by the encryption system. In the decryption example, fig. 6(a) shows an image Lena original image; FIG. 6(b) shows an image Lena with a key K1A reconstructed image is obtained after encryption and decryption by an encryption system; FIG. 6(c) shows an image Lena with a key K1Encrypted by an encryption system and with a key K2And obtaining a reconstructed image after decryption by the encryption system. Wherein the secret key K2And K1In contrast, there is only a slight difference in the portion controlling OCML3 to generate the scrambling sequence, resulting in a de-readIteration initial value x0There is a deviation of 0.001; FIG. 6(d) shows an image Lena with a key K1A reconstructed image obtained by encryption and decryption through an encryption system and a secret key K1Encrypted by an encryption system and with a key K2And obtaining a pixel difference distribution diagram between the reconstructed images after decryption.
The statistical histogram of the digital image often reveals important information to an information thief, so the important information needs to be hidden in the encryption process. The ability of hiding image statistical characteristics of the encryption method provided by the invention is evaluated by taking the image Lena as an example. Fig. 7 shows that the encryption system converts the specific statistical features of the original image into a uniformly distributed state in the ciphertext image, which meets the requirement of hiding the statistical information of the image, where fig. 7(a) is a statistical histogram of the original image Lena; fig. 7(b) is a statistical histogram of a ciphertext image of the Lena image after passing through the encryption system.
There is always some correlation between adjacent pixels of meaningful digital images, and ciphertext images need to eliminate this feature to improve the anti-cracking ability. In order to evaluate the capability of eliminating the correlation between adjacent pixels of the encryption method provided by the invention, the image Lena is taken as an example to randomly select 900 adjacent pixel points in the horizontal direction, the vertical direction and the diagonal direction respectively from a plaintext image and a corresponding ciphertext image of the image Lena for analysis. As can be seen from fig. 8, the correlation between adjacent pixels of the encrypted ciphertext image is significantly reduced. Fig. 8(a) shows the correlation of the original image Lena in the vertical direction; fig. 8(b) is the correlation of the ciphertext image of the image Lena after being encrypted in the vertical direction; fig. 8(c) is the correlation of the original image Lena in the horizontal direction; fig. 8(d) is the correlation of the ciphertext image of the image Lena after being encrypted in the horizontal direction; fig. 8(e) is the correlation of the original image Lena in the diagonal direction; fig. 8(f) is the correlation in the diagonal direction of the ciphertext image after the image Lena is encrypted.
Aiming at the defects of the existing bit-level image encryption method based on the CS and the chaotic system, the invention substitutes Logistic mapping with optimized parameter value range into the OCML system constructed by the bidirectional coupling mapping lattice model to be used as a chaotic sequence generator, thereby improving the chaotic performance of the encryption sequence. In addition, the invention respectively acquires the main information and the secondary information of the image by using the high-low two-stage measurement matrix, and places the main information of the image in the high-bit position part of the ciphertext image and places the secondary information of the image in the low-bit position part of the ciphertext image. Compared with the existing bit-level image encryption method, the method provided by the invention obviously simplifies the operation steps, so that the running expense of an encryption system is smaller and the efficiency is higher.

Claims (1)

1. A bit-level image encryption method based on compressed sensing and optimized coupled-mapping trellis, the method comprising the steps of:
(1) building an optimized coupling mapping lattice OCML system by substituting the Logistic mapping with the optimized parameter value range into a bidirectional coupling mapping lattice model, wherein the Logistic mapping iterative equation with the optimized parameter value range is as follows:
xn+1＝sin((f+500)·π·xn·(1-xn))·cos((f+500)·π·xn·(1-xn))·2
wherein f, xnAnd xn+1Respectively representing the system parameter value, the nth element value and the (n +1) th element value of the system state variable iteration sequence;
the bidirectional coupling mapping grid model is as follows:
xn+1(i)＝(1-ε)·y(xn(i))+ε/2·(y(xn(i-1))+y(xn(i+1)))
wherein ε is the coupling coefficient; n represents the index number of the state variable iteration sequence; i denotes a lattice number, and i ═ 1, 2. L represents the number of lattices of the model; the function y (·) represents a Logistic mapping iterative equation with optimized parameter value range;
(2) extracting system parameter values, state variable iteration initial values, lattice numbers and coupling parameters required by the operation of the OCML system from the key to generate four groups of different encryption sequences S1、S2、S3And S4；
(3) Dividing all element values in an image into high bit position information x by bit positionhAnd low bitLocation information xlBased on the encryption sequence S, respectively1And S2Constructing matrix phi in form of circulant matrixhAnd philAs the above information xhAnd xlThe high bit position information x of the imagehAnd low bit position information xlRespectively refer to the high-order part and the low-order part in the image element value expressed in the form of binary sequence, and the construction method is as follows: representing the image by 8-bit gray scale map, wherein the element values P of the ith row and the jth column in the imagei,jData in binary form
Figure FDA0002879023650000011
Wherein the high bit position information is a four-bit binary number
Figure FDA0002879023650000012
The data is composed of low bit position information of four-bit binary number
Figure FDA0002879023650000013
Composed data, high bit position information in all element values are arranged in sequence to form vector xhThe low bit position information is ordered to form a vector xl；
The structure of the cyclic matrix is as follows:
Figure FDA0002879023650000021
wherein m is the row number of the measurement matrix, and the ratio of the row number of the measurement matrix to the column number n of the measurement matrix is the compression ratio in the measurement process; constant coefficient
Figure FDA0002879023650000022
Is a normalized scale factor and is used for realizing the column normalization of the matrix; a is1、a2、…、anGenerating an encrypted sequence value for the OCML system iteration;
(4) using a measurement matrix phihAnd philHigh bit position information x for respective imageshAnd low bit position information xlMeasuring to obtain corresponding measured value yhAnd yl(ii) a The measurement value is the product of the measurement matrix and the vectorized image information, i.e. the measurement value yh＝Φh·xhMeasured value yl＝Φl·xl；
(5) Measured value yhAnd ylRespectively quantizing to obtain quantized value Q of high bit position measured valuehAnd the quantized value Q of the low bit position measurementl(ii) a The high bit position measurement yhQuantized value Q ofhAnd low bit position measurement ylQuantized value Q oflAll the sequences are sequences formed by 4-bit binary numbers, and the quantization process is carried out in a uniform quantization mode;
(6) using an encryption sequence S3And S4For the quantized value QhAnd QlScrambling and replacing operations are carried out, and data obtained after the operations are recombined into a final ciphertext image C according to weights; the scrambling operation is to use an encryption sequence S with a length of 2m3Sequence numbers in size to Q of length mhAnd QlReordering to obtain sequence Qrc hAnd Qrc lWherein m is the number of rows of the measurement matrix; the replacement operation is to use an encryption sequence S of length 2m4For sequence Qrc hAnd Qrc lExecuting XOR operation to obtain a ciphertext sequence ChAnd ClThe operation process is
Figure FDA0002879023650000023
And
Figure FDA0002879023650000024
the combination process is C (k) ═ Ch(k)·24+Cl(k) And k is 1, 2.. times, m, wherein C (k) is the k-th element value in the ciphertext image C.
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