CN108810313A - Image encryption method based on high-dimension chaotic system and QR codes in revolution domain - Google Patents
Image encryption method based on high-dimension chaotic system and QR codes in revolution domain Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
- H04N1/32—Circuits or arrangements for control or supervision between transmitter and receiver or between image input and image output device, e.g. between a still-image camera and its memory or between a still-image camera and a printer device
- H04N1/32101—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title
- H04N1/32144—Display, printing, storage or transmission of additional information, e.g. ID code, date and time or title embedded in the image data, i.e. enclosed or integrated in the image, e.g. watermark, super-imposed logo or stamp
- H04N1/32149—Methods relating to embedding, encoding, decoding, detection or retrieval operations
- H04N1/32267—Methods relating to embedding, encoding, decoding, detection or retrieval operations combined with processing of the image
- H04N1/32272—Encryption or ciphering
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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
- H04L9/001—Cryptographic mechanisms or cryptographic arrangements for secret or secure communications; Network security protocols using chaotic signals
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N1/00—Scanning, transmission or reproduction of documents or the like, e.g. facsimile transmission; Details thereof
- H04N1/44—Secrecy systems
- H04N1/448—Rendering the image unintelligible, e.g. scrambling
- H04N1/4486—Rendering the image unintelligible, e.g. scrambling using digital data encryption
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Abstract
The invention discloses a kind of image encryption methods based on high-dimension chaotic system and QR codes in revolution domain, include that image to be encrypted is converted to corresponding QR codes f (x by the encryption to original plaintext image and decryption first, y), later by itself and random phase mask r1(x, y) and r2(x', y') carries out revolution transformation, obtains ciphertext image, and guesses the initial estimate f of QR codes0(x,y)；It is iterated in simulated optical system, optics product g will be obtainedk(x "; y ") in amplitude portion replaced carrying out revolution transformation with ciphertext image, the last correlation coefficient value CC using it between QR codes again is as convergence criterion, it is constrained three position detection patterns of QR codes as support, as correlation coefficient value CC=0.9978, terminate iteration to get to the QR codes of decryption.This method has very strong robustness to occlusion attack, attacked by noise, key brute force attack, and has damage resistance ability.
Description
Technical field
The invention belongs to technical field of image processing, and in particular to one kind is based on high-dimension chaotic system and QR codes in revolution domain
Image encryption method.
Background technology
It is well known that realizing that safety of image has become an important subject in recent decades using optical technology.
Since Refregier and Javidi propose the famous figure based on Double random phase (DRPE) in Fourier transform domain
Since encryption system structure, lot of domestic and international experts and scholars have been proposed largely utilizing the image encryption of different optical technologies
Scheme provides potential solution for pure optics cryptographic system.In recent years, Javidi et al., which is outlined, utilizes free space
Optics is in potentiality, latest developments and the challenge for encrypting direction, such as new image encryption method, data compression, phase retrieval calculation
Method, the realization of nanometer or micro-meter scale, ghost image imaging and quantum imaging.
Due to intrinsic linear problem, the Image Encryption Scheme based on DRPE frameworks have serious security risk, i.e., it
It is easy to be attacked by several forms, such as known plain text attack.In order to enhance safety, the architecture based on DRPE is
Various transform domains are expanded to, such as fractional Fourier transform domain, fresnel transform domain, the domain rotator transform (GT), score angular transformation
Domain, score stochastic transformation domain, fractional mellin transform domain, circulator wavelet transformed domain and lifting wavelet transform frequency domain etc..These sides
The output of case is typically the amplitude distribution of complexity, since the optical elements such as spatial light modulator cannot record phase and amplitude simultaneously
Data, therefore be not easy to store and transmit.In order to avoid complicated data are considered as ciphertext, since Zhang Yan and Wang Bo is initially proposed
Normal image is encrypted as two pure phase masks (POMs) without using iterative calculation, therefore is proposed largely based on interference
Scheme.When disposing any one synthesis mask during decryption, the profile information of normal image can be speculatively detected.
In addition, experts and scholars also proposed the Image Encryption Scheme largely based on different chaotic maps, wherein normal image can be compiled
Code is real-valued function.
Invention content
The object of the present invention is to provide a kind of image encryption method based on high-dimension chaotic system and QR codes in revolution domain, solutions
It has determined the problem of reconstruction image problem of dtmf distortion DTMF existing in the prior art and key management inconvenience.
The technical solution adopted in the present invention is the image encryption side based on high-dimension chaotic system and QR codes in revolution domain
Method includes the encryption to original plaintext image and decryption, is as follows：
The ciphering process, specifically includes following steps：
Step 1, image to be encrypted is converted into corresponding QR codes f (x, y)；
Step 2, optical analog modulation is carried out to the QR code f (x, y) obtained after step 1, modulated process is as follows：By QR codes f
(x, y) and random phase mask r1(x, y) is multiplied, and it is α to carry out rotation angle1Revolution transformation, later again with random phase
Position mask r2(x', y') is multiplied, and it is α to carry out rotation angle2Revolution convert to get to ciphertext image；
The decrypting process, specifically includes following steps：
Step 3, according to the ciphertext image obtained in step 2, guess the initial estimate f of QR codes0(x,y)；
Step 4, in simulated optical system, by the initial estimate f of the QR codes obtained after step 30(x, y) is being carried out
F when kth time iterationk(x, y) is irradiated by coherent parallel lights, and with random phase mask r1(x, y) is multiplied, and is rotated
Angle is α1Revolution transformation, later again by the initial estimate f of QR codes0(x, y) and random phase mask r2(x', y') is carried out
It is multiplied, and it is α to carry out rotation angle2Revolution transformation, obtain optics product gk(x″,y″)；
Step 5, the optics product g that will be obtained after step 4kAmplitude portion in (x ", y ") is replaced with ciphertext image, and
It keeps phase bit position constant, obtains optics product
Step 6, by the optics product after step 5Progress rotation angle is α1It is α with rotation angle2Return
Transformation is changed, and optics product is obtained
Step 7, the optics product that will be obtained after step 6Correlation coefficient value CC between QR codes is as receipts
Criterion is held back, using three position detection patterns of QR codes as supporting to constrain, as correlation coefficient value CC=0.9978, terminates to change
In generation, is to get to the QR codes of decryption.
The features of the present invention also characterized in that
In step 2, ciphertext image, as shown in formula (1)：
It is α for rotation angle1Revolution transformation,It is α for rotation angle2Revolution transformation.
In step 2, random phase mask r1(x,y)、r2(x', y'), rotation angle α1With rotation angle α2By Chen systems
System is random to be generated, and is as follows：
The Chen systems, as shown in formula (2)：
In formula (2), control parameter a=35, control parameter b=3, control parameter c ∈ [20,28.4]；
Step 2.1, Chen systems are iterated, enable x0=0.25, y0=1.005 and z0=0.35, then generate three not
The same random sequence x with aperiodic and non-convergent propertyi、yiAnd zi；
Step 2.2, by the random sequence x of the middle generation after step 2.1iAnd yi, retain last m × n iteration respectively
Value, formation sequence S1And S2, as shown in formula (3) and formula (4)：
S1=2 π × ((abs (xi)-floor(abs(xi)))×1014mod(256))/255 (3)；
S2=2 π × ((abs (yi)-floor(abs(yi)))×1014mod(256))/255 (4)；
Step 2.3, the sequence S that will be obtained after step 2.21And S2(reshape (S are carried out respectively1, [], m × n)),
(reshape(S2, [], m × n)) arrangement, that is, obtain two-dimensional matrix S1' (i, j) and S2' (i, j), such as formula (5) and formula (6) institute
Show：
{S1' (i, j) | i=1,2 ..., M；J=1,2 ..., N } (5)；
{S2' (i, j) | i=1,2 ..., M；J=1,2 ..., N } (6)；
Step 2.4, the two-dimensional matrix S that will be obtained after step 2.31' (i, j) and S2' (i, j) respectively carry out (r1(x,y)
=exp (is1' (i, j)) and (r2(x ', y ')=exp (is '2(i, j)) operation, you can obtain random phase mask r1(x, y) and
r2(x′,y′)；
Step 2.5, after step 2.4, retain random sequence ZiIt is last 2K value, formation sequence S3, such as formula (7) institute
Show：
S3=floor ((abs (zi)-floor(abs(zi)))×1014) (7)；
Step 2.6, in the coordinate (m for after step 2.5, randomly selecting either element in flat imagei,ni), coordinate mi
With coordinate ni, respectively as shown in formula (8) and formula (9)：
mi=S3(2i)modM (8)；
ni=S3(2i+1)modN (9)；
Wherein, in formula (8) and formula (9)：I=1,2 ... k；
Step 2.7, after step 2.6, by coordinate miWith coordinate niIt carries out advising such as the calculating of formula (10) and formula (11) respectively
Then, rotation angle α is obtained1With rotation angle α2；
In step 4, optics product gk(x ", y "), as shown in formula (12)：
In step 5, optics productAs shown in formula (13)：
In formula (13), arg (gk(x ", y ")) it is used for the phase bit position of extracting parameter.
In step 6, optics productAs shown in formula (14)：
In formula (14)：It is α for rotation angle1Reverse back transformation change,For rotation angle α2Reverse back transformation
It changes；Conj () is the conjugate of return parameters.
In step 7, convergence criterion, as shown in formula (15) and formula (16)：
In formula (15), β is adjustment parameter, the convergence rate for adjusting iterative process, β=0.09；γ is adjustment parameter,
For ensureing that the denominator in formula (16) is not zero, γ=0.0001；E [] is desired value operator.
The invention has the advantages that the ciphertext in this method is real-valued function, convenient for storing and transmitting for ciphertext；And only
There are three initial values of Chen systems to be used as private key, key management is convenient；In addition, due to Chen system initial value high sensitivities,
Therefore, the safety of the algorithm is substantially increased；It is generated simultaneously as the parameters such as rotation angle of rotator transform are mutual informations
, it cannot directly access, therefore also there is very strong resistivity to the various possible attacks such as known plain text attack.
Description of the drawings
Fig. 1 is that the present invention is based on to be added in the image encryption method embodiment of high-dimension chaotic system and QR codes in revolution domain
Close image；
Fig. 2 is that the present invention is based on QR codes in the image encryption method embodiment of high-dimension chaotic system and QR codes in revolution domain to scheme
Picture；
Fig. 3 is that the present invention is based on the ciphertexts in the image encryption method embodiment of high-dimension chaotic system and QR codes in revolution domain
Image；
Fig. 4 is that the present invention is based on random in the image encryption method embodiment of high-dimension chaotic system and QR codes in revolution domain
Phase mask image r1(x,y)；
Fig. 5 is that the present invention is based on random in the image encryption method embodiment of high-dimension chaotic system and QR codes in revolution domain
Phase mask image r2(x′,y′)；
Fig. 6 be the present invention is based in revolution domain in the image encryption method embodiment of high-dimension chaotic system and QR codes from QR codes
Three position detection patterns of middle extraction；
Fig. 7 is that the present invention is based on pass through solution in the image encryption method embodiment of high-dimension chaotic system and QR codes in revolution domain
Close obtained QR code images；
Fig. 8 is that the present invention is based on restore in the image encryption method embodiment of high-dimension chaotic system and QR codes in revolution domain
Original image；
Fig. 9 is that the present invention is based on initial Q R in the image encryption method embodiment of high-dimension chaotic system and QR codes in revolution domain
Calculated CC curve graphs between code and decryption QR codes；
Figure 10 be the present invention method in as initial value x0When with little deviation, counted between initial Q R codes and decryption QR codes
The CC curve graphs of calculating；
Figure 11 be the present invention method in as initial value y0When with little deviation, counted between initial Q R codes and decryption QR codes
The CC curve graphs of calculating；
Figure 12 be the present invention method in as initial value z0When with little deviation, counted between initial Q R codes and decryption QR codes
The CC curve graphs of calculating；
Figure 13 is that the present invention is based on mistake during the image encryption method of high-dimension chaotic system and QR codes is implemented in revolution domain is first
Initial value x0Decrypted image；
Figure 14 is that the present invention is based on mistake during the image encryption method of high-dimension chaotic system and QR codes is implemented in revolution domain is first
Initial value y0Decrypted image；
Figure 15 is that the present invention is based on mistake during the image encryption method of high-dimension chaotic system and QR codes is implemented in revolution domain is first
Initial value z0Decrypted image；
Figure 16 is the image of 20% occlusion attack in ciphertext image to be decrypted in the method for the present invention；
Figure 17 is the QR codes restored when 20% occlusion attack in ciphertext image to be decrypted in the method for the present invention；
Figure 18 is scanned when being 20% occlusion attack in ciphertext image to be decrypted in the method for the present invention by the QR codes restored
The original image arrived.
Specific implementation mode
The following describes the present invention in detail with reference to the accompanying drawings and specific embodiments.
The present invention is based on the image encryption methods of high-dimension chaotic system and QR codes in revolution domain, including to original plaintext image
Encryption and decryption, be as follows：
Ciphering process specifically includes following steps：
Step 1, image to be encrypted is converted into corresponding QR codes f (x, y)；
Optical analog modulation is carried out to the QR code f (x, y) obtained after step 1, modulated process is as follows：By QR code f (x, y) with
Random phase mask r1(x, y) is multiplied, and it is α to carry out rotation angle1Revolution transformation, later again with random phase mask
r2(x', y') is multiplied, and it is α to carry out rotation angle2Revolution convert to get to ciphertext image, as shown in formula (1)：
It is α for rotation angle1Revolution transformation,It is α for rotation angle2Revolution transformation；
Wherein, random phase mask r1(x,y)、r2(x', y'), rotation angle α1With rotation angle α2By Chen systems
It is random to generate, it is as follows：
Wherein, Chen systems, as shown in formula (2)：
In formula (2), control parameter a=35, control parameter b=3, control parameter c ∈ [20,28.4]；
Step 2.1, Chen systems are iterated, enable x0=0.25, y0=1.005 and z0=0.35, then generate three not
The same random sequence x with aperiodic and non-convergent propertyi、yiAnd zi；
Step 2.2, by the random sequence x of the middle generation after step 2.1iAnd yi, retain last m × n iteration respectively
Value, formation sequence S1And S2, as shown in formula (3) and formula (4)：
S1=2 π × ((abs (xi)-floor(abs(xi)))×1014mod(256))/255 (3)；
S2=2 π × ((abs (yi)-floor(abs(yi)))×1014mod(256))/255 (4)；
Step 2.3, the sequence S that will be obtained after step 2.21And S2(reshape (S are carried out respectively1, [], m × n)),
(reshape(S2, [], m × n)) arrangement, that is, obtain two-dimensional matrix S1' (i, j) and S2' (i, j), such as formula (5) and formula (6) institute
Show：
{S1' (i, j) | i=1,2 ..., M；J=1,2 ..., N } (5)；
{S2' (i, j) | i=1,2 ..., M；J=1,2 ..., N } (6)；
Step 2.4, the two-dimensional matrix S that will be obtained after step 2.31' (i, j) and S2' (i, j) respectively carry out (r1(x,y)
=exp (is1' (i, j)) and (r2(x ', y ')=exp (is '2(i, j)) operation, you can obtain random phase mask r1(x, y) and
r2(x′,y′)；
Step 2.5, after step 2.4, retain random sequence ZiIt is last 2K value, formation sequence S3, such as formula (7) institute
Show：
S3=floor ((abs (zi)-floor(abs(zi)))×1014) (7)；
In formula (7), abs is used to obtain the nearest integer of parameter for calculating absolute value, floor；
Step 2.6, it is (m after step 2.5, randomly selecting either element coordinate in flat imagei,ni), coordinate mi
With coordinate ni, respectively as shown in formula (8) and formula (9)：
mi=S3(2i)modM (8)；
ni=S3(2i+1)modN (9)；
Wherein, in formula (8) and formula (9)：I=1,2 ... k；
Step 2.7, after step 2.6, by coordinate miWith coordinate niIt carries out, such as the transformation of formula (10) and formula (11), obtaining respectively
To rotation angle α1With rotation angle α2；
Decrypting process specifically includes following steps：
Step 3, according to the ciphertext image obtained in step 2, guess the initial estimate f of QR codes0(x,y)；
Step 4, in simulated optical system, by the initial estimate f of the QR codes obtained after step 30(x, y) is being carried out
F when kth time iterationk(x, y) is irradiated by coherent parallel lights, and with random phase mask r1(x, y) is multiplied, and is rotated
Angle is α1Revolution transformation, later again by the initial estimate f of QR codes0(x, y) and random phase mask r2(x', y') is carried out
It is multiplied, and it is α to carry out rotation angle2Revolution transformation, obtain optics product gk(x ", y "), as shown in formula (12)：
Step 5, the optics product g that will be obtained after step 4kAmplitude portion in (x ", y ") is replaced with ciphertext image, and
It keeps phase bit position constant, obtains optics productAs shown in formula (13)：
In formula (13), arg (gk(x ", y ")) it is used for the phase bit position of extracting parameter；
Step 6, by the optics product after step 5Progress rotation angle is α1It is α with rotation angle2Return
Transformation is changed, and optics product is obtainedAs shown in formula (14)：
In formula (14)：It is α for rotation angle1Reverse back transformation change,It is α for rotation angle2Reverse back
Transformation is changed；Conj () is the conjugate of return parameters；
Step 7, the optics product that will be obtained after step 6Correlation coefficient value CC between QR codes is as receipts
Criterion is held back, as shown in formula (15) and formula (16), using three position detection patterns of QR codes as supporting to constrain, works as correlation coefficient value
When CC=0.9978, terminate iteration to get to the QR codes of decryption；
In formula (15), β is adjustment parameter, the convergence rate for adjusting iterative process, β=0.09；γ is adjustment parameter,
For ensureing that the denominator in formula (16) is not zero, γ=0.0001；E [] is desired value operator.
Embodiment
The present invention is based on the image encryption methods of high-dimension chaotic system and QR codes in revolution domain, from USC-SIPI image datas
The gray level image " baboon " selected in library is as image to be encrypted, as shown in Figure 1, picture size is 512*512；
Ciphering process specifically includes following steps：
Step 1, image to be encrypted is converted into corresponding QR codes f (x, y), as shown in Figure 2；
Step 2, optical analog modulation is carried out to the QR code f (x, y) obtained after step 1, modulated process is as follows：By QR codes f
(x, y) and random phase mask r1(x, y) is multiplied, and it is α to carry out rotation angle1Revolution transformation, later again with random phase
Position mask r2(x', y') is multiplied, and it is α to carry out rotation angle2Revolution transformation, as shown in Figure 3 to get to ciphertext image,
As shown in formula (1)：
Wherein, random phase mask r1(x,y)、r2(x', y'), rotation angle α1With rotation angle α2By Chen systems
It is random to generate, it is as follows：
Wherein, Chen systems, as shown in formula (2)：
In formula (2), control parameter a=35, control parameter b=3, control parameter c ∈ [20,28.4]；
Step 2.1, Chen systems are iterated, enable x0=0.25, y0=1.005 and z0=0.35, then generate three not
The same random sequence x with aperiodic and non-convergent propertyi、yiAnd zi；
Step 2.2, by the random sequence x of the middle generation after step 2.1iAnd yi, retain last m × n iterative value, shape
At sequence S1And S2, as shown in formula (3) and formula (4)：
S1=2 π × ((abs (xi)-floor(abs(xi)))×1014mod(256))/255 (3)；
S2=2 π × ((abs (yi)-floor(abs(yi)))×1014mod(256))/255 (4)；
Step 2.3, the sequence S that will be obtained after step 2.21And S2(reshape (S are carried out respectively1, [], m × n)),
(reshape(S2, [], m × n)) arrangement, that is, obtain two-dimensional matrix S1' (i, j) and S2' (i, j), such as formula (5) and formula (6) institute
Show：
{S1' (i, j) | i=1,2 ..., M；J=1,2 ..., N } (5)；
{S2' (i, j) | i=1,2 ..., M；J=1,2 ..., N } (6)；
Step 2.4, the two-dimensional matrix S that will be obtained after step 2.31' (i, j) and S2' (i, j) respectively carry out (r1(x,y)
=exp (is1' (i, j)) and (r2(x ', y ')=exp (is '2(i, j)) operation, you can obtain random phase mask r1(x, y) and
r2(x ', y '), as shown in Figures 4 and 5；
Step 2.5, after step 2.4, retain random sequence ZiIt is last 2K value, formation sequence S3, such as formula (7) institute
Show：
S3=floor ((abs (zi)-floor(abs(zi)))×1014) (7)；
In formula (7), abs is used to obtain the nearest integer of parameter for calculating absolute value, floor；
Step 2.6, either element coordinate (m after step 2.5, is being randomly selected in flat imagei,ni), coordinate miWith
Coordinate ni, respectively as shown in formula (8) and formula (9)：
mi=S3(2i)modM (8)；
ni=S3(2i+1)modN (9)；
Wherein, in formula (8) and formula (9)：I=1,2 ... k；
Step 2.7, after step 2.6, by coordinate miWith coordinate niIt carries out advising such as the calculating of formula (10) and formula (11) respectively
Then, rotation angle α is obtained1With rotation angle α2；
Decrypting process is as follows：
Step 3, according to the ciphertext image obtained in step 2, guess the initial estimate f of QR codes0(x,y)；
Step 4, in simulated optical system, by the initial estimate f of the QR codes obtained after step 30(x, y) is being carried out
F when kth time iterationk(x, y) is irradiated by coherent parallel lights, and random phase mask r is used in combination1(x, y) and r2(x', y') is modulated,
Revolution transformation is carried out, and it is α to turn round transformation angle1, later again by the initial estimate f of QR codes0(x, y) and random phase mask
r2(x', y') is modulated, and carries out revolution transformation, and it is α to turn round transformation angle2, obtain optics product gk(x ", y "), such as formula
(12) shown in：
Step 5, the optics product g that will be obtained after step 4kAmplitude portion in (x ", y ") is replaced with ciphertext image, and
It keeps phase bit position constant, obtains optics productAs shown in formula (13)：
Step 6, by the optics product after step 5Progress rotation angle is α1It is α with rotation angle2Return
Transformation is changed, and optics product is obtainedAs shown in formula (14)：
In formula (14)：It is α for rotation angle1Reverse back transformation change,For rotation angle α2Reverse back transformation
It changes；Conj () is the conjugate of return parameters；
Step 7, the optics product that will be obtained after step 6Correlation coefficient value CC between QR codes is as receipts
Criterion is held back, as shown in formula (15) and formula (16), using three position detection patterns of QR codes as supporting to constrain, as shown in fig. 6, working as
When correlation coefficient value CC=0.9978, terminate iteration to get to the QR codes of decryption, as shown in Figure 7；The QR codes of decryption are moved
Moved end scanning can be obtained original image, as shown in Figure 8；
In formula (15), β is adjustment parameter, the convergence rate for adjusting iterative process, β=0.09；γ is adjustment parameter,
For ensureing that the denominator in formula (16) is not zero, γ=0.0001；E [] is desired value operator.
Verify that the present invention is based on high-dimension chaotic system in revolution domain and QR codes in terms of the convergence rate and robustness two
The feasibility of image encryption method.
First, convergence rate：
The calculated CC curve graphs between initial Q R codes and decryption QR codes, as shown in figure 9, from the curve it is found that 200
After secondary iteration, CC values have been above 0.9978.Therefore, this method has preferable performance in convergence rate；
Second, robustness：
Although Chen systems only use three initial values as private key, facilitate key management, due to the height of these keys
Sensitivity so that the safety of this method greatly improves.Chen systems are iterated, as three initial value x0、y0And z0In
When any one is with little deviation, the calculated CC curve graphs between QR codes and original QR codes are decrypted, respectively such as 10, Figure 11
And shown in Figure 12, as seen from the figure, when arbitrary initial value has little deviation, between decrypted obtained QR codes and original QR codes
The equal very little of related coefficient, and its QR code for decrypting, as shown in Figure 13, Figure 14 and Figure 15, decrypted obtained QR codes all cannot
Restore artwork, this shows that the key space of this method is very big, it is sufficient to resist brute force attack.
In addition, the occlusion attack to this method is analyzed, when 20% image in ciphertext image to be decrypted is hidden
When gear, as shown in figure 16, QR codes still can be recovered by the algorithm, as shown in figure 17, and then scan and obtain original image, such as
Shown in Figure 18, which does not have any information loss, this shows that the algorithm has good anti-occlusion attacking ability.
The method of the present invention has very strong robustness, and uses to nasal obstruction attack, attacked by noise, key brute force attack
QR codes, maximum feature, which is QR codes, has damage resistance ability, can more simply store transmission, while improving DRPE skills
Art, only strength retention information can restore the storage and transfer that original image is more conducive to data, and not have information loss.
Claims (7)
1. the image encryption method based on high-dimension chaotic system and QR codes in revolution domain, which is characterized in that including to original plaintext
The encryption and decryption of image, are as follows：
The ciphering process, specifically includes following steps：
Step 1, image to be encrypted is converted into corresponding QR codes f (x, y)；
Step 2, optical analog modulation is carried out to the QR code f (x, y) obtained after step 1, modulated process is as follows：By QR code f (x, y)
With random phase mask r1(x, y) is multiplied, and it is α to carry out rotation angle1Revolution transformation, covered again with random phase later
Film r2(x', y') is multiplied, and it is α to carry out rotation angle2Revolution convert to get to ciphertext image；
The decrypting process, specifically includes following steps：
Step 3, according to the ciphertext image obtained in step 2, guess the initial estimate f of QR codes0(x,y)；
Step 4, in simulated optical system, by the initial estimate f of the QR codes obtained after step 30(x, y) is carrying out kth time
F when iterationk(x, y) is irradiated by coherent parallel lights, and with random phase mask r1(x, y) is multiplied, and carries out rotation angle and be
α1Revolution transformation, later again by the initial estimate f of QR codes0(x, y) and random phase mask r2(x', y') is multiplied, and
Progress rotation angle is α2Revolution transformation, obtain optics product gk(x″,y″)；
Step 5, the optics product g that will be obtained after step 4kAmplitude portion in (x ", y ") is replaced with ciphertext image, and is kept
Phase bit position is constant, obtains optics product
Step 6, by the optics product after step 5Progress rotation angle is α1It is α with rotation angle2Revolution become
It changes, obtains optics product
Step 7, the optics product that will be obtained after step 6Correlation coefficient value CC between QR codes is accurate as convergence
Then, using three position detection patterns of QR codes as supporting to constrain, as correlation coefficient value CC=0.9978, terminate iteration, i.e.,
The QR codes decrypted.
2. the encryption method according to claim 1 based on the image encryption of high-dimension chaotic system and QR codes in revolution domain,
It is characterized in that, in the step 2, ciphertext image, as shown in formula (1)：
It is α for rotation angle1Revolution transformation,It is α for rotation angle2Revolution transformation.
3. the image encryption method according to claim 1 based on high-dimension chaotic system and QR codes in revolution domain, feature
It is, in the step 2, random phase mask r1(x,y)、r2(x', y'), rotation angle α1With rotation angle α2By Chen
System generates at random, is as follows：
The Chen systems, as shown in formula (2)：
In formula (2), control parameter a=35, control parameter b=3, control parameter c ∈ [20,28.4]；
Step 2.1, Chen systems are iterated, enable x0=0.25, y0=1.005 and z0=0.35, then generate three it is different
Random sequence x with aperiodic and non-convergent propertyi、yiAnd zi；
Step 2.2, by the random sequence x of the middle generation after step 2.1iAnd yi, retain last m × n iterative value, shape respectively
At sequence S1And S2, as shown in formula (3) and formula (4)：
S1=2 π × ((abs (xi)-floor(abs(xi)))×1014mod(256))/255 (3)；
S2=2 π × ((abs (yi)-floor(abs(yi)))×1014mod(256))/255 (4)；
Step 2.3, the sequence S that will be obtained after step 2.21And S2(reshape (S are carried out respectively1, [], m × n)),
(reshape(S2, [], m × n)) arrangement, that is, obtain two-dimensional matrix S1' (i, j) and S2' (i, j), such as formula (5) and formula (6) institute
Show：
{S1' (i, j) | i=1,2 ..., M；J=1,2 ..., N } (5)；
{S2' (i, j) | i=1,2 ..., M；J=1,2 ..., N } (6)；
Step 2.4, the two-dimensional matrix S that will be obtained after step 2.31' (i, j) and S2' (i, j) respectively carry out (r1(x, y)=exp
(is′1(i, j)) and (r2(x ', y ')=exp (is '2(i, j)) operation, you can obtain random phase mask r1(x, y) and r2(x′,
y′)；
Step 2.5, after step 2.4, retain random sequence ZiIt is last 2K value, formation sequence S3, as shown in formula (7)：
S3=floor ((abs (zi)-floor(abs(zi)))×1014) (7)；
Step 2.6, in the coordinate (m for after step 2.5, randomly selecting either element in flat imagei,ni), coordinate miAnd seat
Mark ni, respectively as shown in formula (8) and formula (9)：
mi=S3(2i)modM (8)；
ni=S3(2i+1)modN (9)；
Wherein, in formula (8) and formula (9)：I=1,2 ... k；
Step 2.7, after step 2.6, by coordinate miWith coordinate niIt carries out, such as the computation rule of formula (10) and formula (11), obtaining respectively
To rotation angle α1With rotation angle α2；
4. the image encryption method according to claim 1 based on high-dimension chaotic system and QR codes in revolution domain, the step
In rapid 4, optics product gk(x ", y "), as shown in formula (12)：
5. the image encryption method according to claim 1 based on high-dimension chaotic system and QR codes in revolution domain, the step
In rapid 5, optics productAs shown in formula (13)：
In formula (13), arg (gk(x ", y ")) it is used for the phase bit position of extracting parameter.
6. the image encryption method according to claim 1 based on high-dimension chaotic system and QR codes in revolution domain, the step
In rapid 6, optics productAs shown in formula (14)：
In formula (14)：It is α for rotation angle1Reverse back transformation change,For rotation angle α2Reverse back transformation change；
Conj () is the conjugate of return parameters.
7. the image encryption method according to claim 1 based on high-dimension chaotic system and QR codes in revolution domain, the step
In rapid 7, convergence criterion, as shown in formula (15) and formula (16)：
In formula (15), β is adjustment parameter, the convergence rate for adjusting iterative process, β=0.09；γ is adjustment parameter, is used for
Ensure that the denominator in formula (16) is not zero, γ=0.0001；E [] is desired value operator.
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