CN111246047B - Method for realizing image encryption by differential advance and then realizing image restoration by inertial lag - Google Patents

Method for realizing image encryption by differential advance and then realizing image restoration by inertial lag Download PDF

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CN111246047B
CN111246047B CN201911420825.8A CN201911420825A CN111246047B CN 111246047 B CN111246047 B CN 111246047B CN 201911420825 A CN201911420825 A CN 201911420825A CN 111246047 B CN111246047 B CN 111246047B
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CN111246047A (en
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陈育良
肖之才
顾钧元
秦亮
丛林虎
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Naval Aeronautical University
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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
    • 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

Abstract

The invention provides a method for realizing image encryption based on differential lead and realizing image restoration by adopting inertial lag, which is suitable for image encryption transmission in important information fields such as verification codes. The method mainly comprises the steps of firstly grouping picture file data, then carrying out nonlinear double differential advanced transformation encryption, and then carrying out power square and nonlinear compression transformation encryption for transmission. And sequentially carrying out nonlinear inverse transformation and power inverse transformation decryption at a receiving end, and then carrying out double inertia lag transformation, thereby realizing image decryption. The differential advance has good amplification effect, so that the image data can be utilized, and the important information can be well covered, so that the encryption effect is good, the accurate reduction difficulty is high, and the safety is high.

Description

Method for realizing image encryption by differential advance and then realizing image restoration by inertial lag
Technical Field
The invention relates to the field of image encryption and restoration, in particular to a method for realizing image encryption by differential lead and then realizing image restoration by inertial lag, which can be applied to the fields of secret communication, encrypted image processing and the like.
Background
With the rapid development of computer technology and internet technology, more and more private information is transmitted in the network, thereby creating a series of information security problems, such as: illegal stealing, interception, dissemination of data information, etc. Compared with the traditional characters, the image is more visual and colorful, and due to the development of computer storage technology, the use occasions of the image are more and more convenient, so that the safety of image propagation also draws more and more attention of students.
The traditional image encryption algorithm adopts a scrambling algorithm, and the position order of the original image space is changed by quickly scrambling the pixel position, so that the image becomes disordered or can not be identified or is similar to noise. And in some image encryption algorithms, a chaotic system is introduced, and useful signals are covered in chaotic signals by utilizing the chaotic and chapter-free characteristics of the chaotic signals. And then the decryption is realized through chaotic synchronization at the receiving end. However, the above method has problems of poor encryption effect or complicated encryption and restoration.
Because the differential transformation has differential amplification characteristic to noise signals, the irregular image information can be further amplified by utilizing differential lead transformation, thereby achieving the purpose of disordering the original image information arrangement and strengthening the masking effect after transformation. Meanwhile, the differential lead and the inertia lag are a pair of transformations which are opposite in physical meaning, so that the method is very suitable for encryption and decryption restoration. Therefore, the invention adopts differential advance to encrypt the information and adopts inertial lag to restore the information encrypted by the differential advance, thereby obtaining good restoring effect.
It is to be noted that the information invented in the above background section is only for enhancing the understanding of the background of the present invention, and therefore, may include information that does not constitute prior art known to those of ordinary skill in the art.
Disclosure of Invention
The invention aims to provide a method for realizing image encryption and restoration based on differential advance, and further solves the problem that the time sequence superposition utilization rate of the traditional image encryption and restoration algorithm on self data is not high to a certain extent.
According to one aspect of the present invention, there is provided a method for implementing image encryption and restoration based on differential look-ahead, comprising the following steps:
step S10, converting the image data into matrix form, grouping the data, and then carrying out normalization processing;
step S20, carrying out first differential advanced encryption processing on the normalized image data matrix;
step S30, carrying out secondary differential look ahead encryption processing on the image data matrix after the primary differential look ahead transformation;
step S40, the image data matrix after the second differential advanced transformation is processed by power square and nonlinear compression encryption and is sent and transmitted;
step S50, performing nonlinear and power inverse transform decryption processing on the received image data matrix;
step S60, carrying out second inertia lag transformation decryption processing on the image data matrix after the inverse power transformation;
and step S70, carrying out first inertial lag transformation on the image data matrix after the second inertial lag transformation, and then decrypting and outputting the image.
In one exemplary embodiment of the present invention, performing double differential look-ahead encryption processing on an image data matrix comprises:
Figure GDA0003239215210000021
R(0)＝R(1)；
Ra(n)＝R(n)+T1Dr(n)；
Figure GDA0003239215210000031
Figure GDA0003239215210000032
Rc(n)＝Rb(n)+T2Dr2(n)；
Figure GDA0003239215210000033
wherein T is1As a second differential lead parameter, T2For the second derivative lead parameter, dt is the derivative step, and is typically chosen to be 0.001. R (n) is image data, input data for double differential advanced encryption, Rb(n) output data of first differential look-ahead encryption, Dr(n) is the nonlinear differential of the first transformation, Ra(n)、RcAnd (n) is intermediate data. Dr2Is the nonlinear differential of the second transformation. RdAnd (n) is output data of the second differential look-ahead encryption.
In one exemplary embodiment of the present invention, the encrypting process of the image data by the power-of-square and nonlinear compression transform includes:
Figure GDA0003239215210000034
Figure GDA0003239215210000035
wherein R isd(n) output data of the second differential look-ahead encryption, Re(n) is data obtained after power transformation, Rf(n) is data obtained by performing a nonlinear compression transform, wherein k is1、k2、k3、k4、 k5Is a constant parameter.
In one exemplary embodiment of the present invention, performing decryption processing on the reception-side image data by inverse power-wise and nonlinear transformation includes:
Figure GDA0003239215210000036
Figure GDA0003239215210000041
wherein R isg(n) is receiver data, Rh(n) is data after nonlinear inverse transformation, Rdr(n) is the data obtained after inverse power transformation, where k is6、k7、k8、k9、k10Is a constant parameter.
In one exemplary embodiment of the present invention, performing a dual inertial lag transform decryption process on image data comprises:
Figure GDA0003239215210000042
Rcr(n+1)＝Rcr(n)+Dy*dt；
Figure GDA0003239215210000043
Rbr(n+1)＝Rbr(n)+Dy1*dt；
Rcr(1)＝Rdr(1)，Rbr(1)＝Rcr(1)；
wherein R isdr(n) input data of the second inverse lag inertial transformation, DyLinear differentiation of the output data for the second inverse inertial lag transformation, Dy1Linear differentiation of the output data for the first inverse inertial lag transformation; t is2Selecting the second lag parameter as the same as the second differential lead parameter; dt is the integration step length, and is generally selected to be dt-0.001; t is1The first-time lag parameter is selected to be the same as the first-time differential lead parameter. RcrAnd (n) is output data of the first inverse inertial lag transformation. RbrAnd (n) is output data of the second inverse inertia lag transformation and final output data decrypted by the whole double inertia lag transformation.
The method for realizing image encryption and restoration by adopting differential advance provided by the invention enables the data of the image to be applied in a large quantity, and simultaneously adopts nonlinear transformation, nonlinear differentiation and the like to repeatedly cover the main information of the image. And the current position information of the image is repeatedly obscured by differential amplification of the data around the image due to the differential amplification characteristic. Meanwhile, the inertial lag method can better restore the main information of the image. Therefore, the method has good encryption effect and high reduction difficulty, thereby being suitable for encrypting and transmitting important picture information in the fields of finance and military.
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The accompanying drawings, which are incorporated in and constitute a part of this specification, illustrate embodiments consistent with the invention and together with the description, serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
FIG. 1 is a flow chart of a method for implementing image encryption and restoration using differential look-ahead according to the present invention;
FIG. 2 is an original gray image of a beginner student test paper to be encrypted according to the method provided by the embodiment of the invention
FIG. 3 is an encrypted first two student test paper image according to a method provided by an embodiment of the present invention;
FIG. 4 is a decrypted image of a beginner student's test paper according to a method provided by an embodiment of the invention;
Detailed Description
Example embodiments will now be described more fully with reference to the accompanying drawings. Example embodiments may, however, be embodied in many different forms and should not be construed as limited to the examples set forth herein; rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the concept of example embodiments to those skilled in the art. The described features, structures, or characteristics may be combined in any suitable manner in one or more embodiments. In the following description, numerous specific details are provided to provide a thorough understanding of embodiments of the invention. One skilled in the relevant art will recognize, however, that the invention may be practiced without one or more of the specific details, or with other methods, components, devices, steps, and so forth. In other instances, well-known technical solutions have not been shown or described in detail to avoid obscuring aspects of the invention.
The invention provides a method for realizing image encryption and restoration based on differential advance. The method is different from the traditional Fourier transform method, the original image information can be well covered after being encrypted by twice differential advance and power square and nonlinear compression transformation, and meanwhile, the receiving end can restore the main image information of the transmitting end through a lag restoration technology.
The method for implementing image encryption and restoration based on differential look-ahead according to the present invention will be further explained and explained with reference to the accompanying drawings. Referring to fig. 1, the method for implementing image encryption and restoration based on differential look-ahead includes the following steps:
step S10, converting the image data into matrix form, grouping the data, and then carrying out normalization processing;
firstly, storing picture data as a matrix, wherein the picture can be in different formats such as different JPG, PNG and the like, and can be a black-and-white picture or a color picture. For the purpose of classifying the number, it is assumed that the color picture to be encrypted is defined as figure _ c.jpg, stored as a three-dimensional matrix C (i, j, k).
The matrix C (i, j, k) is first decomposed into three two-dimensional sub-matrices C (i, j,1), C (i, j,2) and C (i, j, 3). Since C (i, j,1), C (i, j,2), C (i, j,3) and B (i, j) are all two-dimensional arrays, the following description will take the two-dimensional array B (i, j) as an example, i rows of data of the two-dimensional matrix B (i, j) are divided into i groups on a row basis, each row is a group, and the number of data in each group is j. And then, normalizing the two-dimensional matrix B (i, j), wherein B (i, j) is an integer between 0 and 255 due to the characteristics of image data, each element of the two-dimensional matrix is reduced by 255 times, and the obtained normalized matrix is denoted as B1(i, j).
Step S20, performing first differential look ahead encryption processing on the image data matrix;
the normalized i-group data of B1(i, j) is subjected to the following double differential look-ahead encryption process. Without loss of generality, any set of data is taken as an example to illustrate the processing method, and the set of data is denoted as R (n), which is a one-dimensional array with the length of j.
Firstly, a first differential advanced encryption processing is carried out, and the method comprises the following three steps:
first, a nonlinear differential D is obtainedrThe calculation method is as follows:
Figure GDA0003239215210000061
where dt is the derivative step, which is generally chosen to be dt-0.001, R (0) ═ R (1) is artificially set because R (0) is not present in the array R (n).
Second, calculate the differential superFront output Ra(n) calculated as follows:
Ra(n)＝R(n)+T1Dr(n)
wherein T is1For the first differential lead parameter, the following embodiment is selected in detail.
Finally, saturation limitation is carried out to obtain output Rb(n) that is
Figure GDA0003239215210000071
Step S30, performing a second differential look-ahead encryption process on the data, which is similarly divided into the following three steps:
first, a nonlinear differential D is obtainedr2The calculation method is as follows:
Figure GDA0003239215210000072
where dt is the derivative step, which is generally chosen to be 0.001, due to the array RbR is not present in (n)b(0) Artificially set Rb(0)＝Rb(1)。
Further, a differential lead output R is calculateda(n) calculated as follows:
Rc(n)＝Rb(n)+T2Dr2(n)
wherein T is2For the second differential lead parameter, the following embodiment is selected in detail.
Finally, saturation limitation is carried out to obtain output Rd(n) that is
Figure GDA0003239215210000073
R is to bed(n) as the output of the double differential lead transform.
Step S40, the cubic transform processing of [0,1] section is performed on the data after the second differential look-ahead encryption processing, so that the density of the data increases at the end close to 0: and then carrying out nonlinear transformation to carry out data compression.
Firstly, the output data R after double differential lead conversion is aimed atd(n) performing power conversion to obtain data Re(n) the transformation method is as follows:
Figure GDA0003239215210000074
second to Re(n) obtaining compressed data R by performing nonlinear conversion as followsf(n)
Figure GDA0003239215210000081
Wherein k is1、k2、k3、k4、k5The parameters are selected from the following examples.
For all i in turnaData R obtained by performing the above determination and conversion on 1,2,3, …, jf(n) is the final data after transformation, then the i-line data of the two-dimensional matrix B (i, j) normalized in the step S10 is divided into each group of i groups, and the transformation of the steps S20, S30 and S40 is sequentially carried out to obtain data RiAnd (n) are sequentially arranged according to rows and stored as a two-dimensional matrix B2(i, j), and then are subjected to inverse normalization to restore the two-dimensional matrix into picture data, namely, each element of the two-dimensional matrix B2(i, j) is increased by 255 times and then rounded, and the two-dimensional matrix B3(i, j) is stored. The above description takes a two-dimensional matrix as an example, if the image is a three-dimensional color image, the two-dimensional image encryption process is repeated for three two-dimensional sub-matrices C (i, j,1), C (i, j,2) and C (i, j,3) in step S10, and finally the three two-dimensional matrices B3(i, j) obtained in sequence are stored as a three-dimensional matrix C3(i, j, k), and finally the data of C3(i, j, k) is stored and written into an image file, which is named as set _ C1.jpg, so as to obtain an encrypted color file. The picture is the encrypted picture and can be sent to the receiving end for decryption. The encrypted picture is difficult to extract and is useful even if intercepted by a third partyAnd (4) information.
And step S50, storing the received pictures into arrays at the receiving end, grouping the arrays, firstly performing nonlinear inverse transformation decryption, and then performing cubic inverse operation decryption processing.
After receiving the transmitted encrypted picture configuration _ B1.jpg, the internet or the remote terminal stores the picture data as an array, for example, two-dimensionally denoted as B3(i, j), and performs data normalization and data grouping to obtain data R in the same manner as in step S10g(n)。
Firstly, to the data Rg(n) performing inverse nonlinear transformation as follows, and performing decryption processing to obtain data Rh(n), the transformations of which are described below:
Figure GDA0003239215210000082
secondly, to Rh(n) inverse power transformation is performed to obtain decrypted data R as followsdr(n), the transformations of which are described below:
Figure GDA0003239215210000083
wherein k is6、k7、k8、k9、k10The parameters are selected from the following examples.
And step S60, performing second inertial lag transformation on the data, and outputting the decrypted image.
Firstly, to the data Rdr(n) performing second inertia lag inverse transformation to perform decryption, wherein the decryption comprises the following two steps:
first, an output linear differential D is obtainedyThe calculation method is as follows:
Figure GDA0003239215210000091
wherein T is2For the second lagA number, which is chosen to be the same as the second differential lead parameter. Due to the array Rcr(n) R has not been calculated in the first stepcr(1) Artificially set Rcr(1)＝Rdr(1)。
Further, the cumulative addition method is adopted to calculate the output R of the inertia lag inverse transformationcr(n) calculated as follows:
Rcr(n+1)＝Rcr(n)+Dy*dt
where dt is the integration step, typically chosen to be 0.001. Since the parameter setting of the lag transformation can avoid the occurrence of the saturation problem, it is not necessary to perform the saturation transformation process here. R thus obtainedcr(n) may be used as decrypted data for the second inverse inertial lag transformation.
And step S70, decrypting the data after the first inertial lag transformation, and outputting the image.
For data Rcr(n) performing first inertial lag inverse transformation to perform encryption processing, and also comprising the following two steps:
first, an output linear differential D is obtainedy1The calculation method is as follows:
Figure GDA0003239215210000092
wherein T is1The first-time lag parameter is selected to be the same as the first-time differential lead parameter. Due to the array Rbr(n) R has not been calculated in the first stepbr(1) Artificially set Rbr(1)＝Rcr(1)。
Secondly, the cumulative method is adopted to calculate the output R of the inertia lag inverse transformationbr(n) calculated as follows:
Rbr(n+1)＝Rbr(n)+Dy1*dt
where dt is the integration step, typically chosen to be 0.001. Also, since the parameter setting of the lag transformation can avoid the occurrence of the saturation problem, it is not necessary to perform the saturation transformation process here. R thus obtainedbr(n) isMay be decrypted data as the first inverse inertial lag transformation.
Then, in the same way, each array formed by the i row data of the two-dimensional matrix B3(i, j) in the step S50 is decrypted in turn to obtain a plurality of RbrAnd (n) the two-dimensional matrix B4(i, j) is arranged in sequence according to rows, stored as a two-dimensional matrix B4(i, j), and then is subjected to inverse normalization to restore the two-dimensional matrix into picture data, namely, each element of the two-dimensional matrix B4(i, j) is increased by 255 times and then rounded, and stored as a two-dimensional matrix B5(i, j). For a three-dimensional color picture, a three-dimensional matrix of the color picture needs to be sequentially decomposed into 3 two-dimensional sub-matrices C (i, j,1), C (i, j,2) and C (i, j,3), according to the same decryption method, three two-dimensional matrices B5(i, j) sequentially obtained are finally stored in a unified manner as a three-dimensional matrix C5(i, j, k), and finally, data of C5(i, j, k) are stored and written into a picture file named as figure _ C1r.
Case implementation and computer processing result analysis
In step S10, a black-and-white image will be described as an example. We select the file to be encrypted, as shown in fig. 2, as part of a math paper for a beginner student. Firstly, the image is converted into a gray picture and then encrypted. According to the method of the invention, the pictures are stored as a matrix, then normalized and finally decomposed into arrays. Since the picture pixels are 1140-1080, the matrix has 1140 rows and 1080 columns. The final decomposition is 1140 arrays, each array having 1080 elements.
In steps S20 and S30, differential upfront encryption processing is performed twice on the image data matrix, and the following double differential upfront encryption processing is performed sequentially on the i-group data of B1(i, j) after the normalization. Any group of data R (n) is selected, which is a one-dimensional array with the length of 1080. Selecting dt equal to 0.001 and first differential lead parameter T1Selecting 0.002 as second differential lead parameter T2The selection was 0.001. In step S40, a parameter k is set1＝3、k2＝2、k3＝2、k4＝1、k5＝2。
In step S50, when the picture is received, the picture is first takenStored as a matrix and decomposed into 1140 arrays, each containing 1080 data. Setting parameter k6＝-2,k7＝2,k8＝1,k9＝-2，k41/3. Setting the second-time lag parameter T in steps S60 and S7020.001, the first hysteresis parameter T is set1And setting the integral step dt to be 0.001 and performing double inertia lag transformation on the data to decrypt the image and output the decrypted image to obtain a decrypted number, wherein the integral step dt is 0.002. Finally, all 1140 arrays are decrypted and arranged into two-dimensional arrays, then inverse normalization is performed, that is, the two-dimensional arrays are enlarged by 255 times and then rounded to obtain a picture format matrix array, and finally the picture format matrix array is stored as a picture file and recorded as a decrypted picture file, as shown in fig. 4.
It can be seen that the decrypted file is sparse and can identify the junior middle school mathematics subject information in the picture, but because of the influence of the saturation and nonlinear differential effect in the encryption algorithm, it is difficult to completely recover the very accurate original image information. Therefore, the encryption algorithm is very suitable for the field needing high confidentiality, and even if the picture is stolen and no accurate parameter exists, the picture information is very difficult to restore. For example, in the field of important account and password storage of banks, the technology can be used for encryption and decryption, and once a secret-losing accident occurs, a secret-stealing party cannot obtain important information through stolen pictures.
Other embodiments of the invention will be apparent to those skilled in the art from consideration of the specification and practice of the invention disclosed herein. This application is intended to cover any variations, uses, or adaptations of the invention following, in general, the principles of the invention and including such departures from the present disclosure as come within known or customary practice within the art to which the invention pertains. It is intended that the specification and examples be considered as exemplary only, with a true scope and spirit of the invention being indicated by the following claims.

Claims (3)

1. A method for encrypting an image by differential lead and restoring the image by inertial lag, comprising the steps of:
step S10, converting the image data into matrix form, grouping the data, and then carrying out normalization processing;
step S20, carrying out first differential advanced encryption processing on the image data matrix after the normalization processing;
step S30, carrying out secondary differential advanced encryption processing on the data after the primary differential advanced transformation;
in the step, the first differential advanced encryption processing and the second differential advanced encryption processing are carried out on the picture data in the following modes:
Figure FDA0003239215200000011
R(0)＝R(1)；
Ra(n)＝R(n)+T1Dr(n)；
Figure FDA0003239215200000012
Figure FDA0003239215200000013
Rc(n)＝Rb(n)+T2Dr2(n)；
Figure FDA0003239215200000014
wherein T is1As a second differential lead parameter, T2The second differential lead parameter is dt, the differential step length is dt, and dt is 0.001; r (n) is image data, input data for double differential advanced encryption, Rb(n) output data of first differential look-ahead encryption, Dr(n) is the nonlinear differential of the first transformation, Ra(n)、Rc(n) is intermediate data; dr2Nonlinear differentiation for second differential look-ahead encryption; rd(n) isOutput data of the second differential advanced encryption;
step S40, the data after the second differential advanced transformation is processed by power square and nonlinear compression transformation encryption and is sent and transmitted;
step S50, performing nonlinear and power inverse transform decryption processing on the received image data matrix;
step S60, carrying out secondary inertia lag transformation decryption processing on the data array after power inverse transformation;
the specific way of decrypting the data array subjected to inverse power square transformation by the double inertia lag transformation in the step is as follows:
Figure FDA0003239215200000021
Rcr(n+1)＝Rcr(n)+Dy*dt；
Figure FDA0003239215200000022
Rbr(n+1)＝Rbr(n)+Dy1*dt；
Rcr(1)＝Rdr(1)，Rbr(1)＝Rcr(1)；
wherein R isdr(n) input data of the second inverse lag inertial transformation, DyLinear differentiation of the output data for the second inverse inertial lag transformation, Dy1Linear differentiation of the output data for the first inverse inertial lag transformation; t is2Selecting the second lag parameter as the same as the second differential lead parameter; dt is an integral step length, and dt is 0.001; t is1Selecting the first time lag parameter as the first time differential lead parameter; rcr(n) is the output data of the first inverse inertial lag transform; rbr(n) is the output data of the second inverse inertial lag transform, and is also the final output data decrypted by the whole double inertial lag transform;
and step S70, performing first inertial lag decryption on the data after the second inertial lag transformation, and outputting the image.
2. The method of claim 1, wherein the encrypting the image data after the second differential look-ahead transform by power and nonlinear compression transform comprises:
Figure FDA0003239215200000031
Figure FDA0003239215200000032
wherein R isd(n) output data of the second differential look-ahead encryption, Re(n) is data obtained after power transformation, Rf(n) is data obtained by performing a nonlinear compression transform, wherein k is1、k2、k3、k4、k5Is a constant parameter.
3. The method of claim 1, wherein performing inverse power-wise and nonlinear compression transformation on the received image data comprises:
Figure FDA0003239215200000033
Figure FDA0003239215200000034
wherein R isg(n) is receiver data, Rh(n) is data after nonlinear inverse transformation, Rdr(n) is the data obtained after inverse power transformation, where k is6、k7、k8、k9、k10Is a constant parameter.
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