CN116633683B - Single-pixel imaging asymmetric encryption method based on 3D Arnod transformation - Google Patents
Single-pixel imaging asymmetric encryption method based on 3D Arnod transformation Download PDFInfo
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04L—TRANSMISSION OF DIGITAL INFORMATION, e.g. TELEGRAPHIC COMMUNICATION
- H04L63/00—Network architectures or network communication protocols for network security
- H04L63/04—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks
- H04L63/0428—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload
- H04L63/0442—Network architectures or network communication protocols for network security for providing a confidential data exchange among entities communicating through data packet networks wherein the data content is protected, e.g. by encrypting or encapsulating the payload wherein the sending and receiving network entities apply asymmetric encryption, i.e. different keys for encryption and decryption
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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
- H04L9/30—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy
- H04L9/3066—Public key, i.e. encryption algorithm being computationally infeasible to invert or user's encryption keys not requiring secrecy involving algebraic varieties, e.g. elliptic or hyper-elliptic curves
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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
- H04L9/40—Network security protocols
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- H—ELECTRICITY
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- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N5/00—Details of television systems
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- H04N5/91—Television signal processing therefor
- H04N5/913—Television signal processing therefor for scrambling ; for copy protection
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- H—ELECTRICITY
- H04—ELECTRIC COMMUNICATION TECHNIQUE
- H04N—PICTORIAL COMMUNICATION, e.g. TELEVISION
- H04N5/00—Details of television systems
- H04N5/76—Television signal recording
- H04N5/91—Television signal processing therefor
- H04N5/913—Television signal processing therefor for scrambling ; for copy protection
- H04N2005/91357—Television signal processing therefor for scrambling ; for copy protection by modifying the video signal
Abstract
The application provides a single-pixel imaging asymmetric encryption method based on 3D Arnod transformation, and belongs to the technical field of image encryption. The method comprises the following steps: carrying out 3D (three-dimensional) Arnod transformation on one-dimensional light intensity signals acquired by a single pixel detector, carrying out encryption processing on parameters of the 3D Arnod transformation, and transmitting the parameters of the 3D Arnod transformation subjected to the encryption processing through a public channel; the public key and the private key of the encryption process are generated through an elliptic curve cryptography.
Description
Technical Field
The application belongs to the technical field of image encryption, and particularly relates to a single-pixel imaging asymmetric encryption method based on 3D Arnod transformation.
Background
As one of the research fronts in the field of computational imaging, single-pixel imaging encodes two-dimensional spatial information of an object scene into a one-dimensional light intensity signal sequence in a structural light illumination or structural detection mode, and compared with the traditional optical imaging technology using array detectors such as CCD (charge coupled device), CMOS (complementary metal oxide semiconductor) and the like, the single-pixel imaging is beneficial to solving imaging problems in the aspects of non-visible light wave band imaging, weak light imaging, turbulence resistance imaging and the like, and has wide application prospects.
The single-pixel imaging can directly realize dimension reduction sampling due to the characteristics of code modulation and calculation demodulation, and the obtained single-pixel detection value can obviously reduce the hardware cost brought by two-dimensional image transmission during transmission. Meanwhile, single-pixel imaging is considered to be very suitable for being applied to encryption of a target, because after the target scene is subjected to coded modulation, a single-pixel detection value signal is in a form of a one-dimensional irrelevant intensity change signal, a coding mode which changes with time can be considered as a secret key, if a measurer directly transmits the signal to a receiver without informing the secret key, the receiver is difficult to reconstruct the target scene directly based on the one-dimensional signal, and therefore, the single-pixel imaging mechanism has the advantages of encryption naturally and is also beneficial to being applied to the field of information security.
The single-pixel imaging encryption method is derived from related imaging related research. The target scene is irradiated by utilizing the random matrix generated in a highly random way, so that a completely irregular barrel detector value can be obtained, a series of random matrices adopted can be directly regarded as a secret key, the barrel detector value can be regarded as a ciphertext, and a receiver can decrypt the target scene after receiving all the ciphertext and the secret key. However, although the method does not change the single-pixel imaging system, the key transmission space is too large, the linear encryption effect is poor, the method is easy to attack, and meanwhile, the decryption image quality is greatly reduced, so that the method is difficult to apply in a practical scene. Another type of single-pixel encryption method is aimed at the random encryption method, the random matrix is changed into an orthogonal base pattern such as a Fourier base, a Hadamard base or a wavelet base, and scene encryption is carried out by utilizing a single-pixel imaging system of the orthogonal base, so that the problems that the transmission space occupation of a traditional single-pixel imaging key is large and the quality of a decrypted image is low can be greatly reduced, but the method based on orthogonal base spectrum inversion is easy to cause great security discount because a stealer knows about orthogonal transformation, and the generated single-pixel detection value signals are arranged too regularly, and then the encrypted image is easy to decrypt by combining with a priori knowledge. Therefore, there is a kind of encryption method that is to scramble such orthogonal base patterns, that is, directly scramble the modulation pattern irradiated on the target scene with a certain rule, which will make the detection value obtained by the single-pixel detector become irregular, and enhance the security of the single-pixel imaging system to a certain extent. However, the encryption operation of the method is complex, each irradiation pattern needs to be operated, the workload and the calculation amount are extremely large, meanwhile, the setting of different pixel scrambling rules also has great influence on the encryption result, the quality of the decrypted image is also greatly influenced by the setting of the illumination section, and the safety and the decryption image effect of the single-pixel imaging system are seriously influenced.
Disclosure of Invention
Aiming at the technical problems that in the single-pixel imaging encryption transmission process, the key transmission space is large, the linear encryption effect is poor and the single-pixel imaging asymmetric encryption method based on 3D Arnod transformation is easy to attack, the application provides a single-pixel imaging asymmetric encryption method based on 3D Arnod transformation.
The application discloses a single-pixel imaging asymmetric encryption method based on 3D Arnod transformation. The method comprises the following steps: carrying out 3D (three-dimensional) Arnod transformation on one-dimensional light intensity signals acquired by a single pixel detector, carrying out encryption processing on parameters of the 3D Arnod transformation, and transmitting the parameters of the 3D Arnod transformation subjected to the encryption processing through a public channel; the public key and the private key of the encryption process are generated through an elliptic curve cryptography.
According to the method of the first aspect of the present application, the 3D arod transform is performed on the one-dimensional light intensity signal acquired by the single-pixel detector, and specifically includes: acquiring a light intensity value in a one-dimensional vector form based on a Hadamard base scanning single-pixel imaging system as the one-dimensional light intensity signal, and representing the one-dimensional light intensity signal as a two-dimensional differential light intensity matrixAndrespectively to using the following formulaAndperforming the 3D arode transformation:
wherein, the liquid crystal display device comprises a liquid crystal display device,andrespectively representing gray values at the same pixel positions before and after the 3D Arnold transformation) And%) Respectively representing the coordinate positions of the same pixel in the light intensity matrix before and after the 3D Arnod transformation,representing the maximum of the one-dimensional light intensity values,for the dimension of the light intensity matrix,to transform the control parameters.
According to the method of the first aspect of the present application, the public key and the private key are generated by the elliptic curve cryptography; the method specifically comprises the following steps: selecting elliptic curve：WhereinThe representation of the finite field is made,is a parameter of an elliptic curve,for the coordinate locations on the elliptic curve,and (2) andrandomly selecting a point from the elliptic curve as a base pointAnd selecting a random positive integerGenerating a first public keyThe method comprises the steps of carrying out a first treatment on the surface of the The sender sends the base pointAnd the first public keyTransmitting to a receiver through the common channel; the receiver receives the base pointThen, any positive integer is selectedAs a private key and generates a second public keyThe second public key is processedTo the sender.
According to the method of the first aspect of the application, the parameters of the 3D Arnold transform are enteredPerforming line encryption processing; the method specifically comprises the following steps: the sender receiving the second public keyEmbedding the parameters into the elliptic curve to obtain pointsUsing the second public keyEncrypting the parameters to generate ciphertextAnd apply the ciphertextAnd sending the message to the receiver.
According to the method of the first aspect of the application, the receiving party receives the ciphertextThereafter, the private key is utilizedFor the ciphertextDecryption is performed by the following formula：
The receiver embeds rules according to the parameters of the elliptic curve based on the calculated parametersAnd extracting the parameters of the 3D Arnold transformation to recover the original one-dimensional light intensity signals acquired by the single-pixel detector.
In summary, the technical scheme provided by the application starts from the demands of making up the defects of the existing encryption method and improving the robustness of key transmission, utilizes 3D Arnod transformation to scramble plaintext information of single-pixel coding measured value, and encrypts the scrambled signal again through elliptic curve encryption algorithm and ECDH key exchange mechanism to obtain ciphertext. The method can directly scramble the single-pixel detection value, greatly enhance the safety of single-pixel measurement signal transmission, solve the problem of key transmission space and improve the reconstruction quality of a decrypted image.
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In order to more clearly illustrate the embodiments of the application or the technical solutions in the prior art, the drawings which are required in the description of the embodiments or the prior art will be briefly described, it being obvious that the drawings in the description below are some embodiments of the application and that other drawings may be obtained from these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flow chart of a single-pixel imaging asymmetric encryption method based on 3D arode transformation according to an embodiment of the present application.
Fig. 2 is a diagram of an apparatus according to a second embodiment of the present application.
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present application more apparent, the technical solutions of the embodiments of the present application will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present application, and it is apparent that the described embodiments are only some embodiments of the present application, not all embodiments of the present application. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
The application discloses a single-pixel imaging asymmetric encryption method based on 3D Arnod transformation. As shown in fig. 1, the method includes: carrying out 3D (three-dimensional) Arnod transformation on one-dimensional light intensity signals acquired by a single pixel detector, carrying out encryption processing on parameters of the 3D Arnod transformation, and transmitting the parameters of the 3D Arnod transformation subjected to the encryption processing through a public channel; the public key and the private key of the encryption process are generated through an elliptic curve cryptography.
In a preferred embodiment, the performing the 3D arode transformation on the one-dimensional light intensity signal acquired by the single-pixel detector specifically includes: acquiring a light intensity value in a one-dimensional vector form based on a Hadamard base scanning single-pixel imaging system as the one-dimensional light intensity signal, and representing the one-dimensional light intensity signal as a two-dimensional differential light intensity matrixAndrespectively to using the following formulaAndperforming the 3D arode transformation:
wherein, the liquid crystal display device comprises a liquid crystal display device,andrespectively representing gray values at the same pixel positions before and after the 3D Arnold transformation) And%) Respectively representing the coordinate positions of the same pixel in the light intensity matrix before and after the 3D Arnod transformation,representing the maximum of the one-dimensional light intensity values,for the dimension of the light intensity matrix,to transform the control parameters.
In a preferred embodiment, the public key and the private key are generated by the elliptic curve cryptography; the method specifically comprises the following steps: selecting elliptic curve：WhereinThe representation of the finite field is made,is a parameter of an elliptic curve,for the coordinate locations on the elliptic curve,and (2) andrandomly selecting a point from the elliptic curve as a base pointAnd selecting a random positive integerGenerating a first public keyThe method comprises the steps of carrying out a first treatment on the surface of the The sender sends the base pointAnd the first public keyTransmitting to a receiver through the common channel; the receiver receives the base pointThen, any positive integer is selectedAs a private key and generates a second public keyThe second public key is processedTo the sender.
In a preferred embodiment, the parameters of the 3D alder transformation are encrypted; the method specifically comprises the following steps: the sender receiving the second public keyEmbedding the parameters into the elliptic curve to obtain pointsUsing the second public keyEncrypting the parameters to generate ciphertextAnd apply the ciphertextAnd sending the message to the receiver.
In a preferred embodiment, the recipient receives the ciphertextThereafter, the private key is utilizedFor the ciphertextDecryption is performed by the following formula：
The receiver embeds rules according to the parameters of the elliptic curve based on the calculated parametersAnd extracting the parameters of the 3D Arnold transformation to recover the original one-dimensional light intensity signals acquired by the single-pixel detector.
Specifically, the technical scheme of the application firstly utilizes a Hadamard orthogonal base pattern to modulate a target scene to obtain one-dimensional light intensity sequence value distribution; then, quantizing and converting the one-dimensional light intensity signals to obtain a positive and negative Hadamard two-dimensional light intensity matrix; then, transforming the two-dimensional matrix by utilizing the improved 3D Arnod transformation formula to obtain a scrambled two-dimensional light intensity matrix, and recording Arnod transformation parameters; then, elliptic curve parameters are randomly selected, the plaintext of the Arnod transformation parameters is embedded into the elliptic curve, and a public key and a private key are generated according to a Difei-Hulman mechanism, so that the safe transmission of the secret key is realized; finally, the receiver decrypts the detection signal according to the private key and the public key of the own party and calculates an initial image, so that the problem of signal encryption transmission safety is solved.
Specifically, the method utilizes the improved 3D Arnod transformation to directly scramble and encrypt one-dimensional light intensity value signals acquired by a single-pixel detector, and encrypts transformation related parameters again through an ECDH key exchange mechanism in elliptic curve cryptography, so that the single-pixel detection signals can be safely transmitted in a public channel.
The method specifically comprises the following steps: transforming the one-dimensional light intensity signal obtained by the single-pixel detector by using the improved 3D Arnod transformation formula; and encrypting the key parameters of the 3D Arnod transformation, generating a public key and a private key by using an elliptic curve cryptography, and directly transmitting the public key and the private key through a public channel to realize encryption with high security and decryption with high reconstruction quality.
First embodiment
Recording the light intensity value based on the Hadamard base scanning single-pixel imaging system, and changing the light intensity value in a one-dimensional vector form into a two-dimensional differential light intensity matrixAndthe method comprises the steps of carrying out a first treatment on the surface of the Respectively toAndperforming 3D Arnorld transformation:
wherein, the liquid crystal display device comprises a liquid crystal display device,andrespectively representing the gray values at the same pixel positions before and after the transformation,representing the maximum of the one-dimensional intensity values. The key parameters of the improved 3D Arnold transformation are as followsAlso included is the number of iterations of the transformation, all set by the information issuer, i.e., the key.
Optionally selecting an elliptic curve：Wherein, hereAnd meet the followingOne point on the elliptic curve is randomly taken as a base pointSelecting a random positive integerGenerating public keysThe sender shares this information to the receiver over the common channel.
In addition, the sender embeds the parameters on the curve, here in terms of parametersFor example, assume that the points on the embedded elliptic curve are。
After receiving the elliptic curve parameters, the receiver selects any one positive integerAs a private key and generates a public keyShared with the sender.
After receiving the public key generated by the receiver, the sender encrypts parameters in the 3D Arnod transformation by combining the public key of the receiver to generate ciphertext，. Ciphertext is sent toAnd simultaneously transmitting the encrypted single-pixel detection value after the 3D Arnold conversion to a receiver to finish encryption.
The receiver receives the ciphertextThereafter, the private key is utilizedDecrypting and countingAnd (3) calculating:
extracting 3D Arnod transformation parameters according to a plaintext embedding rule, carrying out inverse transformation on a light intensity matrix by utilizing the parameters to recover a plaintext single-pixel detection value, and processing the obtained plaintext by using an inverse Hadamard transformation algorithm to finally obtain a decrypted image.
Second embodiment
As shown in fig. 2, a single pixel imaging system apparatus according to the present application is shown. The device comprises a 532nm continuous laser 1, a spatial filter 2, a beam expander 3, a digital micro-mirror device 4, a target 5, a collecting lens 6 and a single-pixel detector 7. The computer loads the generated Hadamard base pattern into the on-board memory of the digital micromirror device. Selecting continuous laser, spatially filtering, collimating and expanding to form near parallel light, irradiating on DMD, spatially modulating by DMD, irradiating on target scene, obtaining reflected light signal of target by single-pixel detector, directly scrambling and encrypting the reflected light signal, encrypting and decrypting by elliptic curve cryptography to realize single-pixel imaging,
(1) The required target imaging resolution is set to be 64 multiplied by 64, a zig-zag sampling path is utilized to generate 64 multiplied by 64 Hadamard patterns, the series of base patterns are loaded on the DMD, the target image Lena is subjected to spatial light modulation after being irradiated by a laser light source after beam expansion collimation, and a single pixel detector is used for collecting light intensity signals.
(2) Setting 3D Arnold transformation parameters as，Setting the transformation iteration times for 500 times for obtaining the maximum value of the single-pixel light intensity, and directly encrypting the plaintext of the single-pixel light intensity value into the ciphertext according to the set parameters.
(3) The parameters set in the 3D Arnod transformation are encrypted and transmitted according to an ECDH key exchange mechanism, and the parameters are selected as，，Is a elliptic curve of (a).
(4) Randomly selecting a point on an elliptic curveAs a base pointSelectingAs abscissa, find plaintext embedding point on elliptic curveAnd set the private key asPublic key generated by algorithmIs that。
(5) Assuming that the receiver receives the elliptic curve parameters and sets the private key asPublic key to be shared at this timeIs thatThe method comprises the steps of carrying out a first treatment on the surface of the Based on the public key provided by the recipientCiphertext generated at this timeIs thatThe key encryption is completed.
(6) The receiver can decrypt out the plaintext embedded point according to the algorithmExtracting parameter information, finishing key decryption, processing the obtained plaintext by using an inverse Hadamard transformation algorithm, and finally obtaining a decrypted image.
Therefore, the technical scheme provided by the application starts from the demands of overcoming the defects of the existing encryption method and improving the key transmission robustness, the 3D Arnod transformation is utilized to scramble the plaintext information of the single-pixel coding measured value, and then the scramble signal is encrypted again through the elliptic curve encryption algorithm and the ECDH key exchange mechanism to obtain the ciphertext. The method can directly scramble the single-pixel detection value, greatly enhance the safety of single-pixel measurement signal transmission, solve the problem of key transmission space and improve the reconstruction quality of a decrypted image.
In summary, the technical scheme provided by the application can realize the encryption of the single pixel detection light intensity value of the target directly through the improved 3D Arnod transformation, and the improvement method not only has the scrambling effect in the two-dimensional position dimension but also in the intensity value dimension, so that the safety is obviously improved, meanwhile, the problem of the encryption transmission of the 3D Arnod transformation parameters is solved by combining with an ECDH key exchange mechanism in elliptic curve cryptography, the safety of a single pixel imaging system is further improved, and the final decrypted image also realizes the high-quality reconstruction of the decrypted image due to the high-quality transmission of the single pixel detection value and the inverse Hadamard transformation algorithm, so that the problem of the image decryption quality reduction caused by the traditional encryption system is solved.
Note that the technical features of the above embodiments may be arbitrarily combined, and all possible combinations of the technical features in the above embodiments are not described for brevity of description, however, as long as there is no contradiction between the combinations of the technical features, they should be regarded as the scope of the description. The above examples illustrate only a few embodiments of the application, which are described in detail and are not to be construed as limiting the scope of the application. It should be noted that it will be apparent to those skilled in the art that several variations and modifications can be made without departing from the spirit of the application, which are all within the scope of the application. Accordingly, the scope of protection of the present application is to be determined by the appended claims.
Claims (4)
1. A single-pixel imaging asymmetric encryption method based on 3D arode transformation, the method comprising:
carrying out 3D (three-dimensional) Arnod transformation on one-dimensional light intensity signals acquired by a single pixel detector, carrying out encryption processing on parameters of the 3D Arnod transformation, and transmitting the parameters of the 3D Arnod transformation subjected to the encryption processing through a public channel;
the public key and the private key of the encryption processing are generated through an elliptic curve cryptography;
the 3D arnold transform is performed on the one-dimensional light intensity signal acquired by the single-pixel detector, and specifically includes:
acquiring a light intensity value in a one-dimensional vector form based on a Hadamard base scanning single-pixel imaging system as the one-dimensional light intensity signalCharacterizing the one-dimensional light intensity signal as a two-dimensional differential light intensity matrix H + And H - H is respectively calculated by the following formula + And H - Performing the 3D arode transformation:
wherein p and p ' respectively represent gray values at the same pixel positions before and after the 3D alder transformation, (x, y) and (x ', y ') respectively represent coordinate positions of the same pixel in the light intensity matrix before and after the 3D alder transformation, M represents a maximum value in the one-dimensional light intensity values, N is a light intensity matrix dimension, and a, b, c, D is a transformation control parameter.
2. A 3D-arode-transformation-based single-pixel imaging asymmetric encryption method according to claim 1, wherein the public key and the private key are generated by the elliptic curve cryptography; the method specifically comprises the following steps:
select elliptic curve E p (α,β)：y 2 modp＝x 3 +αx+βmodp, whereRepresenting a finite field, alpha, beta being elliptic curve parameters, x, y being coordinate positions on said elliptic curve, x, y, alpha,/->And 4α 3 +27β 2 Not equal to 0, randomly selecting a point from the elliptic curve as a base point G, and selecting a random positive integer K to generate a first public key P s ＝KG；
The sender transmits the base point G and the first public key P s =kg is sent to the receiver over the common channel;
after receiving the base point G, the receiver selects any positive integer N u As a private key and generates a second public key P u ＝N u G, the second stepPublic key P u ＝N u G is sent to the sender.
3. A single-pixel imaging asymmetric encryption method based on 3D alder transformation according to claim 2, characterized in that the parameters of the 3D alder transformation are encrypted; the method specifically comprises the following steps: the sender receiving the second public key P u ＝N u G, embedding the parameters into the elliptic curve to obtain a point P m Using the second public key P u ＝N u G encrypting the parameter to generate ciphertext c=p m +KP u And sending the ciphertext C to the receiver.
4. A single-pixel imaging asymmetric encryption method based on 3D arrod transformation according to claim 3, wherein said receiving party uses said private key N after receiving said ciphertext C u Decrypting the ciphertext C, and calculating P by the following method m ：
P m ＝C-N u P s ＝P m +K(N u G)-N u (KG)
The receiver embeds rules according to the parameters of the elliptic curve based on the calculated P m And extracting the parameters of the 3D Arnold transformation to recover the original one-dimensional light intensity signals acquired by the single-pixel detector.
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