A security control method and system based on combined encryption technology

Abstract

The application belongs to the technical field of network security, and more particularly to a security control method and system based on combined encryption technology.The method comprises the following steps: decomposing a control function into an addition part and a multiplication part; mapping controller parameters and signals to a plaintext message space through a mapping function; encrypting the quantized controller parameters and signals by using an RSA cryptographic algorithm; calculating the multiplication part of the control function by using the RSA cryptographic algorithm; decrypting the ciphertext result by using the RSA cryptographic algorithm and encrypting the decrypted value by using a Paillier cryptographic algorithm; calculating the addition part of the control function by using the Paillier cryptographic algorithm; decrypting the ciphertext by using the Paillier cryptographic algorithm; restoring the decrypted control input by using an inverse mapping function; and encrypting the decrypted controller state by using the RSA cryptographic algorithm and feeding back the result.The application solves the problem that the information in the controller and the transmission channel is still subject to eavesdropping attacks, ensures the control efficiency, and guarantees the performance and stability of the closed-loop system.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of network security, and more particularly to a security control method and system based on combined encryption technology. BACKGROUND

[0002] Networked control systems are widely used in water, transportation, power and other industries and critical infrastructures. Networked control systems are vulnerable to malicious attacks due to the transmission and processing of sensitive data through communication networks. Privacy protection and network security have become key issues for networked control systems. Improper handling of these issues can endanger the surrounding environment and even threaten human safety. In recent years, wiretapping attacks in networked control systems have attracted widespread attention. For networked control systems, attackers have the ability to conduct wiretapping attacks on information in the controller and communication channels. Attackers monitor the calculations within the controller and the data transmitted in the channel, and extract important information about the operation of the system to manipulate the control system. Homomorphic encryption is an encryption form that supports ciphertext computation, which can effectively avoid the risk of wiretapping attacks. There are three types of networked control systems based on additive homomorphic encryption, multiplicative homomorphic encryption and fully homomorphic encryption. Ciphertext is transmitted in the channel, and the controller directly operates the encrypted data for privacy computation, providing security for the entire control loop.

[0003] Homomorphic encryption is gradually applied in the field of control engineering. However, it is challenging to implement a fully secure and efficient networked control system because the control function needs to be redesigned according to the homomorphism of the homomorphic encryption algorithm to complete the encrypted computation. The previously proposed networked control systems based on homomorphic encryption still face the risk of wiretapping attacks.

[0004] Chinese patent document CN110750797A discloses a cloud database encryption method based on combined encryption. This method combines additive homomorphic encryption and multiplicative homomorphic encryption to achieve full homomorphic encryption to some extent. On the basis of the combined encryption algorithm, an agent layer is added, and the same operation can be completed at the same time by rewriting the SQL statement to reduce the number of ciphertext updates and the network transmission between the client and the database end.

[0005] In summary, the control system based on the multiplication homomorphic encryption algorithm in the prior art decomposes the control function into addition and multiplication parts according to the homomorphic property, performs multiplication operation between ciphertexts in the controller, and since the addition operation between ciphertexts is not supported, the generated ciphertext result is decrypted, and the decrypted value is returned to the controller in plaintext form, and the data addition operation is completed in plaintext form in the controller, and this process has a security vulnerability. The control system based on the multiplication homomorphic encryption algorithm performs secure operation on the control function in the controller by using the multiplication property, but the transmission of the controller parameters and the controller state is not secure because they are not encrypted. The control system based on the full homomorphic encryption algorithm is not suitable for practical application because the multiplication operation between ciphertexts takes a long time, and usually uses multiplication calculation between ciphertexts and plaintexts, but like the control system based on the multiplication homomorphic encryption algorithm, the controller parameters are not protected.

[0006] Therefore, the information in the controller and the transmission channel still has the risk of eavesdropping attack, and it is of great significance to realize a comprehensive secure and efficient network control system. SUMMARY

[0007] The present application aims to overcome at least one of the above-mentioned defects of the prior art, and provides a secure control method based on combined encryption technology.

[0008] The present application also discloses a system for realizing a secure control method based on combined encryption technology by using the above-mentioned method.

[0009] The detailed technical solutions of the present application are as follows:

[0010] A secure control method based on combined encryption technology, comprising:

[0011] S1, the control function is defined by the controller parameters and the signal, and the control function is decomposed into an addition part and a multiplication part;

[0012] S2, quantize the controller parameters and the signal to the plaintext message space by using a mapping function;

[0013] S3, encrypt the quantized controller parameters and the signal by using the RSA cryptographic algorithm;

[0014] S4, the encrypted controller calculates the multiplication part of the control function by using the multiplication homomorphic property of the RSA cryptographic algorithm, and transmits the generated ciphertext result to be decrypted;

[0015] S5, decrypt the ciphertext result by using the RSA cryptographic algorithm, and then encrypt the decrypted value by using the Paillier cryptographic algorithm, and feed back the obtained encrypted value to the encrypted controller;

[0016] S6. The encryption controller uses the additive homomorphic property of the Paillier cryptographic algorithm to calculate the addition part of the control function and transmits the resulting ciphertext result to the decryption controller.

[0017] S7. Decrypt the ciphertext result generated in S6 using the Paillier cryptographic algorithm to obtain the decrypted control input and controller state.

[0018] S8. Use the inverse mapping function to restore the decrypted control input obtained in S7;

[0019] S9. Encrypt the controller state obtained in S7 using the RSA cryptographic algorithm and feed it back to the encrypted controller.

[0020] Because data encryption slows down computation, it affects control efficiency. The RSA and Paillier cryptographic algorithms mentioned are lightweight, consume very little time, have high computational efficiency, and can be controlled in real time.

[0021] The S1 control function is defined by controller parameters and signals. The control function is specifically decomposed into an addition part and a multiplication part, including:

[0022] S11. The controlled object is controlled by a dynamic output feedback controller, and the control function is defined as follows:

[0023]

[0024] In formula (2) It is time step and It is the set of non-negative integers. It is the controller state, x c (t+1) is the controller state at time t+1, x c (0) is the initial state x0 of the controller. It is the control output, y(t) is the control output at time t. It is the control input, u(t) is the control input at time t, A c B c C c and D c These are controller parameters; among them, Represents a size of n c A set of vectors, The size is m c A set of vectors, Represents a set of vectors of size l, n c ,m c ,l∈N+,N+ is the set of positive integers;

[0025] S12. Rewrite the control function f as follows:

[0026] ψ(t) = Φξ(t) = : f(Φ, ξ(t)) (3)

[0027] In formula (3), the controller parameter Φ, the signal ξ at time t and the signal ψ at time t are defined as:

[0028]

[0029] S13, according to the homomorphism of RSA and Paillier encryption algorithm, f is decomposed into wherein:

[0030]

[0031] In formula (5), f × and f + are the multiplication and addition parts calculated by the controller, respectively, ψ ij is the element of the i-th row and the j-th column of the matrix Ψ, Φ ij is the element of the i-th row and the j-th column of the matrix Φ, ξ j is the j-th element of the vector ξ, ψ 1ii is the element of the i-th row and the first column of the matrix Ψ, is the element of the i-th row and the (n c +m c )th column of the matrix Ψ.

[0032] S2, the controller parameter and the signal are quantized and mapped to the plaintext message space by the mapping function, specifically includes: the homomorphic encryption algorithm can only process positive integer plaintexts, however, in the network control system, the signal usually adopts real number values, therefore, it is necessary to quantize the real number values to the plaintext message space

[0033] S21, the mapping function can map the real number value γ ∈ [-G, G] to a positive integer plaintext, G is a known integer, before converting the real number value, the quantization error is greatly reduced by using an additional quantization gain λ, the mapping function Γ(γ) is represented as follows:

[0034]

[0035] In formula (6), and round(γλ) assign the closest integer in the plaintext message space to the scaled real number value γλ ∈ [-Gλ, Gλ];

[0036] S22, the controller parameter Φ is quantized into the signal ξ is quantized into wherein is the plaintext message space.

[0037] The S3 step of encrypting the quantized controller parameters and signals using the RSA cryptographic algorithm specifically includes:

[0038] S31. RSA Key Generation Algorithm: Randomly select two large prime numbers p and q, calculate n = pq and φ(n) = (p-1)(q-1), select an integer e such that gcd(e, φ(n)), where gcd represents taking the greatest common divisor. Calculate d by the multiplicative inverse of e, i.e., ed ≡ 1 mod φ(n). Then the public key used for encryption is pk. RSA = (e, n), the private key used for decryption is sk RSA = (d, n);

[0039] S32 and RSA encryption algorithms make the plaintext message space... A set of non-negative integers, using a public key PK. RSA =(e,n) for plaintext If encrypted, the ciphertext is calculated as follows:

[0040] c = Enc(m, pk RSA )=m e (modn) (7)

[0041] controller parameters Encryption Signal Encryption

[0042] The S4 encryption controller utilizes the multiplicative homomorphic property of the RSA cryptographic algorithm to calculate the multiplicative part of the control function and transmits the resulting ciphertext result for decryption. Specifically, the RSA cryptographic algorithm possesses the multiplicative homomorphic property; for two plaintexts m1 and m2, the multiplicative part of the control function is calculated. Perform the following calculations:

[0043] Enc(m1,pk RSA )*Enc(m2,pk RSA )=(m1 e (modn))*(m2 e (modn))

[0044] =(m1*m2) e (modn)

[0045] =Enc(m1*m2,pk RSA (8)

[0046] Furthermore, the multiplication part of the control function is calculated using the RSA cryptographic algorithm, as follows:

[0047]

[0048]

[0049] The generated ciphertext is represented as: where is a quantized matrix The element in the i-th row and j-th column, is a quantized vector The j-th element.

[0050] The S5, using RSA cryptographic algorithm to decrypt the ciphertext result, and then using Paillier cryptographic algorithm to encrypt the decrypted value, and feeding back the obtained encrypted value to the encryption controller specifically includes:

[0051] S51, the decryption algorithm of RSA, using the private key sk RSA =(d, n) to decrypt the ciphertext c as follows:

[0052] m = Dec (c, sk RSA )= c d (mod n) (10)

[0053] The decryption result of the ciphertext result using the RSA cryptographic algorithm is:

[0054] S52, the key generation of Paillier cryptographic algorithm: randomly select two large prime numbers p and q independent of each other, to satisfy the greatest common divisor gcd (pq, (1-p) (1-q)) = 1, calculate n = pq and λ = lcm (p-1, q-1); Randomly select an integer is a set of non-negative integers, is a set of all numbers that satisfy gcd (r, n) = 1 in the set , so that gcd (n, L (g λ (mod n 2 ))) = 1 and for each so that L (u) = (u-1) / n, let pk Paillier =(n, g) as the public key, and sk Paillier =(p, q) as the private key;

[0055] S53, the encryption algorithm of Paillier cryptographic algorithm: let the plaintext message space be Randomly select a number is a set of all numbers that satisfy gcd (r, n) = 1 in the set , gcd represents taking the greatest common divisor, so that gcd (r, n) = 1, and using pkPaillier = (n, g) encrypt each plaintext where the ciphertext c is calculated by the following formula:

[0056] c = Enc(m, pk Paillier ) = g m r n (mod n 2 ) (11)

[0057] The decryption result is encrypted using the Paillier encryption algorithm to obtain:

[0058] The S6, the encryption controller uses the additive homomorphism property of the Paillier encryption algorithm to calculate the addition part of the control function, and the ciphertext result generated is transmitted to the decryption, which specifically includes: the Paillier encryption algorithm has the additive homomorphism property, for two plaintexts m1 and The following calculation is performed:

[0059]

[0060] In formula (12), r1 and

[0061] Further, the additive part of the control function is calculated using the Paillier encryption algorithm:

[0062]

[0063] The calculated controller state is The control input is where c is the quantized value of the controller state x (t+1), is the quantized value of the control input u(t), is the matrix the element in the first row and the i-th column, is the matrix the element in the n c +m c row and the i-th column.

[0064] The S7, the ciphertext result generated by S6 is decrypted using the Paillier encryption algorithm to obtain the decrypted control input and controller state, which specifically includes: the decryption algorithm of the Paillier encryption algorithm, using sk Paillier = (p, q) decrypt each ciphertext As follows:

[0065]

[0066] S71, the calculated control input decrypting the control input to obtain a decrypted control input

[0067]

[0068] S72, the iteration of the controller state in the form of ciphertext can cause data overflow in the encryption space, and then the encrypted data cannot be correctly decrypted, in order to avoid this problem, the controller state decrypting to obtain

[0069]

[0070] S8, the decrypted control input obtained by S7 is restored using an inverse mapping function, which specifically includes: in order to obtain a real value corresponding to a quantized value, the inverse mapping function Γ -1 (k) is given by the following formula:

[0071]

[0072] In formula (15), k is a parameter to be inversely mapped;

[0073] Through quantization recovery, the control input is

[0074] S9, the controller state obtained by S7 is encrypted by the RSA cryptographic algorithm and fed back to the encryption controller, which specifically includes: the result of the RSA cryptographic algorithm for encrypting the controller state is and is transmitted to the encryption controller to complete the update of the controller state.

[0075] A system of a secure control method based on a combination encryption technology, comprising:

[0076] Control object, device to be controlled;

[0077] Sensor, measuring the data y(t) of the control object and sending to the encryption controller;

[0078] Mapping module, including a mapping function to quantize data; quantizing the controller parameter Φ, the measured signal y(t) and the initial state x c (0) of the controller into and

[0079] First encryptor, encrypting the input data; encrypting and using the RSA cryptographic algorithm, respectively obtaining and

[0080] The encryption controller controls the ciphertext calculation inside the controller: the multiplication part of the control function is calculated by using the RSA encryption algorithm to obtain The Paillier encryption algorithm is used to operate , and the addition operation of the control function is completed to obtain and

[0081] The decryption device decrypts the ciphertext result calculated by the encryption controller: the Paillier encryption algorithm is used to decrypt to obtain The Paillier encryption algorithm is used to decrypt and to obtain and

[0082] The second encryption device encrypts the input data: the Paillier encryption algorithm is used to encrypt , and the encryption result is The RSA encryption algorithm is used to encrypt to obtain At the same time, the is transmitted and fed back to the encryption controller.

[0083] The inverse mapping module comprises an inverse mapping function, so that the data is restored and transmitted to the actuator; the is restored to u(t), and the u(t) is transmitted to the actuator.

[0084] The actuator receives and executes the control signal u(t) to adjust the control object.

[0085] Compared with the prior art, the beneficial effects of the present application are:

[0086] (1) The security control method and system based on the combined encryption technology provided by the present application comprehensively enhance the security of the network control system by using the combined encryption technology, and the entire control scheme including the controller parameters, the controller state and the control signal is encrypted. In the controller, the multiplication homomorphism property of the RSA encryption algorithm and the addition homomorphism property of the Paillier encryption algorithm are used to perform calculation in the ciphertext space to generate the control command, and the data security of each transmission channel is ensured, including the transmission of the intermediate result and the controller state, so that the risk of eavesdropping attack on the information in the controller and the transmission channel is eliminated, and the stability of the closed-loop system is maintained.

[0087] (2) The security control method and system based on the combined encryption technology provided by the application adopt the lightweight RSA and Paillier encryption algorithms, the combined encryption technology is efficient, and the purpose of real-time control is achieved; the encryption control system uses the mapping function and the inverse mapping function to quantize data, so that the quantization error caused by encryption can be ignored, and the performance and stability of the closed-loop system are ensured. BRIEF DESCRIPTION OF DRAWINGS

[0088] Figure 1 is a flow chart of the security control method based on the combined encryption technology described in the application.

[0089] Figure 2 is a schematic diagram of the security control system based on the combined encryption technology described in the application. DETAILED DESCRIPTION

[0090] The present disclosure will be further described below in conjunction with the accompanying drawings and examples.

[0091] It should be noted that the following detailed description is exemplary and is intended to provide further explanation of the present disclosure. Unless otherwise indicated, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which the present disclosure belongs.

[0092] It should be noted that the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit exemplary embodiments according to the present disclosure. As used herein, the singular form is intended to include the plural form unless the context clearly indicates otherwise, and it should also be understood that when the terms "comprise" and / or "include" are used in the specification, there is a presence of the features, steps, operations, devices, components and / or combinations thereof.

[0093] The embodiments in the present disclosure and the features in the embodiments can be combined with each other without conflict.

[0094] Embodiment 1

[0095] The present embodiment provides a security control method and system based on a combined encryption technology, as shown in Figure 1 The method comprises:

[0096] S1, the control function is defined by the controller parameters and the signal, and the control function is decomposed into an addition part and a multiplication part;

[0097] Taking a discrete-time control object as an example, it is defined as:

[0098]

[0099] In formula (1), A, B and C are control object parameters, is a time step and is a set of non-negative integers, is a controlled object state, x(t+1) is a controlled object state at t+1, is a control input, u(t) is a control input at t, is a control output, y(t) is a control output at t; wherein, represents a set of vectors with size n p , represents a set of vectors with size m c , represents a set of vectors with size l, n p , m p , l ∈ N+.

[0100] S11, a controlled object is controlled by a dynamic output feedback controller, and the control function is defined as:

[0101]

[0102] In formula (2), A c , B c , C c and D c are controller parameters, is a controller state, x c (t+1) is a controller state at t+1, x c (0) is the initial state of the controller x0; wherein, represents a set of vectors with size n c , n c ∈ N+;

[0103] Wherein, the control function is defined by the controller parameters and the signal definition of the content of the control function; defining the control function as f means that the control function is in the dynamic output feedback controller.

[0104] S12, the control function f is rewritten as follows:

[0105] ψ(t) = Φξ(t) =: f(Φ, ξ(t)) (3)

[0106] In formula (3), the controller parameters Φ, the signal ξ at t and the signal ψ at t are defined as follows:

[0107]

[0108] S13, according to the homomorphism of RSA and Paillier encryption algorithm, f is decomposed into Wherein:

[0109]

[0110]

[0111] f × and f + are the multiplication and addition parts of the controller computation respectively, Ψ ij is the element of the matrix Ψ in the i-th row and j-th column, Φ ij is the element of the matrix Φ in the i-th row and j-th column, ξ j is the j-th element of the vector ξ, Ψ 1i is the element of the matrix Ψ in the 1-st row and i-th column, is the element of the matrix Ψ in the n c +m c -th row and i-th column.

[0112] S2, quantize and map the controller parameters and signals into the plaintext message space by a mapping function;

[0113] The homomorphic encryption algorithm can only deal with positive integer plaintexts, however, in networked control systems, signals usually take real values, therefore, it is necessary to quantize the real values into the plaintext message space

[0114] S21, the mapping function can map a real value γ∈[-G,G] into a positive integer plaintext, G is a known integer, before converting the real value, the quantization error is greatly reduced by using an extra quantization gain λ, the mapping function Γ(γ) is expressed as follows:

[0115]

[0116] In formula (6), and round(γλ) assign the closest integer in the plaintext message space to the scaled real value γλ∈[-Gλ,Gλ];

[0117] S22, the controller parameters Φ are quantized into the signals ξ are quantized into where is the plaintext message space.

[0118] S3, encrypt the quantized controller parameters and signals by the RSA cryptographic algorithm;

[0119] S31, the key generation algorithm of RSA: randomly select two large prime numbers p and q, calculate n=pq and φ(n)=(p-1)(q-1), select an integer e such that gcd(e,φ(n))=1, gcd represents the greatest common divisor, find d by calculating the multiplicative inverse of e, i.e. ed≡1modφ(n), then the public key for encryption is pk RSA =(e,n), and the private key for decryption is skRSA = (d, n) ;

[0120] S32, RSA encryption algorithm, the plaintext message space is is a set of non-negative integers, using the public key pk RSA = (e, n) pair plaintext encryption, the ciphertext calculation is:

[0121] c = Enc (m, pk RSA ) = m e (mod n) (7)

[0122] The controller parameters encrypted as signal encrypted as

[0123] S4, the encryption controller uses the multiplication homomorphic property of RSA algorithm to calculate the multiplication part of the control function, and the resulting ciphertext result is transmitted to decryption;

[0124] RSA algorithm has the multiplication homomorphic property, for two plaintexts m1 and has the following calculation:

[0125] Enc (m1, pk RSA ) * Enc (m2, pk RSA ) = (m1 e (mod n) * (m2 e (mod n))

[0126] = (m1*m2) e (mod n)

[0127] = Enc (m1*m2, pk RSA ) (8)

[0128] Using RSA algorithm to calculate the multiplication part of the control function, which is specifically represented as follows:

[0129]

[0130]

[0131] The resulting ciphertext is represented by calculating where is the quantized matrix the i-th row j-th element, is the quantized vector the j-th element.

[0132] S5, decrypt the ciphertext result using the RSA cryptographic algorithm, and encrypt the decrypted value using the Paillier cryptographic algorithm, and feed the obtained encrypted value back to the encryption controller;

[0133] S51, the decryption algorithm of RSA, the ciphertext c uses the private key sk RSA is decrypted as follows:

[0134] m = Dec(c, sk RSA ) = c d (mod n) (10)

[0135] Decrypt the ciphertext result using the RSA cryptographic algorithm, and the decryption result is:

[0136] S52, the key generation algorithm of the Paillier cryptographic algorithm, randomly select two large prime numbers p and q that are independent of each other, to satisfy the greatest common divisor gcd(pq, (1-p)(1-q)) = 1, calculate n = pq and λ = lcm(p-1, q-1). Randomly select an integer is a set of all numbers in the set that satisfy gcd(r, n) = 1, so that gcd(n, L(g λ (mod n 2 ))) = 1 and for each so that L(u) = (u-1) / n, let pk Paillier = (n, g) be the public key and sk Paillier = (p, q) be the private key;

[0137] S53, the encryption algorithm of the Paillier cryptographic algorithm, let the plaintext message space be Randomly select a number gcd represents taking the greatest common divisor, so that gcd(r, n) = 1, and encrypt each plaintext using gcd(r, n) = 1 The ciphertext c is calculated by the following formula:

[0138] c = Enc(m, pk Paillier ) = g m r n (mod n 2 ) (11)

[0139] Encrypt the decryption result using the Paillier cryptographic algorithm to obtain:

[0140] S6, the encryption controller uses the additive homomorphism property of Paillier encryption algorithm to operate the encrypted value to complete the addition part of the control function, and obtains the ciphertext control input and controller state and transmits to the decryption; Paillier encryption algorithm has the additive homomorphism property, for two plaintexts m1 and The following calculation is made:

[0141]

[0142] In formula (12), r1 and

[0143] Further, the addition part of the control function is calculated by using the Paillier encryption algorithm, and is specifically represented as follows:

[0144]

[0145] The calculated controller state is The control input is Wherein is the quantized value of the controller state x c (t+1), is the quantized value of the control input u(t), and is the matrix The element in the first row and the i-th column, is the matrix The element in the n c +m c row and the i-th column.

[0146] S7, the ciphertext result generated by S6, i.e. the calculated controller state and the control input are decrypted by using the Paillier encryption algorithm; the decryption algorithm of the Paillier encryption algorithm uses sk Paillier =(p, q) to decrypt each ciphertext As follows:

[0147]

[0148] S71, the calculated control input is decrypted by using sk Paillier =(p, q) to obtain the decrypted control input is the quantized value of the control input u;

[0149] S72, iteration of the controller state in the form of ciphertext will cause data overflow in the encryption space, and then the encrypted data cannot be correctly decrypted, in order to avoid this problem, the obtained controller state is decrypted, and the decryption result is

[0150] S8, using the inverse mapping function to recover the decrypted control input from S7; in order to obtain the real value corresponding to the quantized value, the inverse mapping function Γ -1 (k) is given by the following formula:

[0151]

[0152] In formula (15), k is the parameter to be inversely mapped;

[0153] By quantization recovery, the control input is:

[0154]

[0155] S9, the controller state obtained in S7 is encrypted by RSA cryptographic algorithm, and is fed back to the encrypted controller through transmission;

[0156] The result of the RSA cryptographic algorithm for encrypting the controller state is And it is transmitted to the encrypted controller to complete the update of the controller state.

[0157] A system of a secure control method based on combined encryption technology, comprising:

[0158] Control object, the device to be controlled, controlled by a dynamic output feedback controller; the dynamic output feedback controller defines a control function;

[0159] Sensor, measuring the data y(t) of the control object, and sending to the encrypted controller;

[0160] Mapping module, including mapping function to quantize data; quantize the controller parameter Φ, the measured signal y(t) and the initial state x c (0) of the controller into and

[0161] First encryptor, encrypting the input data; encrypting and Using RSA cryptographic algorithm, respectively obtaining and

[0162] Encrypted controller, ciphertext calculation in the controller: using RSA cryptographic algorithm to calculate the multiplication part of the control function to obtain Using Paillier cryptographic algorithm to operate , complete the addition operation of the control function to obtain and

[0163] Decrypter, decrypting the ciphertext result calculated by the encrypted controller: using RSA cryptographic algorithm to decrypt Decryption obtains Encrypted by Paillier encryption algorithm And Decryption obtains And

[0164] Second encrypter, encrypts input data: encrypted by Paillier encryption algorithm Encryption, and the encryption result is Encrypted by RSA encryption algorithm Encryption obtains At the same time, the Transmission feedback to the encryption controller;

[0165] Inverse mapping module, comprising inverse mapping function so as to restore the data and transmit to the actuator; the Restore to u(t), and transmit u(t) to the actuator;

[0166] Actuator, accepts and executes control signal u(t), so as to adjust the controlled object.

[0167] Obviously, the above embodiments of the present application are only examples for clearly illustrating the technical scheme of the present application, and are not intended to limit the specific embodiments of the present application. Any modification, equivalent replacement and improvement, etc. made within the spirit and principle of the present application claims shall be included in the protection scope of the present application claims.

Claims

1. A security control method based on a combination encryption technique, characterized by, Comprising; S1, a control function is defined by controller parameters and signals, the control function is decomposed into an additive part and a multiplicative part; S2, the controller parameters and signal quantities are quantized and mapped to a plaintext message space by a mapping function; S3, the quantized controller parameters and signals are encrypted using the RSA cryptographic algorithm; S4, the encrypted controller calculates the multiplicative part of the control function using the multiplicative homomorphic property of the RSA cryptographic algorithm, and transmits the resulting ciphertext result to decryption; S5, the ciphertext result is decrypted using the RSA cryptographic algorithm, and the decrypted value is encrypted using the Paillier cryptographic algorithm, and the obtained encrypted value is fed back to the encrypted controller; S6, the encrypted controller calculates the additive part of the control function using the additive homomorphic property of the Paillier cryptographic algorithm, and transmits the resulting ciphertext result to decryption; S7, the ciphertext result generated in S6 is decrypted using the Paillier cryptographic algorithm to obtain the decrypted control input and controller state; S8, the decrypted control input obtained in S7 is restored using an inverse mapping function; S9, the controller state obtained in S7 is encrypted using the RSA cryptographic algorithm and fed back to the encrypted controller.

2. The security control method based on combined encryption technology according to claim 1, characterized in that, The S1 specifically comprises: S11, a control object is controlled by a dynamic output feedback controller, and the control function is defined as: in equation (2) is a time step and is a set of non-negative integers, is a controller state, x c is a controller state at time t+1, x c is an initial state of the controller, x0, is a control output, y(t) is a control output at time t, is a control input, u(t) is a control input at time t, A c , B c , C c and D c are controller parameters; wherein, represents a set of vectors of size n c , represents a set of vectors of size m c , represents a set of vectors of size l, n c , m c , l e N+, N+ is a set of positive integers; S12, rewrite f as: ψ(t)=Φξ(t)=:f(Φ,ξ(t)) (3) In formula (3), the controller parameters Φ, the signal ξ at time t and the signal ψ at time t are defined as: S13. Decompose f into RSA and Paillier homomorphism wherein: Ψ ij (t) = Φ ij ξ j (t) f × and f + is the multiplication and addition part of the controller computation, Ψ ij is the element of the matrix Ψ in the i-th row and j-th column, Φ ij is the element of the matrix Φ in the i-th row and j-th column, ξ j is the j-th element of the vector ξ, Ψ 1ii is the element of the matrix Ψ in the 1-st row and i-th column, is the element of the matrix Ψ in the (n c + m c )-th row and i-th column.

3. The security control method based on combined encryption technology according to claim 2, characterized in that, The S2 specifically comprises: S21, quantize real values to a plaintext message space by using an additional quantization gain λ, and the mapping function Γ(γ) is represented as follows: In equation (6), and round(γλ) assigns the closest integer in the plaintext message space to the scaled real value γλ∈[-Gλ,Gλ]; the mapping function maps a real value γ∈[-G,G] to a positive integer plaintext, G being a known integer; S22, the controller parameter Φ is quantized into the signal ξ is quantized into where is the plaintext message space.

4. The security control method based on combined encryption technology according to claim 3, characterized in that, The S3 specifically comprises: S31, RSA key generation: randomly select two large prime numbers p and q, calculate n = pq and φ(n) = (p-1)(q-1), select an integer e such that gcd(e, φ(n)) = 1, gcd represents the greatest common divisor, find d by calculating the multiplicative inverse of e, that is, ed≡1modφ(n), then the public key for encryption is pk RSA = (e, n), the private key for decryption is sk RSA = (d, n); S32, the controller parameters encrypted as signal encrypted as 5. The security control method based on combined encryption technology according to claim 4, characterized in that, The S4 specifically comprises: The multiplicative part of the control function is calculated using the RSA cryptographic algorithm: The resulting ciphertext is represented as:

6. The security control method based on combined encryption technology according to claim 5, characterized in that, The S5 specifically comprises: S51, the ciphertext result is decrypted using the RSA cryptographic algorithm, and the decryption result is: S52, Key generation of Paillier encryption algorithm: two large prime numbers p and q independent of each other are randomly selected to satisfy gcd(pq, (1-p)(1-q)) = 1, n = pq and λ = lcm(p-1, q-1) are calculated; an integer g is randomly selected Let S be a set of non-negative integers, Let S be a set of non-negative integers, Let S be a set of non-negative integers, λ (modn 2 ))) = 1 and for each Let S be a set of non-negative integers, Paillier = (n, g) as a public key, and sk Paillier = (p, q) as a private key; S53, encrypt the decryption result using the Paillier encryption algorithm to obtain:

7. The security control method based on combined encryption technology according to claim 6, characterized in that, The S6 specifically comprises The additive part of the control function is calculated using the Paillier cryptographic algorithm: The computed controller state is The control input is where is the controller state x c (t+1) and is the quantized value of the control input u(t), is the matrix the element in the first row and i-th column, is the matrix the element in the n c +m c row and i-th column.

8. The security control method based on combined encryption technology according to claim 7, characterized in that, The S7 specifically comprises: S71, the calculated control input decrypting to obtain S72, to controller state decrypting to obtain 9. The security control method based on combined encryption technology according to claim 7, characterized in that, The S8 comprises: by the inverse mapping function Γ -1 (k) to quantization is recovered as the inverse mapping function Γ -1 (k) is: In formula (15), κ is the parameter to be inversely mapped.

10. A system for security control based on a combination encryption technique according to any one of claims 1 to 9, characterized in that, Comprising; Control object, device to be controlled; Sensor, measuring data of the control object and sending to the controller; Mapping module, comprising a mapping function to quantize data; First encrypter, encrypting input data; Encrypted controller, performing ciphertext calculation inside the controller; Decrypter, decrypting the ciphertext result calculated by the encrypted controller; Second encrypter, encrypting input data; Inverse mapping module, comprising an inverse mapping function to restore and restore data and transmit to the actuator; Actuator, accepting and executing control signals to adjust the control object.

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