Computer Data Encryption System Based on Nonlinear Partial Differential Equations

Data encryption is to convert plaintext data into ciphertext through a data encryption algorithm and then transmit the ciphertext. After the recipient receives the ciphertext, the ciphertext is restored to plaintext, which provides protection and technical support for information security. ­e main purpose of this article is to design a computer data encryption system based on nonlinear partial dierential equations. ­is paper uses the DES encryption algorithm to encrypt data and implements an onion encryption system that encrypts the outer layer of the database and tests and analyzes the encryption eciency and additional overhead of the database encryption system on a general database to verify the design application prospects of ideas. In addition, the overall scheme of the encryption system, the hardware, and software of the system are designed in detail, the system is debugged, the overall test is tested, and the data encryption and decryption are eective and feasible.­e experimental results of this paper show that after the construction of a computer data encryption system based on nonlinear partial dierential equations, the overall security of the data is increased by 25%. In addition, after comparison, the security performance of the onion-type data encryption system is higher than that of theMySQL-type data.­e performance of the encryption system is 21% lower. It has certain practical value and signicance to apply it to the computer data encryption system.


Introduction
With the development of computer network technology and the application of network systems, computer networks have penetrated into all areas of people's lives. For example, study life, work life, and social life all need to use computer networks, greatly facilitating the exchange of information between each other, but also laying down hidden dangers for the security of information. Nowadays, losses caused by information leakage occur every day, such as personal account information leakage, the out ow of personal private les, and so on. Bene ting from the vigorous promotion of digital certi cates in the banking industry, the author has been inspired to develop a personal encryption system similar to a USB ash drive, which can encrypt all kinds of sensitive data of users at any time and escort the information security of each of us.
With the continuous popularity of cloud services, outsourcing encrypted data will become more common, and protecting the privacy of outsourced data will become more and more important. Encryption technology is the main security and con dentiality measure adopted by e-commerce, and it is the most commonly used security and con dentiality means. It uses technical means to convert important data into garbled codes for encrypted transmission and then uses the same or di erent means to decrypt after reaching the destination. e privacy protection problem in outsourcing encrypted data calculation has its particularity: in general, users encrypt their own data and upload it to the cloud server, as long as the encryption algorithm is selected appropriately and the key protection is intact, the privacy of the data can be considered to be guaranteed. However, in the process of outsourcing encrypted data calculation, in addition to protecting the user's original data information, some intermediate information generated in the calculation process must also be protected because the attacker may infer the user's original data by analyzing this information. On the premise of protecting the privacy of user data, processing and analyzing encrypted data on the cloud server so that users can complete the corresponding data analysis tasks is a problem that needs to be solved urgently.
In order to gain an in-depth understanding of data encryption technology, this paper explores the research and discussion of previous scholars. Siddig A proposed a fourthorder image denoising model. Using the fixed point theorem, he determined the existence and uniqueness of entropy solutions. Based on the Fast Explicit Diffusion Scheme (FED), numerical experiments demonstrate the effectiveness of this method in image denoising. e results are compared with three well-known fourth-order models: You and Kaveh models; Lysaker, Lundervold, and Ta models; and the most recent mean curvature (MC) model. e proposed model has advantages in removing noise while retaining image features. However, the performance of this model is not very stable, making the results not very accurate [1]. Ali et al. proposed a multi-mode authentication system that uses encrypted biometric technology for the edge center cloud environment. In the proposed system, a personal portable device is used to encrypt biometrics, thereby optimizing the use of resources and solving another limitation of the cloud environment. However, the design of the encryption system is relatively simple, making data access not very secure [2]. Ye and Huang designed an effective symmetric image encryption algorithm. In order to solve the problem of the low sensitivity of ordinary images measured by the uniform average change intensity and the number of changing pixel rates, he proposed using the premodular operation to preprocess the classic encryption algorithm. Before and after the position exchange, the invariance of the sum of pixels in the pure image, the keystream used for the replacement operation, is designed to depend on the pure image. But for most encryption algorithms, it is difficult to achieve the diffusion of the correlation with the ordinary image operation [3]. e innovations of this article are as follows: (1) many improvements have been made to the DES encryption algorithm. On the basis of maintaining the original functions, the operation steps are reduced and the encryption speed is accelerated. And in terms of code implementation, the use of assembly language with faster execution speed and the programming principle of time first has greatly improved the execution speed of the program. (2) e system uses a USB connection, which enhances the practicability of the system. e hardware part of the whole system is very small, easy to carry, can be used at any time, and is of low cost. e research presented in this paper can provide new ideas for data encryption and can also provide a new direction for the application of nonlinear partial differential equations.

Encryption Algorithm Based on Partial
Differential Equation 2.1. Nonlinear Partial Differential Equations. Partial differential equations originated in the 18th century [4]. e formation and development of their theories are closely related to the development of physics and other natural sciences and promote each other [5]. Partial differential equations have a wide range of applications in explaining and predicting natural phenomena [6].
Various physical quantities in the objective world often change with the changes of time and space position, so they can be expressed as a function of the time coordinate t and space coordinate(x 1 , x 2 , . . . , x n ). And, this kind of physical change law is usually expressed as the relationship between the rate of change of each order of time and space coordinates, that is, the equation of the partial derivative of the function v with respect to t and (x 1 , x 2 , . . . , x n ). For example, in a uniform heat transfer object, the temperature v satisfies Such equations containing unknown functions and their partial derivatives are called partial differential equations (7). Generally, a partial differential equation with v as an unknown function and (x 1 , x 2 , . . . , x n ) as a variable can be written in the following form: Among them, W is a function of its arguments, and the highest order of the partial derivative in the equation is called the order of the equation (8). e above equation can also be written as where W is called a partial differential operator [9]. If a partial differential equation is linear with respect to all its unknown functions and the derivatives of the unknown functions, it satisfies It is called a linear partial differential equation. If not, it is called a nonlinear partial differential equation. e study of nonlinear partial differential equations is the center of current differential equation research. Solving nonlinear partial differential equations is much more difficult than solving linear partial differential equations, and most nonlinear partial differential equations can only rely on numerical solutions.
Partial differential equations can be divided into three categories: elliptic equations, parabolic equations, and hyperbolic equations (10). At present, the research on secondorder partial differential equations has formed a relatively mature system. Higher-order equations, especially higherorder parabolic partial differential equations, have received extensive attention due to their profound physical background [11,12].

DES Algorithm
(1) e DES algorithm is a symmetric cryptosystem in the cryptosystem, also known as the American Data Encryption Standard. e DES encryption algorithm is a 64 bit encryption, and the key is up to 64 bits [13]. After 8 bits are discarded, the effective key is 56 bits, that is, 8 characters. If you want to decipher, you only need to enumerate 256 times to try all the keys, which is not difficult for current supercomputers [14]. e algorithm implementation process is as follows: (2) Given a 64 bit plaintext A, convert A to A 0 through a replacement IP, and the following formula can be obtained: Among them, the left 32 bits of A 0 is T 0 and S 0 is the right 32 bits of A 0 . (3) Combine the data with the key and perform 16 rounds of the same calculation, and the calculation is as follows: Among them, ⊕ represents the exclusive OR between two bit strings, f is a function, each k i is a replacement of the initial key k, and the length is 48 bits, which constitutes a key scheme [15]. (4) Do the inverse permutation of the initial permutation to S 16 T 16 and get the ciphertext as It is particularly important to note that in the last iteration, the left and right sides are not exchanged, but S 16 T 16 is used as the input of IP − 1 to get the ciphertext [16]. e design basis of DES is Shannon's replacement permutation network [17]. is encryption network takes a block of plaintext and a key as input and produces a block of ciphertext by interleaving several "rounds" (or "layers") of substitution and permutation operations. e SP network is based on two basic operations of cryptography. e alternative is called the S-box [18]. It is the only nonlinear part of the DES algorithm [19]. Its strong password determines the entire algorithm. Security strength provides the obfuscation necessary for cryptographic algorithms. e permutation is called a P-box, and its purpose is to provide an avalanche effect, that is, a small change in the plaintext or the key will cause a larger change in the ciphertext [20].

Double DES Algorithm.
As the weaknesses of DES are being studied more and more deeply, it is necessary to improve DES. One of the methods is to compound DES to strengthen its antiattack ability. is algorithm combines the advantages of both the DES and RSA algorithms. e principle is that sender uses the DES key to encrypt important data and transmit the message, and the receiver uses the RSA private key to encrypt the encrypted DES after receiving the message key to decrypt it. e simplest way is to perform secondary DES encryption [21,22]. Given civilization Q and an encryption key L 1 L 2 , the cipher text is expressed as Given a plaintext, there are 2 64 possible ciphertexts after double DES encryption. e key length used by double DES should be 112 bits, so there is a 2 112 possibility to choose the key.
at is to say, for a given ciphertext, there are 2 48 possibilities to encrypt it into the same ciphertext [23].

Triple DES Algorithm.
is article uses triple DES, which means that the plaintext is encrypted three times with three different keys so that the effective key is 168 bits and there are 24 characters in total. If you try to decipher, you must try 2168 keys, which increases the strength of the password many times and can effectively prevent brute force cracking [24].
Triple DES is a variant of the very popular DES algorithm. 3DES was designed to provide a relatively simple way to avoid similar attacks by increasing the key length of DES, rather than designing an entirely new block cipher algorithm. It is widely used in network security and data transmission. It is simple and easy to use, low in cost, and low in hardware requirements. In this article, the data transmission between the upper computer and the lower computer is a block transmission method, the block size is 64 bits, and the DES encryption algorithm is the same block encryption algorithm, so the 64 bit block length is the basic encryption unit, and the 64 bit encryption key performs a series of calculations and finally outputs a 64 bit ciphertext. In this article, a two-dimensional array key [8][8] is used to represent a block encryption unit, and a two-dimensional array Date [8][8] is used to represent a unit of key length. In order to improve the speed and efficiency of data encryption, the function DES is written in assembly language, which improves the execution efficiency of the code, saves the operating space of the single-chip microcomputer, and makes encryption of large amounts of data a reality [25].

Encryption System RSA Algorithm.
Symmetric keys have the advantages of fast encryption speed and convenient software and hardware implementation, but they have disadvantages such as complex key management and the inability to perform digital signatures. Although the RSA algorithm can achieve digital signature and key management, the amount of calculation is very large [26]. e decryption speed is very slow. Now the common practice is to combine the two, encrypt the file with AES, and then encrypt the key with RSA to give full play to their respective advantages [27].
RSA security is equal to the mathematical problem of decomposition of large numbers. In order to ensure data security, the choice of prime numbers is usually very large, which causes many problems in the calculation speed. Not only that, but RSA also has the most useful feature of the public key cryptosystem; that is, anyone can use the public key, which allows the attacker to leave traces when performing selective ciphertext attacks. erefore, it should be recommended to implement a protective measure for public key security. In response to the above problems, this article improves the RSA algorithm and proposes a new encryption algorithm, that is, more information communication [28].
rough the analysis of the RSA algorithm, it can be seen that if three or more prime factors are used, that is, N � qwe or more, the algorithm is still valid and will not be proved here. Rabin has achieved good results by using qwe as a private key in an encryption algorithm based on the secondary residue [29]. erefore, the improved algorithm proposed in this paper uses three prime factors and will be used as a private key.
At present, RSA allows to choose the size of the public key. A 512 bit key is considered insecure; a 768 bit key has no fear of being compromised by anything other than the National Security Administration (NSA); and 1012 bits in the RSA algorithm are considered safe, so the number of qwe bits is about 490. e improved algorithm uses three prime numbers. If they are all around 490 bits, the result will reach 1450 bits, which will make the algorithm safer. As the number of digits increases, if the factor is not known, the calculation will become more difficult, and it will become more difficult to crack the algorithm by calculating N. If you want to decompose N, you need to get four 490 bit prime factors. Assuming that one 490 bit prime factor is obtained, you still need to decompose 980 bits n to crack the algorithm [30].

Overall Design of the Data Encryption System.
e design of a data encryption system mainly involves hardware circuit design, single-chip principle and program design, USB interface technology, DES encryption program design, and host computer software design. In the design concept, modular design is used to separate the entire system into several subsystems, which is conducive to the orderly completion of the design. e expectation of the data encryption system based on the USB interface is to design a portable device similar to a USB disk to encrypt the data on the computer and use the USB interface to connect the two. In order to improve the security of encryption, the subject chose to separate the encryption device and the operation page. According to this requirement, the data encryption system is divided into two parts: the upper computer and the lower computer, as shown in Figure 1.
In this system, the upper computer is the computer that sends operation commands. e design of the host computer uses VC++ programming to develop an application program, which is used to perform encryption operations, allowing users to send operation commands, send data, receive data, select files, display execution speeds, etc., on the page; the design of the host computer includes two parts: layout design and functional design. e layout design mainly develops the front-end operation page, and the functional design mainly realizes the entire process of communicating with the lower computer through the USB interface, including a series of USB interface operations, data sending, and receiving. e lower computer mainly executes the corresponding operation according to the command of the upper computer and specifically refers to the hardware encryption device in this system. It contains the USB interface, the microcontroller and its peripheral circuits, and the program code packaged by the microcontroller. e work of the lower computer mainly revolves around the single-chip microcomputer, reads the command of the upper computer through the code in the single-chip microcomputer, and performs corresponding operations. e data encryption system realizes the separation of two machines. e application program of the upper computer is installed on the computer, and the lower computer is a plug and play encryption device. e user inserts the lower computer into the computer's USB slot, then opens the PCside application, and sends the preprocessed data, and the lower computer receives the data, processes it according to the instructions of the microcontroller, and finally sends the data back to the upper computer to complete an operation.
According to the function of the host computer, it is divided into layout design and functional design. Layout design is mainly to design a user operation page. On the page, you can enter a 24 bit key, select the storage location of the encrypted and decrypted files and the processed file, and send the encryption, decryption, and reset commands. In the lower part of the page, the progress of data encryption and decryption, the start and end execution time of the program, and the total time spent in program execution are displayed. e function design should call for the software development kit to realize operations such as opening, closing, and refreshing the device. In addition, the handshake process with the lower computer must be designed, including command information sending and receiving and data sending and receiving.
is effectively strengthens the combination of system functions. e design of the lower unit is based on the C8051F340 microcontroller, and the design of the entire hardware circuit is very simple. e peripheral circuit must be designed for the normal operation of the microcontroller, including the provision of a 3.3 V power supply and the design of an external reset circuit. Connect two LED lights to the singlechip microcomputer. One indicates whether the single-chip microcomputer is powered on, and the LED is on when it is normally powered on; the other indicates data transmission. When there is data flow on the USB, the LED flashes. e single-chip microcomputer programming uses C language to write functional functions and realizes the functions required by the system by calling the built-in software development kit, including USB interface operation, "handshake" with the host computer, sending data, receiving data, storing data, and calling encryption algorithm program to process data.

Data Encryption Algorithm Improvement Experiment.
e plaintext data to be encrypted are initially transformed into the unit of basic block length [31,32]. e 64 bit plaintext is divided into 8 columns each with 8 bits as a line, and the rows and columns are exchanged. In the program design, the DES_IP() function is defined to realize the data e rows and columns are interchanged, but it does not make the left and right plaintext physical space continuous as in the DES general algorithm, but only makes it logically continuous, and the odd and even rows are stored interleaved. ere is no need to change the storage order, which simplifies the code and improves execution efficiency.
First, open up the space R, using two layers of loops, and the first layer of the loop indicates the line and the second layer of loop shifts to the left. When the first column is taken, Data [1][j] is shifted to the left as a whole, and Data [1], [1] becomes the overflow bit, which is stored in the first bit of R0. en cyclically shift down, Data [2][j] is shifted to the left as a whole, Data [ [1] from left to right, so that the first column becomes the first row. When the second column is taken, the same operation is performed, and finally, after 64 cycles of left shifting, the row and column exchange of the data is realized. en the obtained 64 bit plaintext block is divided into two parts, each with 32 bits, and the left block is the left plaintext, and the right block is the right plaintext. In the array, odd numbers are left plaintext and even numbers are right plaintext.

Onion Encryption Model Design.
e basic technology of the architecture server interface database encryption system is to realize the encryption of various SQL functions in the ciphertext. Literally speaking, this technology encrypts the data layer by layer like an onion, making the data look like an onion. e SQL function corresponding to each layer of the onion is different. e top layer uses the most secure encryption algorithm to ensure the security of all database data. In SQL functions, data are always stored in ciphertext, but the ciphertext encryption algorithm is different. e design of the security model of the onion encryption structure is mainly based on the classification of SQL functions to design a function that satisfies the SQL. ese four models complete the functions of SQL and perform confidential operations on database data. e four encrypted onions are nested into onion encryption by seven different cryptographic systems. Among the seven cryptographic systems, RND is the encryption system with the strongest encryption performance. It cannot perform homomorphic calculations and maximize data security. In the design of the onion model, search and add onions are purely functional onions, with two layers; equivalent onions and comparison onions are full performance onions, which are designed with four layers, and the outer layer encryption is highly secure. e encryption scheme is used to ensure that no information is leaked. e inner encryption is an encryption scheme with a gradual decrease in security, which can only be accessed when the corresponding inquiry is required.
Since users initiate various queries, which onion type and layer of onion layers need to be accessed for different queries, the data encryption agent in the proxy architecture of the database encryption system is mapped to different encryption layers according to the query. In addition, the database management server needs to dynamically record the status of each onion of each data item in the database. en, according to the query, the data are decrypted or encrypted for the corresponding onion layer.

Data Encryption Algorithm Analysis.
Confusion and diffusion are the bases of Shannon's design of encryption algorithms, and chaotic systems have exactly this property. Since the chaotic system is sensitive to the initial value, even a small disturbance in the initial value will bring about a huge difference, which is just in line with the avalanche effect of the algorithm. Chaotic systems generally use nonlinear equations, which are particularly critical for cryptographic design. Usually, the core of an algorithm is its nonlinear part because the linear part is vulnerable to differential attacks.

Data encryption system
Host computer Lower computer USB interface Host-side application Peripheral circuit Wrapper Figure 1: Overall structure of the data encryption system.

Mobile Information Systems
For example, the core of DES is its nonlinear S-box, and the reason why the MH backpack algorithm is easy to crack is not only due to its low density but an important reason is that its threshold function adopts a linear structure, which greatly reduces its security. e chaotic system has good characteristics, so it is used in the design of encryption algorithms, and the effect is significant; it solves the problem of image encryption.
e specific results are shown in Figure 2.
From the graph, we can see that even if the initial value is very small, it cannot be decrypted correctly, which is caused by the sensitivity of chaos to the initial value. Also, the gray distribution of the ciphertext image is more uniform, which can effectively resist probability density attacks.
Since chaotic encryption belongs to symmetric encryption, in practice, the key, that is, the control parameter, can be transmitted using public key encryption algorithms such as RSA and ECC. At the same time, we can see that when we chaotically encrypt the image, we mainly apply the chaotic sequence to the plaintext image. In order to make the ciphertext image more complex and difficult to identify, we can use some complex transformations, such as wavelet changes. Its main feature is that it can fully highlight the characteristics of some aspects of the problem through transformation, can analyze the localization of time and frequency, gradually refine the signal at multiple scales through scaling and translation operations, and finally achieve time subdivision at high frequencies. At the same time, in the selection of chaotic sequences, different sequences of multiple chaotic systems can also be used for superposition, which is more random and achieves a better encryption effect.

Performance Analysis of the Data Encryption System.
e performance test of TPC-C query mixing was carried out on MySQL and the onion database encryption systems. e test results are given through analysis, which shows the TPC-C query throughput on servers with different core numbers. It can be seen that when the number of cores is 1 to 2, the throughput of MySQL and the onion database encryption system is similar. As the number of cores increases, the performance of the onion database encryption system is worse than that of MySQL. Of course, this is because the onion database encryption system is inevitably caused by operations on ciphertext data, but the overall throughput of the onion database encryption system is only 21%-26% less than that of MySQL.
is efficiency can make the onion database encryption system practical, as shown in Figure 3.
In order to understand the resource overhead of the onion database encryption system, different types of SQL queries were tested through throughput in TPC-C, and the test results of the onion database encryption system and MySQL were compared, as shown in Figure 4. It can be seen that compared with MySQL, the onion database encryption system has less throughput on different types, and the highest value is only 3.5 × 10 4 , but the difference is less. Mainly SUM, the efficiency loss on Upd.inc is large.
In order to understand and analyze the time difference between the onion database encryption system processing various standard SQL queries, we have completed the program-level test on different types of SQL processing time of the onion database encryption system and MySQL, as shown in Table 1. As shown by the time expenditure results of the database encryption system and MySQL on different SQL queries, the related test results show that the overall overhead on the server has increased by 19% or 0.03 ms. Onion database encryption system agents add 0.05 ms to each query, of which 23% are used for MySQL agents, 24% are used for data encryption and decryption, and 49% are used for query analysis and processing.
According to the performance test results, the efficiency of the onion database encryption system is slower than that of MySQL. is is because the onion database encryption system performs SQL queries on encrypted data while MySQL performs SQL queries on plaintext data. Encryption and decryption will inevitably lead to a reduction in efficiency. But, this loss will not affect the practicality of the onion database encryption system. erefore, the onion database encryption system is a practical design idea for an encrypted database system, that can execute complete SQL queries on encrypted data.

Evaluation and Analysis of the Data Encryption System.
is article surveys 400 professional encryption personnel. rough statistics and analysis of data, they can get their evaluation of the computer data encryption systems. Among them, 54% of the professionals are very satisfied with the evaluation of the computer data encryption systems. e computer data encryption system is handy, and 33% of professionals are generally satisfied with the computer data encryption system, and 9% are dissatisfied with the computer data encryption system. Finally, 4% of the professionals are very satisfied with the computer data encryption system. If they are satisfied, it may be that they are used to the previous encryption system, as shown in Figure 5.
A comprehensive analysis can conclude that most professionals are still satisfied with the data encryption system, and their knowledge of information security has also improved to a certain extent during the learning process of encryption algorithms. e encryption algorithm is the core of information security. At the same time, there are many aspects such as key distribution, key management, security protocol, and authentication protocol. If applied to the database, the information security system will be greatly protected. In the communication protocol, there are still only a few types of algorithms. I hope to design more and more encryption algorithms, signature algorithms, hash algorithms, etc., so that multiple algorithms can be crosscombined so that the communication protocol will also be richer and there will be more choices.

Conclusions
is paper improves the efficiency of the data encryption algorithm, improves the decryption efficiency and security of the algorithm, and reduces the encryption efficiency a little bit. At the same time, by combining the symmetric encryption algorithm and the public key algorithm, a new encryption system is proposed.
e system integrates identity authentication, protection of public keys, digital signatures, and other technologies. It can resist attacks by multiple means and meet the needs of modern communication.
Based on the design idea of ciphertext database processing, this paper designs an encryption model for onion databases, provided that the fully unified encryption cannot meet the practical requirements and the start-up and implementation of the database encryption system have been completed. In this article, by creating a simple test environment, the performance tests of the MySQL database encryption system and the onion basic system are carried out, and the encryption efficiency of the overhead time is compared and analyzed, and the onion database is verified by indicators such as encryption efficiency.
With the in-depth development of scientific research, experts and scholars have found that the description of the specific model of the variable coefficient nonlinear partial differential equation is closer to the reality. erefore, the research on the fractional order nonlinear partial differential equation can be used for deeper variable coefficient fractional nonlinear partial differentiation in the future. e equation's direction develops. When selecting auxiliary equations, you can not only limit yourself to the auxiliary equations in the text, but also you can exchange them for other auxiliary equations, such as the Bernoulli equation. You can explore their Backlund transformation and nonlinear superposition formula. e research machine of the data encryption system is complex. e experiments in this paper are carried out under the exclusion of many interference factors, and there are still shortcomings in the scale of use. In the future research process, we will continue to improve this point and improve the quality of work.

Data Availability
No data were used to support this study.

Conflicts of Interest
e authors declare no conflicts of interest.