# Application of Differential Evolution Algorithm in the Construction and Simulation of Interactive English Translation Teaching Mode

Authors: Chi Che
Journal: Advances in Multimedia
 (2022)

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## Abstract

To improve the effect of English translation teaching, this paper combines the differential evolution algorithm to construct and simulate the interactive English translation teaching mode and analyzes the differential enumeration attack. Moreover, this paper studies the algorithm structure of the LowMC algorithm and evaluates the rationality of the LowMC algorithm round number setting by analyzing the actual attack effect of the key initial round number of a specific linear layer. Additionally, by studying whether the key initial round number can reach the theoretical value under the actual linear layer, the effect of differential evolution algorithm processing teaching information is evaluated. Through expert evaluation, it can be seen that the interactive English translation teaching model based on the differential evolution algorithm proposed in this paper has good effects and can improve the quality of English translation teaching.


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## Body

## 1. Introduction

A social network is a collection of multiple points and connections between points, and the points in the social network are social actors, and the connections in the social network are the relationships between actors. Moreover, a social network refers to a relatively stable social network formed by individual members in a society due to interaction. Social networks are divided into two types: friend networks or explicit networks; interaction networks or implicit networks. The first one is presented in the form of a user’s friend list, which is a network established by explicit social relationships. The second is presented in the form of an association through the user’s online interaction behavior. The online learning interaction network is an interaction network constructed based on two types of nodes between teachers and students, teacher–student interaction, and student-student interaction.In the online learning environment, teachers no longer understand the learning situation and performance of each student through teaching or face-to-face communication as in traditional face-to-face classrooms but can record and analyze students’ various learning behaviors through data mining and big data analysis technologies [1], including login, browsing, homework, communication, and testing, to understand students’ learning performance in real-time through these behavioral data and give precise positioning and accurate intervention to different students based on these data [2]. In online learning, teachers should focus on the learners themselves, rather than teaching technology, teaching resources, and organization and arrangement of teaching activities. Moreover, teachers are no longer the only imparters of knowledge and controllers of learning activities and should pay attention to the development of students’ online learning activities and the personal growth and development of students [3]. At the same time, students are participants in learning activities. In traditional classrooms, learning activities are mainly led by teachers, and students exist as pure activity participants [4]. In contrast, online learning platforms can provide learners with more autonomous learning space and learning resources, thereby greatly improving learners’ activity participation and giving full play to their activity subjectivity. Based on the support of the online learning platform, students can obtain various learning resources for their own learning needs in real-time, communicate with classmates, teachers, or other relevant personnel through various online interactive media, and share learning resources and learning experiences. Moreover, students can carry out independent learning or group collaborative learning on computer terminals through the network, which is not limited by face-to-face classroom teaching in terms of resources, the number of people, space, and time [5]. At the same time, with the support of such online learning activities, students’ participation in activities will be more active, conscious, and more in line with the needs of individual development [6].Collect the interactive data on the online learning platform according to a certain period of time, clean the collected data, remove the content data published by users who have no interaction relationship, then clean up the nontext and meaningless corpus, clear the interactive content data not published by teachers or students, and finally obtain online learning interactive data [7]. Standardize the data: [publisher, publisher role, reply object, reply object role, release time, reply content]. On this basis, the online learning network is represented: [publisher, publisher role, reply object, reply object role, interaction weight (number of times)]. Taking teachers or students as nodes and three interaction types as relationships, an online learning interaction network is constructed [8].From the perspective of communication, interaction is the information transmission between the sender and the receiver. All classroom teaching processes have interactive behaviors, but different types of courses have different interaction forms and characteristics [9]. Teacher–student interaction plays a very important role in the teaching process, and the effect of teacher–student interaction has a very direct impact on the quality of classroom teaching. In synchronous classroom teaching, especially, there is a sense of spatial distance between the main lecturer and the remote students. Through effective teacher–student interaction, the teaching and learning of teachers and students in different places can be reintegrated. Compared with traditional classroom interaction, it is more complicated and easier to derive more new questions [10].The external world is a complex entity. People are in this environment; they need to know and understand it and have various connections with it, to establish an individual-specific cognitive system within themselves, including human beings [11]. In the face-to-face interaction between people, the voice information from the mouth is mainly used, and the eye information expressed by the eyes and the facial expression information are supplemented to form the information transmission structure between people and people. In some special cases, such as the lack of language consensus between the two sides of the communication, the gesture information and written text information are expressed by the hand as a supplementary form of transmission after the language information. When the communication between people changes from “direct face-to-face communication” to “communication through computer as a medium” and the external world becomes a computer environment, the communication between people becomes “person-computer-one-person” interactive activities [12]. After the input of various human sensory information is recognized and integrated by the computer, it is output through various output devices, especially the emergence of virtual reality technology, which makes the communication between people through the computer more natural and richer. Therefore, to make human-to-human communication natural and efficient, it is necessary for computers to understand human mental models and behavioral models and establish a user model that supports collaborative perception, to better support human-to-human interaction [13]. Therefore, including the content of the user model that supports collaborative perception in the computer interaction system and the establishment of a computer behavior system based on the human psychological model is a necessary means to make the interaction process between people and people through the computer conform to human psychology and behavior. Computer-mediated human-to-human interaction is different from human–computer interaction. It emphasizes the communication and collaboration between people. Therefore, this human-to-human interaction technology should be established in combination with human interaction patterns in real life [14]. It is necessary to study how people conduct daily communication in real life, including the way people express their intentions, the way they receive information from the outside world, and the intentions expressed to people in the outside world and the response model of people when they ask questions. These expression models and response models are associated with the type of user and the user’s experience, abilities, skills, and preferences in the domain [15]. At the same time, different users have different computer knowledge, comprehensive abilities, and various factors that affect their processing interactions. Therefore, it is necessary to understand the characteristics of all aspects of user behavior (from behavior to primary perception) and establish corresponding user models so as to establish user models in corresponding application fields to support the improvement of interaction efficiency [16]. Through the analysis of user characteristics, we have a more detailed understanding of the skills and experience of most users in a certain field, so that the system based on the user model can better understand the user's intention and give corresponding interactive feedback so as to better support the collaborative activities between users [17].The profile features of the user model include the learner’s login information, background knowledge, personal preferences, and current state. The login information is that when the learner logs into the network and enters the learning environment, the user model gives the learner’s personal identification, name, login password, photo, resume, role set, user validity period, and current task to the system [18]. Background knowledge refers to the learner’s age, gender, and knowledge level. Personal preference refers to the learner’s preferred learning strategy, media format, interaction style, and interface style.Current status refers to the last logout status or current learning status of learners, including the current spatial location, whether to participate in group activities, whether group activities are online, etc. The psychological characteristics of the user model include the learner’s cognitive ability, subjective willingness, and the ability to collaboratively perceive [19]. Cognitive ability includes the learner’s learning ability, memory, thinking, attention, and learning motivation. Subjective willingness refers to whether the learner is willing to use the adaptive mechanism and whether he is willing to cooperate with others in learning. The ability of collaborative perception refers to learning. The learning effect is produced by the sensory ability of various senses and the use of various interactive devices [20].This paper combines the differential evolution algorithm to construct and simulate the interactive English translation teaching mode to improve the effect of English translation teaching and promote the interaction of English translation teaching.


## 2. Differential Evolution Algorithm

### 2.1. Differential Enumeration Attack Method

The classical differential attack method researches the probability propagation of a specific plaintext differential in the encryption process and discovers the output differential whose propagation probability has obvious advantages compared with the uniform distribution and uses the nonrandomness of the differential to realize the key recovery attack. To mine this nonrandom feature, it is usually necessary to apply many plain-ciphertext pairs to the discriminator to obtain a statistical distribution result.The classical differential enumeration attack method also utilizes the known differential propagation property in classical differential analysis and obtains all possible output differentials by passing an input differential through the differential propagation property. Moreover, it directly represents the state value in an enumerated manner by means of some special probability or truncation difference of fixed special position. To reduce the implementation complexity, when the differential enumeration attack is implemented, the differential state value is not directly obtained by enumeration, but the differential state obtained after tracking the input differential and output differential of the S box.After all possible differences are obtained through the differential propagation property, the differential enumeration attack discriminator is constructed by usingr rounds of differential sets. After the differential enumeration attack discriminator is obtained, it can be judged whether the guessed key is correct, to recover the correct key. Specifically, in offline operation, for a given input differential, create a list of differences that can be reached after r rounds of encryption. During online operation, for a pair of plain ciphertexts satisfying a given input difference, it is necessary to guess the key to perform partial encryption and decryption operations. If the obtained difference is in the difference set constructed in the offline process, the guessed key may be the correct key; otherwise, it must be the wrong key. At the same time, an effective discriminator needs to satisfy two basic conditions.(1)
In order to improve the probability of wrong key exclusion, the size of the difference list can be much smaller than the size of all difference lists.(2)
The complexity of enumerating differences is lower than that of exhaustive search.The principle of the meet-in-the-middle attack is to divide the block cipherE into two parts E=E1. The key involved in E2,E1 is denoted as k1, and the key involved in E2 is denoted as k2. For the selected plaintext pair (P, Q), we use the key k1 to encrypt the plaintext P, and use the key k2 to decrypt the ciphertext C. If the two obtained values are the same, the guessed key may be correct; otherwise, it must be the wrong key. The essence of meet-in-the-middle attack is to rely on the method of time-space balance, at the expense of the higher storage complexity of the precomputing process, which significantly reduces the time complexity of the online attack phase, and the method has strong universality.


### 2.2. Combination of Differential Enumeration Attack and Meet-in-the-Middle Attack

It is noted that, in the classical differential enumeration attack, it is necessary to enumerate all possible output differences, but the size of the differential set will expand rapidly with the increase of the number of rounds, which becomes an important defect that restricts the application of the classical differential enumeration attack to the long-round algorithm attack. To solve this problem, Tang et al. proposed a combination of differential enumeration attack and meet-in-the-middle attack. This shortens the number of expansion rounds in one direction of the difference, reduces the complexity of the construction of the differentiator, and lengthens the total number of rounds of the differentiator, to achieve a better attack effect (as shown in Figure1).Figure 1
Differential enumeration attack.Specifically, for a given input differentialΔin∈F2n, by analyzing the differential propagation characteristics of the forward encryption r1 round, all possible differentials reachable at r1 round are obtained, and a differential list D1 is constructed. For a given output differential Δout∈F2n of r1+r2 round, by analyzing the differential propagation characteristics of reverse decryption r2 round, all possible differentials reachable at r1 round are obtained, and a differential list D2 is constructed. If D1 and D2 collide, a differential route of length r1+r2 is obtained, and the key can be recovered by analyzing the differential route. If the output difference is obtained by taking the difference after r1+r2 rounds of encryption of plaintext pairs satisfying the difference Δin, then D1 and D2 must collide. If the output difference is randomly selected, then the probability of collision must be less than 1.To ensure the validity of the constructed discriminator, it is necessary to ensure that the sum of the complexity of generating the difference list and obtaining the collision is less than the complexity of the exhaustive search. In general, the time complexity of collisions is fixed and usually negligible, so only the complexity of generating the difference list needs to be analyzed.Definition 1.
Differential Uniformity. For the function Sx:F2n⟶F2m1, δ=maxx|Sx⊕Sx⊎α=β,x∈F2n, and δ is the differential uniformity of S(x).
After a rough analysis, it can be seen that the upper bound of the number of differences that can be achieved afterr rounds of encryption is δrm, where δ is the difference uniformity of S boxes, and m is the number of S boxes in each round. Since not all S-boxes are active when passing through the nonlinear layer, the number of inactive S-boxes can be smaller than the difference uniformity. In order to obtain a more accurate number of differences, consider reducing the number of achievable differences from δrm to λrm, where λ is the number of output differences that can be achieved after a random input difference passes through the S box.
The random input difference can reach the estimated valueλr1m of the number of output differences after r1 rounds, which determines the size of the difference list D1; namely,(1)D1=λr1m.
In the same way, the size of the difference listD2 obtained by the output differential backpropagation r2 rounds is obtained:(2)D2=λr2m.
In summary, the total time complexity of constructing the discriminator isD1+D2, and the following conditions are obtained:(3)D1+D2<2k.
To ensure the basic condition that the time complexity of enumeration difference is less than that of exhaustive search, the first condition satisfied by the number of rounds of the discriminator is obtained by transforming the previously mentioned conditions:(4)maxr1,r2<klog2λm.
On the other hand, to avoid false collisions, the probability of two difference lists colliding should be less than 1; that is, the following conditions are met:(5)D1×D2<2n.
After the transformation, the second condition to be satisfied by the number of differentiator rounds is obtained:(6)r1+r2<nlog2λm.
Combining conditions (4) and (6), and taking r1=r2 will reach the longest number of rounds, we can obtain the final conditions that the number of differentiator rounds needs to meet:(7)r1=r2<min1/2nlog2λm,klog2λm.


### 2.3. Application of Differential Enumeration Attack in LowMC Algorithm Analysis

Although the differential enumeration attack method combined with the meet-in-the-middle attack idea significantly improves the number of attackable rounds of the target algorithm, it can be seen from condition (7) that when the key length is greater than half of the block length, the number of attack rounds will be controlled by the block length. To solve this problem, Rechbergerd et al. extended the study of the propagation characteristics of single difference to the propagation characteristics of d-dimension difference grouping composed of d differences. The d difference is defined as follows.Definition 2.
S-polytope An s-polytope onF2n is defined as an s-tuple on F2n.Definition 3.
d Difference. The d difference corresponding to a d+1 polytope x0,x1,…,xd is defined as x0⊕x1,x0⊕x2,…,x0⊕xd,d, and the number of differences d in the m difference is called the difference dimension.
Combined with the previously mentioned definitions, the single differential enumeration attack can be extended to the differential enumeration attack of d differential. There are two parts to adjust.(1)
The average output differential number corresponding to a random input differential is changed to the average output differential number corresponding to a random inputd differential.(2)
d differential collisions are used instead of single differential collisions.
The adjusted differential enumeration attack discriminator can be extended to ad-dimensional differential enumeration attack discriminator. The basic idea of d-dimensional differential enumeration attack is summarized as follows. For the input d difference Δin1,Δin2,…,Δind, Δini∈F2n, by analyzing the difference propagation law of the forward encryption r1 round, the difference list Dd1 that can be reached at the r1 round can be obtained. For a given output d difference Δout1,Δout2,…,Δoutd, Δouti∈F2n of r1+r2 round, the reachable difference list Dd2 at r2 round can be obtained by analyzing the differential propagation law of reverse decryption r1 round. If Dd1 and Dd2 collide, a differential route of length r1+r2 is obtained. Similarly, due to the round function structure of the LowMC algorithm, only part of the state bits passes through the S box, so for some special input d differences, there is always an r0 round difference route with a probability of 1. We call the number of r0 round of the differential route with the probability of establishment of the differential route as 1 as the key initial round number, which is defined as follows.Definition 4.
Key Initial Round Number. The critical initial round number is defined as the length of the differential route with a propagation probability of 1 obtained by selecting an appropriate input differential in some nonlinear layers.
This differential route with probability 1 can always be placed before the classical differential enumeration attack, thus extending the length of the differential enumeration attack differentiator tor0+r1+r2 rounds. The differential enumeration attack on the LowMC algorithm is shown in Figure 2.
Similar to the analysis in Section1, the upper limit of the number of differences that can be achieved after r1 rounds of encryption is δdrm, where δd is the d difference uniformity of the S box, and the maximum value of δd is 2d from the definition of d difference. Similarly, in order to obtain a more accurate differential diffusion number, the achievable differential number is reduced from δdrm to λdrm, where λd is the number of d output differentials that can be achieved after a random d differential passes through the S box. Moreover, as λd increases, it gradually tends to δd.
Similar to the derivation of the difference listD1,D2 obtained in the classic differential enumeration attack, the sizes of the two d difference lists Dd1 and Dd2 obtained after the d difference through differential propagation are(8)Dd1=λdr1m,Dd2=λdr2m.
From condition (3), we can obtain the first condition of the number of differentiator rounds by analogy as(9)maxr1,r2<klog2λdm.
On the other hand, after the single difference is extended tod difference, the size of all possible difference lists is extended from 2n to 2dn, so that the upper limit of the number of achievable differences is extended, and the second condition to be satisfied by the number of differentiator rounds is derived:(10)Dd1×Dd2<2dn.
Combining conditions (2) and (3), the maximum number of attack rounds under the d differential enumeration attack is obtained as follows:(11)r1=r2<min1/2dnlog2λdm,klog2λdm.
In addition, it should be noted that the number of differences in thed difference should also meet the corresponding restrictions. The most basic restriction is to be smaller than the amount of data available for the attack, and second, according to condition (4), d can be obtained to a maximum of ⌈2k/n⌉. At this time, the maximum number of attack rounds is controlled by the key length, and increasing the differential dimension will only increase the complexity but will not lengthen the number of attack rounds.
Specific to the LowMC algorithm differential enumeration attack, formula (11) gives good estimates of r1 and r2. The designer’s estimate of r0 assumes that the linear layer of the LowMC algorithm is completely random. The designer’s estimate assumes that the linear layer of the LowMC algorithm is completely random. In the process of differential enumeration attack, the number of S-boxes that may be activated increases by at most m for each additional round of differential routes. The number of bits passing through the S box is correspondingly increased by at most 3m; then after r0 rounds of encryption, the number of bits passing through the active S box is at most 3r0m. Therefore, there are 2n−3r0m differences that do not activate any S box. In order to ensure that there is a d differential feature with a probability of 1 in the r0 round, the relevant parameters need to satisfy 2n−3r0m>d, so the theoretical maximum value of r0 is derived as follows:(12)r0=n−log2d3m.
We call the value in formula (12) the theoretical key starting round number. When the critical initial round number reaches the theoretical maximum value, the round number of differential enumeration attack can be maximized.Figure 2
Application of differential enumeration attack on LowMC algorithm.∗Δxi: the i-th difference of the x th round; r0: critical starting rounds; r1: encryption direction diffusion rounds; r2: decryption direction diffusion rounds.


## 2.1. Differential Enumeration Attack Method

The classical differential attack method researches the probability propagation of a specific plaintext differential in the encryption process and discovers the output differential whose propagation probability has obvious advantages compared with the uniform distribution and uses the nonrandomness of the differential to realize the key recovery attack. To mine this nonrandom feature, it is usually necessary to apply many plain-ciphertext pairs to the discriminator to obtain a statistical distribution result.The classical differential enumeration attack method also utilizes the known differential propagation property in classical differential analysis and obtains all possible output differentials by passing an input differential through the differential propagation property. Moreover, it directly represents the state value in an enumerated manner by means of some special probability or truncation difference of fixed special position. To reduce the implementation complexity, when the differential enumeration attack is implemented, the differential state value is not directly obtained by enumeration, but the differential state obtained after tracking the input differential and output differential of the S box.After all possible differences are obtained through the differential propagation property, the differential enumeration attack discriminator is constructed by usingr rounds of differential sets. After the differential enumeration attack discriminator is obtained, it can be judged whether the guessed key is correct, to recover the correct key. Specifically, in offline operation, for a given input differential, create a list of differences that can be reached after r rounds of encryption. During online operation, for a pair of plain ciphertexts satisfying a given input difference, it is necessary to guess the key to perform partial encryption and decryption operations. If the obtained difference is in the difference set constructed in the offline process, the guessed key may be the correct key; otherwise, it must be the wrong key. At the same time, an effective discriminator needs to satisfy two basic conditions.(1)
In order to improve the probability of wrong key exclusion, the size of the difference list can be much smaller than the size of all difference lists.(2)
The complexity of enumerating differences is lower than that of exhaustive search.The principle of the meet-in-the-middle attack is to divide the block cipherE into two parts E=E1. The key involved in E2,E1 is denoted as k1, and the key involved in E2 is denoted as k2. For the selected plaintext pair (P, Q), we use the key k1 to encrypt the plaintext P, and use the key k2 to decrypt the ciphertext C. If the two obtained values are the same, the guessed key may be correct; otherwise, it must be the wrong key. The essence of meet-in-the-middle attack is to rely on the method of time-space balance, at the expense of the higher storage complexity of the precomputing process, which significantly reduces the time complexity of the online attack phase, and the method has strong universality.


## 2.2. Combination of Differential Enumeration Attack and Meet-in-the-Middle Attack

It is noted that, in the classical differential enumeration attack, it is necessary to enumerate all possible output differences, but the size of the differential set will expand rapidly with the increase of the number of rounds, which becomes an important defect that restricts the application of the classical differential enumeration attack to the long-round algorithm attack. To solve this problem, Tang et al. proposed a combination of differential enumeration attack and meet-in-the-middle attack. This shortens the number of expansion rounds in one direction of the difference, reduces the complexity of the construction of the differentiator, and lengthens the total number of rounds of the differentiator, to achieve a better attack effect (as shown in Figure1).Figure 1
Differential enumeration attack.Specifically, for a given input differentialΔin∈F2n, by analyzing the differential propagation characteristics of the forward encryption r1 round, all possible differentials reachable at r1 round are obtained, and a differential list D1 is constructed. For a given output differential Δout∈F2n of r1+r2 round, by analyzing the differential propagation characteristics of reverse decryption r2 round, all possible differentials reachable at r1 round are obtained, and a differential list D2 is constructed. If D1 and D2 collide, a differential route of length r1+r2 is obtained, and the key can be recovered by analyzing the differential route. If the output difference is obtained by taking the difference after r1+r2 rounds of encryption of plaintext pairs satisfying the difference Δin, then D1 and D2 must collide. If the output difference is randomly selected, then the probability of collision must be less than 1.To ensure the validity of the constructed discriminator, it is necessary to ensure that the sum of the complexity of generating the difference list and obtaining the collision is less than the complexity of the exhaustive search. In general, the time complexity of collisions is fixed and usually negligible, so only the complexity of generating the difference list needs to be analyzed.Definition 1.
Differential Uniformity. For the function Sx:F2n⟶F2m1, δ=maxx|Sx⊕Sx⊎α=β,x∈F2n, and δ is the differential uniformity of S(x).
After a rough analysis, it can be seen that the upper bound of the number of differences that can be achieved afterr rounds of encryption is δrm, where δ is the difference uniformity of S boxes, and m is the number of S boxes in each round. Since not all S-boxes are active when passing through the nonlinear layer, the number of inactive S-boxes can be smaller than the difference uniformity. In order to obtain a more accurate number of differences, consider reducing the number of achievable differences from δrm to λrm, where λ is the number of output differences that can be achieved after a random input difference passes through the S box.
The random input difference can reach the estimated valueλr1m of the number of output differences after r1 rounds, which determines the size of the difference list D1; namely,(1)D1=λr1m.
In the same way, the size of the difference listD2 obtained by the output differential backpropagation r2 rounds is obtained:(2)D2=λr2m.
In summary, the total time complexity of constructing the discriminator isD1+D2, and the following conditions are obtained:(3)D1+D2<2k.
To ensure the basic condition that the time complexity of enumeration difference is less than that of exhaustive search, the first condition satisfied by the number of rounds of the discriminator is obtained by transforming the previously mentioned conditions:(4)maxr1,r2<klog2λm.
On the other hand, to avoid false collisions, the probability of two difference lists colliding should be less than 1; that is, the following conditions are met:(5)D1×D2<2n.
After the transformation, the second condition to be satisfied by the number of differentiator rounds is obtained:(6)r1+r2<nlog2λm.
Combining conditions (4) and (6), and taking r1=r2 will reach the longest number of rounds, we can obtain the final conditions that the number of differentiator rounds needs to meet:(7)r1=r2<min1/2nlog2λm,klog2λm.


## 2.3. Application of Differential Enumeration Attack in LowMC Algorithm Analysis

Although the differential enumeration attack method combined with the meet-in-the-middle attack idea significantly improves the number of attackable rounds of the target algorithm, it can be seen from condition (7) that when the key length is greater than half of the block length, the number of attack rounds will be controlled by the block length. To solve this problem, Rechbergerd et al. extended the study of the propagation characteristics of single difference to the propagation characteristics of d-dimension difference grouping composed of d differences. The d difference is defined as follows.Definition 2.
S-polytope An s-polytope onF2n is defined as an s-tuple on F2n.Definition 3.
d Difference. The d difference corresponding to a d+1 polytope x0,x1,…,xd is defined as x0⊕x1,x0⊕x2,…,x0⊕xd,d, and the number of differences d in the m difference is called the difference dimension.
Combined with the previously mentioned definitions, the single differential enumeration attack can be extended to the differential enumeration attack of d differential. There are two parts to adjust.(1)
The average output differential number corresponding to a random input differential is changed to the average output differential number corresponding to a random inputd differential.(2)
d differential collisions are used instead of single differential collisions.
The adjusted differential enumeration attack discriminator can be extended to ad-dimensional differential enumeration attack discriminator. The basic idea of d-dimensional differential enumeration attack is summarized as follows. For the input d difference Δin1,Δin2,…,Δind, Δini∈F2n, by analyzing the difference propagation law of the forward encryption r1 round, the difference list Dd1 that can be reached at the r1 round can be obtained. For a given output d difference Δout1,Δout2,…,Δoutd, Δouti∈F2n of r1+r2 round, the reachable difference list Dd2 at r2 round can be obtained by analyzing the differential propagation law of reverse decryption r1 round. If Dd1 and Dd2 collide, a differential route of length r1+r2 is obtained. Similarly, due to the round function structure of the LowMC algorithm, only part of the state bits passes through the S box, so for some special input d differences, there is always an r0 round difference route with a probability of 1. We call the number of r0 round of the differential route with the probability of establishment of the differential route as 1 as the key initial round number, which is defined as follows.Definition 4.
Key Initial Round Number. The critical initial round number is defined as the length of the differential route with a propagation probability of 1 obtained by selecting an appropriate input differential in some nonlinear layers.
This differential route with probability 1 can always be placed before the classical differential enumeration attack, thus extending the length of the differential enumeration attack differentiator tor0+r1+r2 rounds. The differential enumeration attack on the LowMC algorithm is shown in Figure 2.
Similar to the analysis in Section1, the upper limit of the number of differences that can be achieved after r1 rounds of encryption is δdrm, where δd is the d difference uniformity of the S box, and the maximum value of δd is 2d from the definition of d difference. Similarly, in order to obtain a more accurate differential diffusion number, the achievable differential number is reduced from δdrm to λdrm, where λd is the number of d output differentials that can be achieved after a random d differential passes through the S box. Moreover, as λd increases, it gradually tends to δd.
Similar to the derivation of the difference listD1,D2 obtained in the classic differential enumeration attack, the sizes of the two d difference lists Dd1 and Dd2 obtained after the d difference through differential propagation are(8)Dd1=λdr1m,Dd2=λdr2m.
From condition (3), we can obtain the first condition of the number of differentiator rounds by analogy as(9)maxr1,r2<klog2λdm.
On the other hand, after the single difference is extended tod difference, the size of all possible difference lists is extended from 2n to 2dn, so that the upper limit of the number of achievable differences is extended, and the second condition to be satisfied by the number of differentiator rounds is derived:(10)Dd1×Dd2<2dn.
Combining conditions (2) and (3), the maximum number of attack rounds under the d differential enumeration attack is obtained as follows:(11)r1=r2<min1/2dnlog2λdm,klog2λdm.
In addition, it should be noted that the number of differences in thed difference should also meet the corresponding restrictions. The most basic restriction is to be smaller than the amount of data available for the attack, and second, according to condition (4), d can be obtained to a maximum of ⌈2k/n⌉. At this time, the maximum number of attack rounds is controlled by the key length, and increasing the differential dimension will only increase the complexity but will not lengthen the number of attack rounds.
Specific to the LowMC algorithm differential enumeration attack, formula (11) gives good estimates of r1 and r2. The designer’s estimate of r0 assumes that the linear layer of the LowMC algorithm is completely random. The designer’s estimate assumes that the linear layer of the LowMC algorithm is completely random. In the process of differential enumeration attack, the number of S-boxes that may be activated increases by at most m for each additional round of differential routes. The number of bits passing through the S box is correspondingly increased by at most 3m; then after r0 rounds of encryption, the number of bits passing through the active S box is at most 3r0m. Therefore, there are 2n−3r0m differences that do not activate any S box. In order to ensure that there is a d differential feature with a probability of 1 in the r0 round, the relevant parameters need to satisfy 2n−3r0m>d, so the theoretical maximum value of r0 is derived as follows:(12)r0=n−log2d3m.
We call the value in formula (12) the theoretical key starting round number. When the critical initial round number reaches the theoretical maximum value, the round number of differential enumeration attack can be maximized.Figure 2
Application of differential enumeration attack on LowMC algorithm.∗Δxi: the i-th difference of the x th round; r0: critical starting rounds; r1: encryption direction diffusion rounds; r2: decryption direction diffusion rounds.


## 3. Construction and Simulation of Interactive English Translation Teaching Mode Based on Differential Evolution Algorithm

In the process of information dissemination in English translation teaching, each dissemination subject is affected by external factors and can participate in information interaction through different forms of network tools or applications, as shown in Figure3.Figure 3
Six degrees of propagation mode.Based on the actual situation of online English translation teaching, this paper proposes a network information dissemination model, which involves elements such as communicators, information, network media, audiences, and feedback, as shown in Figure4.Figure 4
Network information dissemination mode.The virtual community of English translation online teaching is a medium and channel of Internet information dissemination. The process of information dissemination in the virtual community of English translation online teaching is shown in Figure5.Figure 5
Information dissemination process in virtual community of English translation online teaching.The fifth stage of the five-stage model of knowledge transfer is the assimilation stage of knowledge, as shown in Figure6. In this stage, it is necessary for the recipient of the knowledge to integrate the new knowledge transferred by the knowledge transferer. This new knowledge is transformed into a habit, experience, or method of their own reality, which can better promote and promote the further dissemination and improvement of knowledge to a certain extent.Figure 6
Five-stage model.There is a lot of information in the online learning interaction network that is worth considering comprehensively to analyze the influence of the dominant node. Therefore, this paper constructs a comprehensive analysis model of the influence of the dominant node of the online learning interaction network, as shown in Figure7. It is mainly based on the static and dynamic properties of the online learning interactive network and comprehensively analyzes and processes the influence of the dominant node.Figure 7
Comprehensive analysis of the influence of dominant nodes in the online learning interaction network.This paper cleverly conceives the questioning method of synchronous classroom teaching. Based on its existing questioning model, this research designs a synchronous classroom teacher–student interaction model as shown in Figure8.Figure 8
Synchronous classroom interaction model.Based on the previously mentioned research, the model proposed in this paper is validated, the interactive effect of English translation teaching is counted, and the promotion effect of English translation teaching is evaluated. The results are shown in Table1 and Figure 9.Table 1
Evaluation of interactive English translation teaching mode based on differential evolution algorithm.
NumInteractive evaluationTeaching evaluationNo.Interactive evaluationTeaching evaluation190.0972.501089.7272.95288.6277.521189.3480.72387.9477.461291.6076.08492.0772.181392.6178.95590.4772.641491.6772.31688.9881.731592.7779.29789.0881.251692.5875.08889.4976.581792.4378.07988.1772.481889.6978.17Figure 9
Statistical diagram of expert evaluation data.The interactive English translation teaching model based on the differential evolution algorithm proposed in this paper has good effects and can improve the quality of English translation teaching.


## 4. Conclusion

The nodes of the online learning interaction network are teachers and students, where teachers, as the organizer of online learning activities, are helpers, supporters, and guides of students. Students, as the participants of the activities, are the main body of the online learning activities. Online learning activities put more emphasis on giving full play to the autonomy of learners and emphasizing respect for individual differences of learners. Therefore, the teacher no longer plays the leading role in the traditional teaching classroom. However, this does not mean that the role of teachers is no longer important, but being a leader, mentor, and helper of activities has become an important factor in online learning. This paper combines the differential evolution algorithm to construct and simulates the interactive English translation teaching mode. Through expert evaluation, the interactive English translation teaching model based on differential evolution algorithm proposed in this paper has good effects and can improve the quality of English translation teaching.



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*Source: 6182551-2022-06-17.xml*