Management and Future Technologies | Volume 2, Issue 3 | № 007

pozalariga vizual yaqinlashuvni ta’minladi. Bu aralash ehtimollik taqsimotining noaniqlikni modellashtirish qobiliyati bilan izohlanadi. Umuman, sifat tahlillari shuni ko‘rsatadiki, Aralash zichlik tarmog‘i va raqobatli yondashuvlar modelni turli jihatdan yaxshilaydi. Bunda biri reallikni, ikkinchisi esa ifodalilikni oshiradi, natijada yanada tabiiy va tushunarli imo-ishoralar ketma-ketliklari hosil qilinadi. Raqobatli o‘qitish va Aralash zichlik tarmog‘i asosidagi yondashuvlar miqdoriy natijalar bo‘yicha o‘xshash ko‘rsatkichlarga ega bo‘lsa-da, ular sign tushunarliligini yaxshilashda turlicha mexanizmlar orqali ishlaydi. Raqobatli o‘qitish diskriminatorning realizmga yo‘naltiruvchi bosimi orqali chiqishlarni vizual jihatdan tabiiylashtirsa, Aralash zichlik tarmog‘i yondashuvi aralash ehtimollik taqsimotidan foydalanib “o‘rtacha regressiya” muammosini kamaytiradi hamda ifodalilikni oshiradi. Umumiy natija sifatida, ikkala usul ham soddalashtirilgan va ifodadan xoli pozalar o‘rniga yanada realistik va silliq sign ketma-ketliklarini ta’minlaydi. Qo‘shni kadrlar orasidagi bo‘g‘in koordinatalarining bir-biriga yaqin joylashgani modelning nozik artikulyatsiyalarni o‘zlashtira olganidan dalolat beradi. Bu esa signlar orasidagi o‘tishlarning silliq bo‘lishini ta’minlab, og‘zaki tilning diskret generatsiyasidan farqli ravishda tabiiy uzluksizlikni shakllantiradi. Shunga qaramay, ba’zi cheklovlar kuzatildi: murakkab qo‘l shakllarini sadoqat bilan qayta tiklash qiyinligi, qo‘lning berkinishi sababli trening ma’lumotlari sifatining pasayishi, hamda to‘g‘ri otlar va maxsus entitetlar uchun yetarli grammatik kontekstning yo‘qligi ishlab chiqarishni qiyinlashtiruvchi omillar sifatida qayd etildi. Kiruvchi matn va glosslar Ular UY uyni aylanib AYLANMOQ yurganlarni ULAR ketkazib yuborish KETMOQ shart. SHART Imo-ishora videosidan olingan kadrlar Videodan olingan kiruvchi pozalar ketmaketligi Model generatsiya qilgan pozalar ketma-ketligi 7-rasm. Aralash zichlik tarmog‘i va raqobatli o‘qitish modeli chiqishida bashorat natijalar Oxirgi natijalarni yanada aniqroq ifodalash uchun yuqoridagi vizual misoldan foydalanish mumkin. Unda berilgan gap va glossalar (“Ular uyni aylanib yurganlarini ketkazib yuborish shart”) ketma-ketligi uch xil taqdimotda ko‘rsatilgan: 1. Imo-ishora videosidan olingan kadrlar - bu kiruvchi yorliqlangan tasvir bo‘lib, imo-shora diktorining haqiqiy imo-ishoralari namoyish etilgan. 2. Video orqali olingan kirituvchi pozalar ketma-ketligi - Mediapipe yordamida avtomatik ajratib olingan tana harakat nuqtalari ifodalari. Bu bosqichda qo‘l va tana harakatlarining asosiy koordinatalari saqlanadi. 20

3. Model generatsiya qilgan pozalar ketma-ketligi - SLT modelining yakuniy chiqishi bo‘lib, kiritilgan gloss va matnga mos ravishda avtomatik ravishda hosil qilingan uzluksiz imo-ishora ketma-ketligi. Ushbu taqqoslashdan ko‘rinadiki, model tomonidan yaratilgan pozalar asl signchining imoishoralariga yaqin, vizual jihatdan silliq va semantik mos keladigan ketma-ketliklarni hosil qilgan. Bu nafaqat modelning matndan-to‘g‘ridan-to‘g‘ri sign generatsiya qilish qobiliyatini tasdiqlaydi, balki qo‘l va tana koordinatalarining yaxlitligini ham ta’minlaganini ko‘rsatadi. Natijada, sign ketma-ketliklari foydalanuvchilar uchun tushunarli va tabiiy chiqishlarni yaratishga qodir ekanligi isbotlandi. Xulosa Ushbu tadqiqot doirasida matndan to‘g‘ridan-to‘g‘ri uzluksiz 3D imo-ishora poza ketmaketliklarini generatsiya qiluvchi yangi yondashuv taklif etildi. Modelning asosiy o‘ziga xosligi shundan iboratki, u u progressiv transformer arxitekturasi asosida ishlab chiqilib, sanoq bo‘yicha dekodlash texnikasi yordamida ketma-ketliklarni izchil va silliq shaklda dekodlash imkoniyatini yaratdi. Bu yondashuv imo-ishora tillarining tabiiy oqimliligini ta’minlashda muhim omil bo‘lib xizmat qildi. Shuningdek, tadqiqotda xatolarni yig‘ilishi muammosini kamaytirishga qaratilgan ma’lumot kengaytirish usullari qo‘llanildi. Raqobatli o‘qitish hamda Aralash zichlik tarmog‘i integratsiyasi modelning barqarorligini oshirib, generatsiya qilingan imo-ishoralarning realizm darajasini sezilarli ravishda yaxshiladi. Ushbu qo‘shimcha mexanizmlar natijaviy ketma-ketliklarning uzluksizligi va tabiiyligini kuchaytirishda muhim ahamiyat kasb etadi. Tajriba sinovlari tanlangan yondashuvning samaradorligini amaliy jihatdan isbotlab berdi. Natijalar shuni ko‘rsatdiki, matndan-to‘g‘ridanto‘g‘ri poza tarjimasi gloss vositachiligiga asoslangan modellardan ustun bo‘lishi mumkin. Bu esa kelgusi tadqiqot ishlarida imo-ishora tarjimasi jarayonida gloss bosqichini chetlab o‘tish orqali yanada soddalashtirilgan va samarali tizimlarni yaratish imkonini ochib beradi. Foydalanuvchilar ishtirokidagi baholashda esa generatsiya qilingan imo-ishoralar hali mukammal darajaga yetmagan bo‘lsa-da, qo‘shimcha silliqlash va shovqinlarni kamaytirish orqali ularning sifatini sezilarli darajada oshirish mumkinligi aniqlandi. Shu jihatdan, taklif etilgan yondashuv kelgusida yanada takomillashtirilsa, ta’lim, tibbiyot va ijtimoiy hayotning boshqa muhim sohalarida keng amaliy qo‘llanilishi mumkin bo‘lgan istiqbolli yo‘nalish sifatida qaralishi mumkin. Adabiyotlar 1. 2. 3. Rastgoo, R., Kiani, K., & Escalera, S. (2021). Sign language recognition: A comprehensive review. Expert Systems with Applications, 164, 113794. https://doi.org/10.1016/j.eswa.2020.113794 Ko, S., Lee, J., Kim, H., & Kim, C. (2023). SignNet II: Multimodal sign language translation with bidirectional architecture. IEEE Transactions on Pattern Analysis and Machine Intelligence, 45(2), 210–225. Pratikaki, A., Theodorakis, S., & Maragos, P. (2025). Text-to-pose transformer for Greek sign language generation. Computer Speech & Language, 83, 101518. 21

4. Saunders, B., Camgoz, N. C., & Bowden, R. (2020). Adversarial training for continuous sign language production. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR), 10786–10795. 5. Saunders, B., Camgoz, N. C., & Bowden, R. (2021). MoMP: Mixture of Motion Primitives for sign language generation. International Journal of Computer Vision, 129(12), 3312–3331. 6. Walsh, S., Saunders, B., Camgoz, N. C., & Bowden, R. (2022). Enhancing gloss representations with HamNoSys for sign language production. Proceedings of the European Conference on Computer Vision (ECCV). 7. Walsh, S., Saunders, B., & Bowden, R. (2024). Sign stitching: Generating continuous sign sequences from fragments. Pattern Recognition Letters, 172, 56–65. 8. Zhou, Y., Wang, X., & Li, Z. (2025). Data augmentation for sign language translation using generative methods. Neural Networks, 169, 234–247. 9. Lopez, A., Martinez, P., & Gomez, J. (2025). Spatio-temporal transformers for sign language translation. Computer Vision and Image Understanding, 231, 103684. 10. Ebling, S., & Huenerfauth, M. (2015). Bridging the gap between sign language avatars and real signers: Evaluation of the comprehensibility of generated content. Universal Access in the Information Society, 14(4), 551–562. 11. Elliott, R., Glauert, J., Kennaway, J., & Parsons, M. (2008). Linguistic modelling and language-processing technologies for avatar-based sign language presentation. Universal Access in the Information Society, 6(4), 375–391. 12. Lu, P., Huenerfauth, M., & Gu, E. (2010). Evaluation of motion capture for American Sign Language avatar animation. Proceedings of the International Conference on Computers Helping People with Special Needs (ICCHP), 243–250. 13. Kayahan, H., Akar, G., & Akarun, L. (2019). Rule-based approaches in sign language translation: A comparative study. IEEE Access, 7, 105632–105643. 14. Devlin, J., Chang, M. W., Lee, K., & Toutanova, K. (2019). BERT: Pre-training of deep bidirectional transformers for language understanding. Proceedings of NAACL-HLT, 4171– 4186. 15. Goodfellow, I., Pouget-Abadie, J., Mirza, M., et al. (2014). Generative adversarial nets. Advances in Neural Information Processing Systems (NeurIPS), 27, 2672–2680. 16. Zhang, Y., Sun, S., Galley, M., et al. (2019). Dialog state tracking with neural networks. Proceedings of ACL. 17. Saunders, B., Camgoz, N. C., & Bowden, R. (2021). Continuous 3D sign language production using mixture density networks. Proceedings of ICCV. 18. Walsh, S., Saunders, B., & Bowden, R. (2024). Integrating MDNs into transformers for naturalistic sign language production. IEEE Transactions on Affective Computing. 19. Jurayev, D. B. “Matndan o‘zbek imo-ishora tiliga tarjima qilish uchun MediaPipe asosida ma’lumotlar to‘plamini tayyorlash texnologiyasi.” Raqamli texnologiyalarning nazariy va amaliy masalalari xalqaro jurnali, 8(3), 82–88. ISSN 2181-3086. (2025). https://doi.org/10.62132/ijdt.v8i3.290 22

DEEP LEARNING MODEL FOR HUMAN FACE ANIMITY DETECTION IN A DISTANCE LEARNING PLATFORM Khamdamov Utkir, Khalilov Sirojiddin, Omonullayeva Faragiza, Akhmedov Farrukh, Umarov Mukhriddin Department of Communication and Digital Technologies, University of Management and Future Technologies Department of Digital Technologies, VATAN UNIVERSITY Digital Technologies and Artificial Intelligence Research Institute E-mail: muhriddin.umarov.1992@gmail.com Abstract: This article presents the results of experimental research on practical issues related to the general structure and functional capabilities of an information system for automatically monitoring violations of established rules during exams, based on biometric identification of students’ educational activities in the distance learning process. Face recognition is one of the new technologies used in many applications. One of the important aspects of facial recognition is security monitoring systems, where captured images are compared with thousands or even millions of stored images. The problem arises in the process of processing images taken in different situations and with different noise. In this research paper, a CNN-LSTM network is proposed for human face recognition on a distance learning platform by analyzing different feature-based face recognition approaches. Keywords: Computer vision, face tracking, face recognition, real time, video surveillance, CNN-LSTM. Introduction The issue of identifying fake faces on distance education platforms is relevant today, and it is important not only to increase the safety of the platforms, but also to ensure the effectiveness of the educational process. Through the use of fake faces (deepfake) or similar technologies, the student's identity can be incorrectly verified or the access of illegal users can negatively affect the quality of distance education. The development of face detection models and algorithms based on deep neural networks is of great importance in the solution of this problem. In recent years, with the development of technology, interest in distance education has increased. But in this process, the problem of verifying the identity of the reader or user arises. Traditional biometric methods may not provide sufficient security and accuracy. In particular, opportunities for personal identification fraud through deepfake technologies are increasing [1]. In distance learning systems, mere photo or video authentication may not be sufficient to verify identity. Therefore, there is an increasing need to develop and apply facial recognition algorithms based on artificial intelligence and deep learning methods. Face recognition has become a very active research area since the 1970 is due to its wide application in many fields such as public safety, human-computer interaction, and computer vision and inspection [2]. However, there are major drawbacks or concerns with facial recognition systems, including the fact that maintaining privacy becomes somewhat difficult. 23

Literature Review At this point, the issue by several foreign researchers, Xun et al. [3] applied some geometric features of the face through Laplace coordinates of eye-to-midline distance, horizontal eye-level deviation, eye-mouth angle vertical midline deviation, ear-nose angle, mouth angle, eye-mouth diagonal, and face features. The authors stated that these features increased the chances of comparison with features obtained from a set with denser facial features. In addition, Abdelghafour and Khalid [4] discussed the concept of key features by developing a Bag of Words algorithm for image classification. The authors linked the image classification to key points obtained by the Speeded-Up Robust Features (SURF) algorithm. In 2018, Schroff et al. [5] proposed different face detection algorithms based on hybrid methods of local feature extraction and dimensionality reduction approaches. In 2016, 3. Girshick et al. [6] developed a Local Multiple Pattern (LMP) feature descriptor based on Weber's face extraction and familiarity law. They modified the Weber ratio and added direction of change to quantize several intervals and create a map of several symbols to describe different changes. Next, LMP was used to represent the images, focusing on the histogram of points where object maps do not intersect. Also, since LMP can only capture small-scale structures, more discriminators have proposed a multiscale block LMP (MB-LMP) to generate reliable visual features. This combined MB-LMP approach can also cover both large-scale and small-scale structures. They noted that MB-LMP is computationally efficient when using the integral representation. Researches proposed by Umarov and Khamdamov et al. used pre-trained models such as YOLO, Simplified Gabor Wavelets and CNNs, and we developed a CNN-LSTM architecture that achieved the best results on the Replay-Mobile dataset. The improvement in our work is seen in obtaining accurate edges and preserving the location of the edges by applying non-linear diffusion to the frame series, and also by passing the diffused frames to the CNN-LSTM network [8]. Linear diffusion smooths the input image at the same rate in all directions and removes noise. Therefore, the smoothing process does not take into account important image features, such as edge information [14]. The solution of the linear diffusion equation is given by: 𝜕𝑆/𝜕𝑡 = 𝑑𝑖𝑣(𝑑∇𝑆) (1) where is Sthe image, is dthe scalar diffusion coefficient, and div is the divergence operator. In a sense, this is equivalent to convolution of the image with a Gaussian kernel, and linear diffusion can be considered as a low-pass filtering process. Problem Statement The nonlinear diffusion image results in strong noise reduction due to the edge clustering function because it preserves the information in the high spatial frequency components [9]. Anisotropic diffusion, i.e., nonlinear diffusion based on partial differential equations, avoids the blurring and localization problems associated with linear diffusion, and by focusing on image noise reduction, the image does not reduce the significant parts of the edges. This improves scale space, enforces boundaries, and preserves edges [10]. The diffusion coefficient is locally adapted and selected as a function of the image gradient, which varies depending on the location and orientation of the gradient edges, allowing edge preservation. The nonlinear diffusion process is defined by the following equation (2). 𝜕𝑆/𝜕𝑡 = 𝑑𝑖𝑣(𝑔|∇𝑆|∇𝑆) (2) 24

where ∇Sis the gradient and is a function of the gradient gif the diffusion coefficient ∇S. The Additive Operator Splitting (AOS) scheme solves the regularization problem associated with anisotropic diffusion [11]. This semi-fuzzy scheme is stable for all time steps and ensures that all coordinate axes are treated equally, as defined by the equation below. AOS provides fast diffusion, which results in smoothing of edges in fake images and preserving edges in real images. In AOS, the iterative solution is given in equation (3). (𝑆𝑘 )𝑡+1 = ∑𝑛𝐼=1(𝑛𝑆 − 𝜏𝑛2 𝐴𝐼 )−1 𝑆𝑘𝑡 ′ (3) where S_kis the spread image, nis the number of dimensions, krepresents the channel, I is the identity matrix, A_Iis the diffusion, and tis the time step. In the two-dimensional case, n=2 and the equation is expressed as: (𝑆𝑘 )𝑡+1 = (2𝑆 − 4𝜏𝐴1 )−1 𝑆𝑘𝑡 +(2S−4𝜏𝐴1 ) 𝑆𝑘𝑡 ′ (4) Here A_1, and A_2 denote the horizontal and vertical diffusion. The equation is divided into two parts in the operator separation scheme. The solution of each is calculated separately and the results are combined [12, 13]. The Tridiagonal Matrix Algorithm (TMA) is a simplified form of Gaussian subtraction with a block solution, useful in tridiagonal systems. Thus, the AOS scheme together with the TMA can be used for efficient solution of the nonlinear scalar diffusion equation. We use the first-order AOS scheme in our research. In the proposed architecture, the original image is first fed to a proctor network to calculate the smoothness value of the diffusion parameter. It is a neural network consisting of a dense layer of one neuron that outputs a proctor after a hidden layer of 15 neurons. A rectified linear unit (ReLU) activation function is applied to neurons in these layers. The SCNN model consists of convolutional layers C1, C2, and C3 with 16, 32, and 64 feature maps, respectively, with kernel sizes of 15×15, 7×7, and 5×5 used in convolutions. After each convolution, the set is normalized and maximally combined into layers C1 and C2. A high filter size in the C1 layer is important for obtaining diffusion enhanced features are used for liveness detection. After normalizing the C3 layer, a dense layer of 64 neurons and a dense output layer of one neuron are transferred. The ReLU activation function is applied to the convolution layers of the hidden layer, and the sigmoid activation function is applied to the output layer [7]. Figure 1. End-to-End architecture using a specialized convolutional neural network (SCNN). We replace the CNN part of Figure 1 with the Inceptionv4 network to determine whether the alternative network CNN leads to higher accuracy. However, instead of using an alpha network that 25

calculates the smoothness (alpha) of the diffusion, we adjust the alpha value to improve real-time performance. The first stage is the nonlinear diffusion stage, whose input is the original 64×64 input image captured by the webcam, followed by the Inception v4 network architecture. The seed network is a CNN architecture designed as a deep and wider network. It works together with interconnected primitive modules and subsampling layers to reduce the resolution, thereby reducing image distortion and distortion. The Inception v4 mesh architecture consists of the initial base, three different initial blocks, called initial A, B, and C, which are repeated 4, 7, and 3 times, respectively, as well as the resolution of the mesh. consists of two reduction blocks for modification. Convolution in initial modules within a block is performed by applying filters of different sizes to the same layer, which expands the network and improves feature detection at different scales. The resulting object maps are collected and transferred to the next level. The complete architecture of this method is shown in Figure 2. The image obtained in the nonlinear diffusion step using the specified alpha value and propagated to the next step, the Inception v4 mesh base, where the output is the initial A blocks, the reduction block A, the Inception-B blocks, the reduction block B and is processed in initial C blocks, followed by an average pulling layer, thresholding, and a dense output layer with two-neuron SoftMax activation. The network was trained using the Adam optimization algorithm. Since our targets are in a pseudotrue two-class categorical format, we used categorical cross-entropy as the loss function. Figure 2. Sequence architecture using the Inception v4 network. We suggest that it tracks data in a sequence of frames to detect liveness in video frames. With this in mind, the presented architecture consists of diffusion, which is transferred to the CNN shortterm memory layer (LSTM) as shown in Fig. Each LSTM cell provides continuous analogues of 26

write, read and restore operations for multiplicative unit layers called gates (input, output, forget). These layers of blocks learn to open and close access to a constant stream of errors through their internal states. The input intersection gate specifies how much of the new data should be stored based on the state of the cells. The memory gate (intersection) indicates which state of the internal part can be erased. The output intersection indicates which state of the cell can be used as a temporary state. Based on the integration of LSTM with CNN, successful identification of the person using the lip texture position has been achieved, three-dimensional walking detection and re-identification using video has been achieved. The integration of deep bipartite LSTM with CNN has been successful in re-identifying the image of a person. Our innovation is the inclusion of our initial diffusion processing in the validity detection (Figure 3). Experimental Research The CNN part of our CNN-LSTM network has convolutional layers C1 and C2, one subsampling layer, and a fully connected layer of 50 neurons. This is followed by an LSTM layer consisting of 60 cells and a feedforward output layer of two neurons. A sigmoidal activation function is applied to the output layer, which gives an output in the range 0 to 1. Nonlinear diffusion is first applied to the frames of each input sequence, and the extracted frames are fed to the CNN. CNN captures spatial information sequentially by extracting complex and deep discriminative features, and the hidden layer of CNN generates 50 features for each frame. Figure 3. Convolutional Neural Network and Long Short-Term Memory (CNN-LSTM). The input to the LSTM layer is three-dimensional, where three-dimensional time steps and feature samples (ie, batch size 20 50), where 20 is the number of frames in the sequence (Figure 4). The short-term memory layer detects long-term temporal correlations between consecutive frames 27

and provides the ability to extract 60 features from the layer. As a result, it classifies real and fake attributes from a sequence of 20 frames. Figure 4. Face recognition and liveness check. Liveness detection is only performed on flattened faces. The simplest model for liveness detection is the CNN (convolutional neural network) neural network model with successive layers. The CNN, we propose consists of simple multi-stage filters. All images uploaded to the model will be resized to 32*32. The intensity of all pixels is measured in the interval (0, 1). The proposed model is shown in Figure 5. In this model, ReLu (Rectified Linear Unit) function is activated and 2*2 size is always accepted for MaxPooling 2D. Different functions are activated for testing in turn. If the probability returned by the liveness model is less than 0.5, the detected face is considered to be a fake face, otherwise it is considered to be a real face. Figure 5. Model of validity check. If a fake face is detected, the autoproctoring will give a warning. If several real faces are detected during the exam, the system will report to the proctor that multiple faces have been detected, and the examinee will be expelled from the process. In addition, the examiner's head, eye 28

and lip movements are also checked. Head, eye, and lip locations are done as follows to reduce computations. Test-takers can get help from others in the room, or they can get help from laptops and other resources placed in the room. Such decemption can be detected by assessing head and eye orientation. Head position is evaluated only for aligned faces. If the examinee is constantly looking at a certain angle to other different directions such as left and right, the autoproctor will send a warning to the user. In the proposed autoproctoring system, head position estimation is performed using an Affine transformation matrix. The rotation and intersection of the scale of affine transformations are actually linear transformations, and are represented by matrix multiplication of a point represented as a vector. The gradual process of assessing the condition of the head is as following: Attentive network model is used to calculate features such as the tip of the nose, the left corner of a left eye, the corner of the right eye, the corner of left mouth, the corner of right mouth. In addition, model points are also evaluated for 3D projection. The following internal parameters f_xand f_ygiven as input to c_xthe SolvePnP ( Perspective-n-Point (PnP) pose computation - OpenCV) function, the focal lengths expressed in pixel units and the base unit (c_x, c_y) are included in the matrix. SolPnP functions estimate the object position by taking into account a set of object points, their corresponding image projections, as well as the camera’s internal matrix and distortion coefficients. 𝑓𝑥 0 𝑐𝑥 [ 0 𝑓𝑦 𝑐𝑦 ] (5) 0 0 1 The SolvePnP function is designed for direct linear transformation. A direct linear transformation is used to solve for a set of variables from a set of similarity relations such as 3*3 rotation matrix (R`) and 3*1 transformation vector (t) are calculated as follows. 𝑅′ 𝑡 𝐾𝑐 = [ ]𝐾 (6) 0 1 𝑤 𝑠11 𝑠12 𝑠13 𝑡𝑥 𝑅′ 𝑡 𝑠 [ ] = [ 21 𝑠22 𝑠23 𝑡𝑦 ] (7) 0 1 𝑠31 𝑠32 𝑠33 𝑡𝑧 The left and right movement of the head can be determined from the above procedure. If the head turns left or right, the autoproctoring will give a warning. In this study, an experiment was conducted based on the proposed CNN-LSTM architecture for human face recognition and facial recognition. The goal is to investigate the face and user authentication process under different noise and conditions. A total of 10,000 face images were used in the experiment. The images were taken in different conditions (light, angle, etc.), and the data set was expanded and normalized. The proposed CNN-LSTM architecture consists of the following parts: 1. Linear Diffusion: The images are scanned at the same rate to remove noise. This process ignores important image features, including line and edge information. 2. Part of CNN: Convolutional layers were used to extract features from face images. 3. LSTM part: LSTM layers were used in time series analysis through extracted features. This part stores time information for face detection in noisy conditions. 29

The developed model was trained with 80% data set and tested with 20% data set. The Adam optimizer and the categorical crossentropy loss function were used in the training process. At each epoch, the accuracy rate and loss value of the model were monitored (Tables 1, 2). Table 1. Accuracy and loss for different models Accuracy Model Loss (%) CNN-LSTM (Diffusion) 98.3 0.1 CNN-LSTM (only) 95.7 0.12 CNN (Broadcast) 92.7 0.15 LSTM (only) 92 0.18 Table 2. Results in noisy conditions Conditions Accuracy (%) Loss The light is good 93 0.12 Light is average 91 0.14 The light is bad 89 0.17 (a) The results of the model testing are as follows: - Accuracy level: The accuracy of the model was 98.3%, which is a high result compared to other methods. 30

- Loss value: During the training process, the loss value is reduced to 0.1, which shows the effectiveness of the model. - Rate in noisy conditions: In noisy conditions, the model showed 95.7% accuracy. - Accuracy: Our CNN-LSTM model achieved an accuracy of 95.7% when linear diffusion was added, which shows a significant improvement compared to other models (CNN-LSTM 98.3%, LSTM 92%). - Loss: In the model combined with diffusion, the loss dropped to 0.1, giving the lowest performance. This shows a balance between high precision and low loss. - Noisy conditions: Even in noisy conditions, the diffusion-enhanced model maintains high accuracy, increasing its performance in real-world conditions. (b) Figure 6. Model accuracy (a) and loss (b) comparison in normal and noisy conditions This study shows significant results in human face recognition by using the diffusion process. Linear diffusion is effective in reducing noise and improves the accuracy and stability of the model (Figure 6). The results also highlight the need to preserve key features in image processing. Conclusion The results of this research can be applied in the following areas: 1. Security Monitoring: Facial recognition systems, for example, in security at airports or institutions. 2. Biometric Identity Verification: In identification and authentication processes in banks and financial institutions. 3. Social Networks: Identifying and personalizing users through facial recognition. 4. Healthcare: In the analysis of medical images, for example, in the detection of problems through the face. 31

The effectiveness of this model is proven by high accuracy and low loss indicators in noisy conditions. These indicators are also necessary for real-time operation. The model performs especially well in low-quality images or in complex conditions (for example, changes in lighting). In the future, to further improvement in the model work can be carried out in the following directions: In this study, human face recognition process based on CNN-LSTM architecture was successfully investigated. The obtained results showed that an effective model has been created that provides high accuracy in various noise and situations. The model has high potential for use in proctoring systems, and future testing with other datasets and exploration of additional approaches is planned. References 1. Bu W, Xiao J, Zhou C, Yang M, Peng C (2017) Acascade frame work formasked face detection. https://doi.org/10.1109/ICCIS.2017.8274819. 2. Chen W, Zhou Q, Hu H (2019) Face alignment by discriminative feature learning. https://doi.org/10.1109/ICIP.2019.8803112. 3. Khalilov, S.P., Yusupov, I., Mannapova, M.G., Nasrullayev, N.B., Botirov, F. “Effectiveness of Deep Learning Based Filtering Algorithm in Separation of Human Objects from Images” Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)this link is disabled, 2023, 13741 LNCS, pages 230–238 ORCID 58250916200. 4. Zhang E, Zhang Y. (2009). Average Precision. In: LIU L, ÖZSU M.T. (eds) Encyclopedia of Database Systems. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-39940-9_ 5. Schroff F, Kalenichenko D, Philbin J (2015) FaceNet: a unified embedding for face recognition and clustering. https://doi.org/10.1109/CVPR.2015.7298682. 6. U. Khamdamov, M. Umarov, J. Elov, S. Khalilov and I. Narzullayev, “Uzbek traffic sign dataset for traffic sign detection and recognition systems,” 2022 International Conference on Information Science and Communications Technologies (ICISCT), Tashkent, Uzbekistan, 2022, pp. 1-5, doi: 10.1109/ICISCT55600.2022.10146832. 7. M. Avaz and K. Sirojiddin, “Basic principles of wavelet filtering,” 2021 International Conference on Information Science and Communications Technologies (ICISCT), Tashkent, Uzbekistan, 2021, pp. 1-3, doi: 10.1109/ICISCT52966.2021.9670311. 8. Khamdamov, U.R., Umarov, M.A., Khalilov, S.P., Kayumov, A.A., Abidova, F.S. (2024). Traffic Sign Recognition by Image Preprocessing and Deep Learning. In: Choi, B.J., Singh, D., Tiwary, U.S., Chung, WY. (eds) Intelligent Human Computer Interaction. IHCI 2023. Lecture Notes in Computer Science, vol 14532. Springer, Cham. https://doi.org/10.1007/978-3-0 9. Khamdamov, U., Abdullayev, A., Mukhiddinov, M., Xalilov, S. “Algorithms of multidimensional signals processing based on cubic basis splines for information systems and processes,” Journal of Applied Science and Engineering (Taiwan)this link is disabled, 2021, 24(2), страницы 141–150, ORCID 58250916200 10. Mahmudovich, M.M., Ilkhamovna, A.M., Shukhrat Ogli, T.B. Image Approach to Uzbek Speech Recognition. International Conference on Communication Technology Proceedings, ICCT, 2022, 2022-November-November, страницы 1201–1206. 32

11. M. Umarov, J. Elov, S. Khalilov, I. Narzullayev and M. Karimov, "An algorithm for parallel processing of traffic signs video on a graphics processor," 2022 International Conference on Information Science and Communications Technologies (ICISCT), Tashkent, Uzbekistan, 2022, pp. 1-5, doi: 10.1109/ICISCT55600.2022.10146809. 12. A. Mirzaev and S. Khalilov, “Digital Signal Processing Based On Spline Functions,” 2019 International Conference on Information Science and Communications Technologies (ICISCT), Tashkent, Uzbekistan, 2019, pp. 1-7, doi: 10.1109/ICISCT47635.2019.9012038. 13. B. Xiao, P. Georgiou, B. Baucom, and S. Narayanan. Head motion modeling for human behavior analysis in dyadic interaction. IEEE Trans. Multimedia, 17(7):1107–1119, 2015. 33

NEWHSA OQIMLI SHIFRLASH ALGORITMINING APPARAT DARAJADAGI SAMARALI TADBIQI VA ARXITEKTURAVIY TAHLILI Rahmatullayev Ilhom; Abduraximov Baxtiyor Raqamli texnologiyalar va sunʼiy intellektni rivojlantirish ilmiy-tadqiqot instituti doktoranti Mirzo Ulug‘bek nomidagi O‘zbekiston milliy universiteti “Amaliy matematika va kompyuter tahlili” kafedrasi professori, f.-m.f.d. ilhom9001@gmail.com Annotatsiya: Ushbu ilmiy maqolada resurslari cheklangan qurilmalar uchun mo‘ljallangan, apparat darajasida samarali ishlovchi yengil oqimli shifrlash algoritmi NewHSA taklif etiladi. Taklif etilgan algoritm to‘rtta siljitish registri, 23 ta XOR va 3 ta AND mantiqiy elementlaridan iborat bo‘lib, umumiy hisobda atigi 830 ta mantiqiy element (gate)dan foydalanadi. Algoritmning arxitekturasi 74LS74 turidagi D-triggerlar asosida modellashtirilgan bo‘lib, yuqori tezlikda va past energiya sarfi bilan ishlash imkonini beradi. Taklif etilgan modelning samaradorligi va tasodifiylik darajasi NIST SP 800-22 statistik test to‘plami yordamida baholangan hamda barcha testlardan muvaffaqiyatli o‘tgan. Yangi algoritmning soddaligi, ixchamligi va apparatga moslashuvchanligi uni IoT qurilmalari, simsiz sensor tarmoqlari va boshqa past quvvatli xavfsiz tizimlarda qo‘llash uchun istiqbolli nomzod sifatida ko‘rsatmoqda. Kalit so‘zlar: Oqimli shifrlash, apparatga yo‘naltirilgan kriptografiya, D-trigger, XOR, AND, gamma generator, NIST testlari, LFSR, IoT xavfsizligi. Kirish Zamonaviy raqamli axborot tizimlarining keng ko‘lamda qo‘llanilishi bilan bir qatorda, ularning axborot xavfsizligini ta’minlash muammosi ham dolzarb ahamiyat kasb etmoqda. Ayniqsa, past quvvat va cheklangan hisoblash imkoniyatlariga ega bo‘lgan qurilmalar — masalan, IoT (Internet of Things) qurilmalari, simsiz sensor tarmoqlari (WSN), aqlli datchiklar va RFID tizimlarida samarali, ixcham va tezkor kriptografik himoya vositalariga bo‘lgan talab keskin ortib bormoqda. Bunday tizimlarda an’anaviy blokli shifrlash algoritmlari, resurs talablari yuqoriligi sababli, har doim ham mos kelavermaydi. Shu sababli, yengil oqimli shifrlash algoritmlari real vaqt rejimida ishlash, minimal apparat murakkabligi va yuqori tezlik kabi afzalliklari bilan muqobil yechim sifatida e’tirof etilmoqda. Oqimli shifrlash algoritmlari doimiy ravishda gamma oqimi generatsiya qilib, uni ochiq matn bilan 2 modul bo‘yicha qo‘shish (XOR) orqali shifrlashni amalga oshiradi. Ushbu yondashuv past kechikishli real vaqt tizimlari uchun ayniqsa qulay bo‘lib, apparat darajasida soddaligi bilan ajralib turadi. Shu bilan birga, oqimli shifrlarning samaradorligi ularning apparatda ishlashga mosligi, energiya samaradorligi va statistik tasodifiylik darajasiga bevosita bog‘liqdir [9]. Hozirgi paytda kriptografik jamoatchilik orasida apparatga yo‘naltirilgan oqimli shifrlash algoritmlarining dizayni va baholanishi borasida faol tadqiqotlar olib borilmoqda. Jumladan, ECRYPT II doirasida tashkil etilgan eSTREAM loyihasi oqimli shifrlarning xavfsizlik, samaradorlik va apparat moslashuvchanligi mezonlari asosida baholanishiga asos bo‘ldi. Ushbu loyihada ishtirok etgan Trivium, Grain, Mickey, va A5/1 kabi algoritmlar yengil apparat muhiti uchun maxsus ishlab chiqilgan bo‘lib, ularning har biri o‘zining struktura murakkabligi va 34

xavfsizlik darajasi bilan farqlanadi. Masalan, Trivium algoritmi yuqori kriptobardoshlilikka ega bo‘lsa-da, uning apparatga tatbiq etilishi uchun 3400 dan ortiq mantiqiy elementlar talab qilinadi, bu esa resurs cheklangan muhitlar uchun noqulay hisoblanadi. Ushbu maqolada taklif etilayotgan NewHSA oqimli shifrlash algoritmi apparat darajasidagi soddalik va ixchamlik tamoyillariga asoslangan holda ishlab chiqilgan bo‘lib, mavjud yengil shifrlash algoritmlarining afzalliklarini birlashtirgan holda takomillashtirilgan modeldir. NewHSA algoritmi oddiy mantiqiy elementlar – D-triggerlar, XOR va AND elementlari asosida qurilgan bo‘lib, umumiy apparat murakkabligi atigi 830 ta element bilan cheklangan. Algoritmning arxitekturasi sxematik soddalik va tezkor ishlash imkonini beruvchi yondashuvlar asosida shakllantirilgan. Maqola davomida ushbu yangi algoritmning arxitekturasi, apparatga tatbiqi, NIST statistik testlari asosida gamma oqimining tasodifiylik darajasi va mavjud algoritmlar bilan qiyosiy tahlili bayon etiladi. Natijalar NewHSA algoritmini IoT kabi past quvvatli xavfsizlik talab qiluvchi tizimlar uchun istiqbolli yechim sifatida baholash imkonini beradi. Adabiyotlar sharhi (Literature Review) Axborot xavfsizligi sohasida oqimli shifrlash algoritmlarining ahamiyati so‘nggi yillarda jadal ortib bormoqda, ayniqsa, apparat resurslari cheklangan IoT qurilmalari, sensor tarmoqlar va simsiz aloqa tizimlarida. Ushbu muhitlar uchun eng mos algoritmlarni ishlab chiqish bo‘yicha ko‘plab ilmiy izlanishlar olib borilmoqda. Shuning uchun mavjud algoritmlarni tahlil qilish, ularning imkoniyat va cheklovlarini aniqlash yangi yondashuvlar uchun zarur asos bo‘lib xizmat qiladi. Good va Benaissa tomonidan olib borilgan tadqiqotlarda [1] eSTREAM tanlovining 3bosqichiga o‘tgan oqimli shifrlash algoritmlarining apparatdagi ishlash samaradorligi baholangan. Aynan ushbu tadqiqotda apparat arxitekturasi, energiya sarfi va ishlash chastotasiga oid mezonlar asosida Trivium, Grain va boshqa algoritmlar tahlil qilingan. Ularning aksariyati murakkab NLFSR va FSR strukturalarga asoslangan bo‘lib, bu ayrim hollarda apparatni ortiqcha yuklaydi. Canniere va Preneel tomonidan ishlab chiqilgan Trivium algoritmi [2] eSTREAM loyihasida eng muvaffaqiyatli oqimli shifr sifatida tan olingan. 80 bitli kalit va 288 bitli ichki holatga ega bo‘lgan Trivium o‘zining yuqori kriptobardoshliligi bilan ajralib turadi. Biroq, uning apparat tatbiqi 3400 dan ortiq mantiqiy elementlar talab qilishi sababli past quvvatli tizimlar uchun har doim ham qulay emas. A5/1 algoritmi, Golic tomonidan tahlil qilinganidek [3], GSM mobil aloqa protokollari uchun ishlab chiqilgan va uchta LFSR asosida qurilgan. U apparatda nisbatan ixcham bo‘lsa-da, zamonaviy tahlillarga nisbatan zaif ekani aniqlangan va bu algoritm hozirgi xavfsizlik standartlariga mos kelmaydi. Salsa20 algoritmi esa, D.J. Bernstein tomonidan taklif etilgan [4], asosan dasturiy ta’minotga yo‘naltirilgan bo‘lsa-da, yengil qurilmalarda qo‘llashga mos modifikatsiyalari mavjud. Biroq, uning apparatga moslashtirilgan versiyalari ham resurslar nuqtai nazaridan cheklovlarga ega. Tasodifiylik darajasini aniqlashda NIST tomonidan ishlab chiqilgan SP 800-22 statistik testlar to‘plami [5] xalqaro mezon hisoblanadi. Ushbu testlar oqimli shifrlar tomonidan generatsiya qilingan gamma oqimlarining deterministik emasligini, statistik barqarorligini va haqiqiy tasodifiylikka yaqinligini baholashga imkon beradi. Shu sababli, ko‘plab tadqiqotlarda aynan ushbu testlar oqimli algoritmlarni baholashda asosiy vosita sifatida qo‘llaniladi. 35

Zamonaviy adabiyotlarda apparatga yo‘naltirilgan kriptografik dizaynlar ko‘pincha LFSR/NLFSR asosidagi strukturaviy yondashuvlarga tayangan. Katz va Lindell [6] tomonidan umumlashtirilganidek, oqimli shifrlarning samaradorligi ularning arxitektura soddaligi, xavfsizlik darajasi va ishlash tezligi o‘rtasidagi muvozanat bilan belgilanadi. Bu esa yengil, lekin ishonchli apparat dizaynlarini ishlab chiqish zaruratini tug‘diradi. IEEE Access jurnalida Zheng va Huang tomonidan taqdim etilgan tahlillar [7] esa past resursli qurilmalar uchun mo‘ljallangan yengil oqimli shifrlar modellashtirilishida D-triggerlar asosidagi strukturaviy yondashuvlarning samaradorligini ko‘rsatadi. Aynan D-triggerlar yordamida tashkil etilgan siljitish registrlari va XOR/AND kombinatsiyalari bilan ishlovchi gamma generatorlar apparat resurslarini tejash imkonini beradi. Shuningdek, gamma oqimining sifatini aniqlashda NIST SP800-22 statistik testlari global standart hisoblanadi. Ushbu testlar yordamida algoritmning deterministik naqshlarsiz, ehtimollik nazariyasiga mos, haqiqiy tasodifiy ketma-ketlik generatsiyasini baholash mumkin [8]. Shu tariqa, mavjud ilmiy ishlanmalar NewHSA algoritmi uchun konseptual va texnik asos yaratib beradi. Ularning afzalliklarini umumlashtirgan va kamchiliklarini bartaraf etishga qaratilgan holda, NewHSA apparatda soddalashtirilgan, energiyaga tejamkor va statistika asosida baholangan yondashuvni taklif etadi. Bu algoritmni oqimli shifrlash sohasidagi mavjud ishlanmalar fonida zamonaviy va istiqbolli alternativ sifatida baholash mumkin. Tadqiqot maqsadi va vazifalari Ushbu tadqiqotning asosiy maqsadi – apparat darajasida samarali ishlaydigan, ixcham va kriptografik jihatdan ishonchli yangi oqimli shifrlash algoritmi — NewHSA (New hardware stream algorithm)ni taklif etish va uning amaliy samaradorligini sxematik modellashtirish, statistik baholash hamda mavjud ilg‘or algoritmlar (Trivium va A5/1) bilan qiyosiy tahlil qilishdan iborat. Taklif qilinayotgan yangi NewHSA (New hardware stream algorithm) oqimli shifrlash algoritmi apparatda amalga oshirishga qulay, ko‘rinishi va tuzilishi bo‘yicha LFSR asosiga qurilgan A5/1 shifrlash algoritmiga va NLFSR asosidagi Trivium algoritmiga o‘xshash. Shu sababli, qiyosiy tahlillar mazkur algoritmlar bilan amalga oshiriladi. NewHSA algoritmi apparatga yo‘naltirilgan bo‘lib, past quvvatli va resurslari cheklangan qurilmalar uchun mo‘ljallangan. Shuningdek, u sxemaviy soddalik, yuqori ishlash tezligi, tasodifiylik va xavfsizlikning optimal muvozanatini ta’minlashga qaratilgan. Maqsadga erishish uchun quyidagi aniq ilmiy va texnik vazifalar belgilab olindi: 1. Algoritm arxitekturasini loyihalash: NewHSA algoritmining sxematik arxitekturasini ishlab chiqish, asosiy komponentlar — siljitish registrlari, XOR va AND mantiqiy elementlari asosida qurilgan gamma generatorni tavsiflash. 2. Apparat modellashtirish: Algoritmni apparat darajasida 74LS74 turidagi sinxron Dtriggerlar yordamida modellashtirish, holat registrlarining ishlash mexanizmini aniqlash. 3. Apparat murakkabligini baholash: Mantiqiy elementlar sonini hisoblash orqali algoritmning apparat darajasidagi umumiy murakkabligini (gate-level complexity) aniqlash. 4. Kriptografik tasodifiylikni tahlil qilish: Generatsiya qilingan gamma oqimlarning statistik xususiyatlarini NIST SP800-22 testlar to‘plami asosida baholash va natijalarni tahlil qilish. 5. Qiyosiy tahlil o‘tkazish: NewHSA algoritmini apparatdagi murakkablik va kriptobardoshlilik ko‘rsatkichlari asosida Trivium va A5/1 algoritmlari bilan qiyoslab tahlil qilish. 36

Tadqiqot metodologiyasi NewHSA oqimli shifrlash algoritmining apparatga yo‘naltirilgan samarali amalga oshirilishini ta’minlash uchun tadqiqot jarayonida kompleks tizimli yondashuv qo‘llanildi. Metodologiya algoritmni modellashtirishdan tortib, apparat arxitekturasini qurish, funksional testlash va statistik baholashgacha bo‘lgan bosqichlarni o‘z ichiga oladi. Har bir bosqich ISO/IEC 18033 va NIST SP800-22 kabi xalqaro kriptografik standartlarga mos holda ishlab chiqilgan. Arxitektura dizayni va sxemaviy modellashtirish Algoritmning yadro qismini tashkil qiluvchi gamma generator sxemasi to‘rtta siljitish registri (RA, RB, RC, RD) va ularning bog‘lovchi kombinatsion mantiqiy elementlaridan tashkil topgan (1rasm). Har bir registr 74LS74 turidagi sinxron D-triggerlar asosida qurilgan bo‘lib, ularning chiqishlari 23 ta XOR va 3 ta AND elementlari orqali bog‘lanadi. Siljitish va qayta aloqa jarayonlari siklik ravishda, umumiy soat (CLOCK) signali asosida boshqariladi. NewHSA ning boshlang‘ich holati umumiy uzunligi 64 bit bo‘lgan 4 ta siljish registridir. Har bir holat o‘ngga siklik siljish registrlaridagi bitlarni chiziqsiz uzatish va qayta aloqa kombinatsiyasi orqali o‘zgartiriladi. Shifrni ishga tushirish uchun 128 bit uzunlikga ega K kalit qiymatlari 4 siljish registrlariga berilgan qoida bo‘yicha yoziladi va algoritm 16*64 = 1024 marta bajariladi, shundan so‘ng registr bitlariga kalitning qolgan 64 bit qismi ikki modul bo‘yicha qo‘shiladi va algoritm yana 1024 marta bajariladi, bu boshlang‘ich holatning har bir biti kalitning va initsializatsiya vektorining har bir bitiga bog‘liqligini kafolatlaydi. a) b) c) 1-rasm siljitish registorlari d) 37

Ushbu arxitektura bit-oriented dizayn tamoyiliga asoslangan bo‘lib, apparat soddaligini, energiya samaradorligini va yuqori ishlash chastotasini ta’minlashga qaratilgan. Gamma oqimi har bir takt impulsida yangilanadigan bitlar asosida hosil qilinadi va oqimli shifrlash uchun foydalaniladi. Apparat darajasidagi murakkablik tahlili Algoritmning apparatdagi murakkablik darajasi (gate-level complexity) quyidagi parametrlar asosida aniqlandi: • 1 dona D-trigger ≈ 12 NAND • 1 dona XOR ≈ 2.5 gate • 1 dona AND ≈ 1.5 gate Bu mezonlar asosida umumiy hisobda 830 ta mantiqiy elementdan tashkil topgan apparat sxemasi shakllantirildi. Ushbu natija, mavjud algoritmlar bilan qiyoslaganda, juda ixcham va samarali arxitektura ekanligini ko‘rsatadi. Initsializatsiya bosqichidan o‘tgandan so‘ng, har bir siklda chiquvchi kalit oqimining yangi a‘zosi hosil bo‘ladi, u matnning keyingi biti bilan XOR (2 modul bo‘yicha qo‘shish) amali yordamida qo‘shiladi. Shifrni ochish jarayoni teskari tartibda amalga oshiriladi - shifrlangan matnning har bir biti chiquvchi kalit oqimining har bir biti bilan XOR amali yordamida qo‘shiladi amali yordamida qo‘shiladi. Initsializatsiya. Initsializatsiya jarayoni Algoritm 64 bitli kalitni 64 (17+19+13+15) bitli boshlang‘ich holat registrlariga yuklash orqali ishga tushiriladi. Initializatsiya jarayonini quyidagi psevdokod yordamida tavsiflash mumkin. (𝐾0 , … , 𝐾16 ) → (𝑎0 , 𝑎1 , … , 𝑎16 ) (𝐾17 , … , 𝐾35 ) → (𝑏0 , 𝑏1 , … , 𝑏18 ) (𝐾36 , … , 𝐾48 ) → (𝑐0 , 𝑐1 , … , 𝑐12 ) (𝐾49 , … , 𝐾63 ) → (𝑑0 , 𝑑1 , … , 𝑑14 ) 𝑓𝑜𝑟 𝑖 = 0 𝑡𝑜 1023 𝑑𝑜 𝑎5 ⨁𝑎8 ∙ 𝑎9 ⨁𝑎10 ⨁𝑎14 ⨁𝑎16 ⨁𝑏10 → 𝑡0 𝑏7 ⨁𝑏12 ∙ 𝑏13 ⨁𝑏14 ⨁𝑏16 ⨁𝑏18 ⨁𝑐9 → 𝑡1 𝑐4 ⨁𝑐6 ∙ 𝑐7 ⨁𝑐8 ⨁𝑐10 ⨁𝑐12 ⨁𝑑11 → 𝑡2 𝑑6 ⨁𝑑8 ∙ 𝑑9 ⨁𝑑10 ⨁𝑑12 ⨁𝑑14 ⨁𝑎13 → 𝑡3 (𝑡3 , 𝑎0 , … , 𝑎15 ) → (𝑎0 , … , 𝑎16 ) (𝑡2 , 𝑏0 , … , 𝑏17 ) → (𝑏0 , … , 𝑏18 ) (𝑡1 , 𝑐0 , … , 𝑐11 ) → (𝑐0 , … , 𝑐12 ) (𝑡0 , 𝑑0 , … , 𝑑13 ) → (𝑑0 , … , 𝑑14 ) 𝑒𝑛𝑑 𝑓𝑜𝑟. (𝑎0 ⨁𝐾64 , 𝑎1 ⨁𝐾65 , … , 𝑎16 ⨁𝐾80 ) (𝑏0 ⨁𝐾81 , 𝑏1 ⨁𝐾82 , … , 𝑏18 ⨁𝐾99 ) (𝑐0 ⨁𝐾100 , 𝑐1 ⨁𝐾101 , … , 𝑐12 ⨁𝐾112 ) (𝑑0 ⨁𝐾113 , 𝑑1 ⨁𝐾114 , … , 𝑑14 ⨁𝐾127 ) 𝑓𝑜𝑟 𝑖 = 0 𝑡𝑜 1023 𝑑𝑜 𝑎5 ⨁𝑎8 ∙ 𝑎9 ⨁𝑎10 ⨁𝑎14 ⨁𝑎16 ⨁𝑏10 → 𝑡0 38

𝑏7 ⨁𝑏12 ∙ 𝑏13 ⨁𝑏14 ⨁𝑏16 ⨁𝑏18 ⨁𝑐9 → 𝑡1 𝑐4 ⨁𝑐6 ∙ 𝑐7 ⨁𝑐8 ⨁𝑐10 ⨁𝑐12 ⨁𝑑11 → 𝑡2 𝑑6 ⨁𝑑8 ∙ 𝑑9 ⨁𝑑10 ⨁𝑑12 ⨁𝑑14 ⨁𝑎13 → 𝑡3 (𝑡3 , 𝑎0 , … , 𝑎15 ) → (𝑎0 , … , 𝑎16 ) (𝑡2 , 𝑏0 , … , 𝑏17 ) → (𝑏0 , … , 𝑏18 ) (𝑡1 , 𝑐0 , … , 𝑐11 ) → (𝑐0 , … , 𝑐12 ) (𝑡0 , 𝑑0 , … , 𝑑13 ) → (𝑑0 , … , 𝑑14 ) 𝑒𝑛𝑑 𝑓𝑜𝑟. a) b) 2-rasm. Elementlarning ikki modul bo‘yicha qo‘shish jarayoni Gamma oqimining tasodifiyligini baholash Yaratilgan algoritm yordamida generatsiya qilingan gamma oqimlarining statistik xossalari NIST SP800-22 test to‘plami yordamida baholandi. Har bir oqim uzunligi 2¹⁰⁴ bit bo‘lib, 15 ta asosiy test – Monobit, Runs, Approximate Entropy, Linear Complexity va boshqalar bo‘yicha tahlil qilindi. Bu testlar oqimning deterministik naqshlardan holi, ehtimollik nazariyasiga mos va kriptografik nuqtai nazardan xavfsiz ekanligini aniqlash imkonini beradi. Testlar Python va MATLAB muhitida yozilgan maxsus skriptlar asosida avtomatlashtirilgan holda bajarildi. 39