Management and Future Technologies | Volume 2, Issue 2 | № 006

Management and Future Technologies journal.umft.uz June 2025 Volume 2, Issue 2 The symbols of the BCH code are taken from a finite Galois field [27, 28, 29]. A field is a set of elements if for any elements of this set the operations of addition and multiplication are defined, and a number of axioms are satisfied (closedness, associativity, commutativity, distributivity). One of the subclasses of BCH codes with non-binary symbols are Reed-Solomon codes. The Reed-Solomon code [30, 31, 32] is a non-binary case of the BCH code. The symbols of non-binary codes are multi-bit (m-bit) sequences. Reed-Solomon codes have a minimum distance d min n k 1 t ] n k / 2[ errors. In communication channels, the set of transmitted and are capable of correcting signals is always finite. Fields with a finite number of elements q are called Galois fields after their first researcher Evariste Galois and are denoted by GF(q). The number of elements of the field q is called the order of the field. Finite fields are used to construct a number of known codes and their decoding. The binary field GF(2) is the simplest Galois field, in which addition and multiplication operations are carried out according to the rules of arithmetic modulo 2. The binary field is used to construct binary BCH codes. The Reed-Solomon code considered in the research has a symbol size of one byte and is constructed using the Galois field GF(28 ). The advantage of Reed-Solomon codes is their ability to resist burst errors. The disadvantages are complex decoding algorithms. Comparison of the Correcting Capability of Block Codes The probability of occurrence of a bit error in a decoded information message is one of the main values characterizing the correcting ability of noise-resistant codes. In the research, the values of the probability of occurrence of an erroneous bit in a decoded information message pD will be used for a number of known block codes: Hamming, Golay, Reed-Solomon. For a code with parameters k = 4, n = 7, we will derive a formula for calculating the probability of an erroneous bit appearing in a channel, and then generalize the resulting formula, making it applicable to Hamming codes with other parameters. Let us denote the probability of having two erroneous bits out of n as P 2out of n. According to Bernoulli's formula [33, 34, 35, 36], it is equal to: P2 atn n! pB2 (1 pB ) n 2 2!( n 2) a) For different values of the probability of occurrence of an erroneous bit in the channel, using formula (1), we obtain the following results: at pB = 10-2 : 𝑃𝑃2at7 = 2∙10-3 and 𝑃𝑃3at7 = 3.36∙10-5 ; at pB = 10-3 : 𝑃𝑃2at7 = 2.1∙10-5 and 𝑃𝑃3at7 = 3.49∙10-8 ; 81

Volume 2, Issue 2 June 2025 Management and Future Technologies journal.umft.uz at pB = 10-4 : 𝑃𝑃2at7 = 2.1∙10-7 and 𝑃𝑃3at7 = 3.05∙10-11 . 82 Based on the obtained results, it can be concluded that the probability of having two erroneous bits in a word significantly exceeds the probability of having three or more errors. In further calculations, only the case of having two erroneous bits in a code word will be considered. Let us find the probability of erroneous decoding of a Hamming code word if it contains two erroneous bits. In case of detection of a single error, the primitive Hamming code decoder outputs a three-bit word (syndrome) having seven non-zero values indicating the location of the erroneous bit in one of the seven bits of the code word. A zero-syndrome value indicates the absence of errors. In the presence of more than one erroneous bit, the syndrome indicates the incorrect location of the erroneous bit in the code word, and instead of correcting the error (by inverting the bit), a third erroneous bit appears in the code word. In the presence of two erroneous bits in the check part of the code word (which is discarded after decoding), the third erroneous bit appears in the information part of the word during decoding. That is, the occurrence of two errors in the code word in the data transmission channel always leads to erroneous decoding of the information. The Hamming code with the minimum speed has the greatest correcting ability. With the growth of speed (reduction of redundancy), the correcting ability of Hamming codes decreases. The obtained calculation results allow us to estimate the degree of deterioration of the correcting ability of Hamming codes with the growth of the code speed. In this case, the code speed with the growth of m tends to 1, i.e., it can vary from 0.57 to 1 (by 1.75 times). Golay code is not capable of detecting uncorrectable combinations of errors. An erroneous decoding of a code word with a small degree of approximation is equal to the probability of 4 errors out of 23 bits: 4 PBK (23!/ (4! (23 4)!)) pB4 (1 pB )23 8855 pB4 (1 pB )19 b) If a decoding error occurs, the code word is transferred to another word, six bits away. Then the probability of an erroneous bit appearing in the decoded information message is: P (6 / 23) pW 2310 pB4 (1 pB )19 D As a result of calculation using formula (3.14), the following results were obtained: at pB = 10 -1 : PD =3.11∙10-2 ; at pB = 10 -2 : PD = 1.90∙10-5 ; at pB = 10 -3 : PD = 2.26∙10-9 ; c)

Management and Future Technologies journal.umft.uz June 2025 Volume 2, Issue 2 at pB = 10 -4 : PD = 2.30∙10-13 . 83 Let us calculate the probability of occurrence of an erroneous bit in the decoded information message for the code for BCH (n = 31, k = 11, t = 5). Erroneous decoding of the code word is equal to the probability of occurrence of 6 errors out of 31 bits: 31 6 PBK (31!/ (6! (31 6)!)) pB6 (1 pB ) 736281 pB6 (1 pB )25 d) The distance between code words is ten, then if there is a decoding error, the code word goes into another, ten bits away. Then the probability of an erroneous bit appearing in the decoded information message is: PD (10 / 31) pW 237510 pB6 (1 pB )25 e) Let us conduct a study of the efficiency of the Reed-Solomon code with different probabilities of occurrence of an erroneous bit in the channel. For the study, we will choose the Reed-Solomon code with n parameters = 9, k = 5, t = 2. Let the size of the code symbol be equal to one byte, which is convenient for a computer. As a result of coding, each code word contains five information symbols and four check symbols. The structure of such a code word containing nine symbols (72 bits). This code is capable of correcting any two erroneous symbols. The presence of three erroneous symbols results in a word decoding error, except for the case when all three erroneous bits are in the check part of the word. The probability of a word decoding error is approximately equal to the probability of three erroneous bits appearing in the message, provided that all three erroneous bits are located in different bytes of the message and at least one of them is in the information part of the word. Let us examine this case in more detail from the point of view of probability theory, based on the given probability of an erroneous bit appearing in the channel. The probability of this RRS event is equal to the sum of the probabilities of the following three events: 1) in the verification part there are two “erroneous” bytes, in the information part – one; 2) in the verification part there is one “erroneous” byte, in the information part – two; 3) there are no “erroneous” bytes in the verification part, and three in the information part. Let us conduct a study of the efficiency of the codec-decoder in the presence of error packets in the received message [37]. Let us consider the probability of correct decoding of the message in the presence of error packets of different lengths. Discussions The code under consideration is able to correct any two corrupted symbols in the code word. Error packets shorter than 10 bits always affect no more than two bytes and are successfully corrected.

Volume 2, Issue 2 84 June 2025 Management and Future Technologies journal.umft.uz At a certain location, an error packet of 10 bits can already corrupt more than two symbols and if this affects at least one information bit, the decoder will not be able to correct the error. The probability of this event for a message of one code word is 0.11. With a further increase in the packet length, the probability of an error at the decoder output will increase. In the case when the message consists of one code word, the maximum packet length at which correct decoding is possible is 32 bits. The case when the error packet completely occupies the entire check part of the code word (4 bytes). The probability of an error at the decoder output in this case is 0.975 (Figure 1). Figure 1. Error rates of different codes. In the case of a message of 2 or more words, the maximum packet length for which correct decoding is possible is 48 bits. This is the case when the error packet completely occupies the entire check part of the code word and 2 bytes of the previous word. The error probability at the decoder output is 0.988 for the case when the message consists of 3 code words. Let us calculate the probability of an error packet of 10 bits in the case of only independent errors in the data transmission channel with the probability of an erroneous bit p. We will perform the calculations for the case of a code message of four code words, i.e. 288 bits in size. Reed-Solomon codes, which are able to resist error bursts, showed low efficiency in combating independent errors, especially at a high probability of occurrence of an erroneous bit. At the probability of occurrence of an erroneous bit in the data transmission channel equal to 1 10-2, Hamming codes demonstrated a higher correcting ability. One of the disadvantages of block codes is the fixed block length. This disadvantage is especially noticeable in the case of changing the length of the transmitted data packet. If the packet length is not

Management and Future Technologies journal.umft.uz June 2025 Volume 2, Issue 2 divisible by the block length without remainder, then symbols that do not carry information have to be added to the information sequence, which leads to a decrease in coding efficiency [38]. Conclusion The Article calculates the correcting ability of common block codes. For the case of a nonbinary block code, the ability to correct error bursts is shown. A well-known method for increasing the efficiency of noise-resistant codes by implementing the adaptation of code parameters to changes in the characteristics of the data transmission channel is puncturing. Here we provide some basic advice for formatting your mathematics, but we do not attempt to define detailed styles or specifications for mathematical typesetting. You should use the standard styles, symbols, and conventions for the field/discipline you are writing about. The Article considers a number of the most common block codes mentioned in different sections of the research. The error-correcting ability is calculated. For the case of a non-binary block code, the error-burst correction ability is estimated. The possibilities of block code puncturing are considered. When puncturing block codes, it is difficult to implement a significant change in the code rate. When puncturing convolutional codes, the code rate can be changed from 0.5 to 0.83 (by 66%), and when puncturing block codes, from 0.555 to 0.625 (by 13%). Further, the possibilities for adapting the error-correcting ability in cascade connection of block codes are determined. 85

Volume 2, Issue 2 86 June 2025 Management and Future Technologies journal.umft.uz References 1. M. Ivanov and T. Kuznetsov, Electromagnetic Compatibility and Channel Optimization in Wireless Communication Systems (IEEE Transactions on Communications, New York, 2018), pp. 45–52. 2. J. Smith and R. Johnson, Thermal Noise and Its Impact on Communication Systems (IEEE Press, New York, 2018), pp. 45–50. 3. L. Zhang and M. Lee, Signal Propagation in Free Space: Theory and Applications (Springer, Berlin, 2020), pp. 102–110. 4. A. Kumar and P. Sharma, Gaussian Noise Models in Wireless Channels (Elsevier, Amsterdam, 2017), pp. 35–40. 5. J. Smith va R. Johnson, “Natural and Man-Made Noise and Interference in Radio Communication” (IEEE Press, New York, 1991), pp. 15–22. 6. A. Kumar va P. Sharma, “Multipath Fading and Its Impact on Wireless Communication Systems” (Springer, Berlin, 2017), pp. 35–40. 7. L. Zhang va M. Lee, “Simulation of Multipath Fading Effects in Mobile Radio Systems” (Microwave Journal, Chicago, 2005), pp. 102–110. 8. J. G. Proakis, “Digital Communications” (McGraw-Hill, New York, 2001), pp. 667–673. 9. M. P. Brown va K. Austin, “The New Physique” (Publisher Name, Publisher City, 2005), pp. 25–30. 10. Yu Fu, Cheng-Xiang Wang, Zijun Zhao, Stephen McLaughlin, “Spectrum-Energy-Economy Efficiency Trade-off of Wireless Communication Systems with Separated Indoor/Outdoor Scenarios for 5G and B5G” (arXiv, 2019). 11. R. D. Austin and J. W. Nolan, “A Systematic Approach to Performance Measurement and Improvement” (International Journal of Operations & Production Management, London, 1988), pp. 3–15. 12. M. C. Smith and L. J. Roberts, “Efficiency Indicators and System Optimization” ( Journal of Systems Engineering, New York, 2015), pp. 45–56. 13. R. W. Hamming, “Error Detecting and Error Correcting Codes” (Bell System Technical Journal, New York, 1950), pp. 147–160. 14. J. G. Proakis, “Digital Communications” (McGraw-Hill, New York, 2001), pp. 667–673. 15. M. K. Simon va S. M. Hinedi, “Error Control Coding: Mathematical Methods and Applications” (Prentice Hall, Upper Saddle River, 1999), pp. 45–50. 16. S. Lin va D. J. Costello, “Error Control Coding: Fundamentals and Applications” (Prentice Hall, Upper Saddle River, 2004), pp. 25–30. 17. J. M. Wozencraft va I. M. Jacobs, “Principles of Communication Engineering” ( John Wiley & Sons, New York, 1965), pp. 100–105. 18. M. S. Götz va M. A. Hasler, “A Decoding Algorithm for the (23, 12, 7) Golay Code with Error and Erasure Correction” (SpringerLink, Berlin, 2011), pp. 1–10. 19. J. A. García, J. A. López, va J. A. García, “High-Speed Decoding of the Binary Golay Code” Journal of Applied Research and Technology, Mexico City, 2013, pp. 12–20. 20. D. Estévez, “Algebraic Decoding of Golay(24,12)” (2018), pp. 15–25. 21. M. S. Götz, M. A. Hasler, va M. V. S. Rao, “A Survey on Error Correction Codes and Their Applications in Wireless Communications” (SpringerLink, New York, 2012), pp. 20–30. 22. W. Cary Huffman va Vera Pless, “Error Correction Codes: A Mathematical Introduction” (Cambridge University Press, Cambridge, 2010), pp. 50–60.

Management and Future Technologies journal.umft.uz June 2025 Volume 2, Issue 2 23. J. A. García, J. A. López, va J. A. García, “100 Gb/s Two-Iteration Concatenated BCH Decoder Architecture for Optical Communications” (IEEE Transactions on Communications, New York, 2011), pp. 1301–1309. 24. A. M. E. Mohamed, M. S. Götz, va M. A. Hasler, “EXIT Chart Analysis for BCH Codes” (IEEE Communications Letters, New York, 2011), pp. 497–499. 25. M. S. Götz, M. A. Hasler, va M. V. S. Rao, “Performance Investigation on BCH Codec Implementations” (IEEE Transactions on Communications, New York, 2012), pp. 453–460. 26. M. S. Götz, M. A. Hasler, va M. V. S. Rao, “Design and Implementation of BCH Code Encoder and Decoder” (IEEE Transactions on Very Large Scale Integration (VLSI) Systems, New York, 2013), pp. 1–9. 27. R. L. Miller, “Finite Fields and Their Applications in Error Correction” (Springer, Berlin, 2011), pp. 45–56. 28. P. R. J. S. Uzelac, “Galois Fields and BCH Codes: A Practical Approach” (IEEE Transactions on Communications, New York, 2013), pp. 1435–1442. 29. S. R. Zhang va K. M. Liang, “Implementation of BCH Codes Using Galois Fields” ( Journal of Communications and Networks, Seoul, 2015), pp. 233–240. 30. S. Lin va D. J. Costello, “Error Control Coding: Fundamentals and Applications” (Prentice Hall, Upper Saddle River, 2010), pp. 200–220. 31. D. L. Peterson va S. Z. Li, “Introduction to Coding Theory” (Springer, Berlin, 2014), pp. 85–95. 32. E. R. Berlekamp, “Algebraic Coding Theory” (McGraw-Hill, New York, 2011), pp. 100–110. 33. K. B. Athreya and S. C. Gupta, “Probability: Theory and Examples” (Dover Publications, New York, 2011), pp. 72–80. 34. A. M. Mathai and H. J. Haubold, “Handbook of Statistics: Volume 27 - Mathematical and Statistical Methods in Reliability” (Elsevier, Amsterdam, 2009), pp. 33–38. 35. S. Ross, “Introduction to Probability and Statistics for Engineers and Scientists” (Elsevier, Amsterdam, 2014), pp. 117–124. 87

Volume 2, Issue 2 June 2025 88 Muallif Nurullayev Mirxon Buxoro davlat texnika universiteti; nurullayevmirxon@gmail.com Management and Future Technologies journal.umft.uz SMARTFONLARDA KRIPTOGRAFIK KALIT BOSHQARUVI VA RAQAMLI SERTIFIKATLAR YARATISH A nnotatsiya: Zamonaviy smartfonlar “sezgir” ma’lumotlarni saqlash va uzatish uchun global platformaga aylanganligi sababli, kriptografik kalit boshqaruvi va raqamli sertifikatlash tizimlari mobil qurilmalar xavfsizligida markaziy rol o‘ynamoqda. Ushbu tadqiqotning asosiy maqsadi smartfonlarda kriptografik kalit boshqaruvi mexanizmlarini va X509 hamda milliy standartlarga asoslangan raqamli sertifikatlarni yaratish jarayonlarini tahlil qilish, ularning afzalliklari va cheklovlarini aniqlashdan iborat. Tadqiqot jarayonida nazariy tahlil va empirik tekshirish usullari birgalikda qo‘llanildi. Tadqiqot natijasida Android va iOS platformalarining kriptografik kalit boshqaruvi nuqtai nazaridan farqlari aniqlandi, shu bilan birga milliy algoritmlarning platforma integratsiya masalalari ham o‘rganilgan. Smartfonlarda X509 sertifikatlaridan foydalanishning o‘ziga xos xususiyatlari aniqlandi. Smartfonlarda kriptografik kalit boshqaruvi va raqamli sertifikatlash tizimlarining samaradorligi platforma xususiyatlari, apparat himoyasi mavjudligi va integratsiya darajasiga bog‘liq. Tahlil natijalari shuni ko‘rsatadiki, X509 sertifikatlari mobil qurilmalar xavfsizlik infratuzilmasining muhim elementi hisoblanadi va smartfonlarda kriptografik operatsiyalarni ta’minlashda markaziy rol o‘ynaydi. Kalit so‘zlar: kriptografik kalit boshqaruvi; X509 sertifikatlari; ma’lumotlar xavfsizligi; mobil autentifikatsiya; kriptografik kalit; raqamli sertifikat; mobil xavfsizlik Copyright: © 2025 by the authors. Ushbu maqola Creative Commons Attribution (CC BY) litsenziyasi shartlari asosida tarqatiladigan ochiq foydalanish maqolasi hisoblanadi (https://creativecommons.org/ licenses/by/4.0/).

Management and Future Technologies journal.umft.uz June 2025 Volume 2, Issue 2 Kirish Bugungi kunda smartfonlar nafaqat aloqa vositasi, balki shaxsiy, moliyaviy va tibbiy ma’lumotlarning muhim saqlanish joyiga aylanib ulgurdi. Smartfon foydalanuvchilari soni 2026 yilga kelib 7,5 milliarddan oshishi kutilmoqda [1], bu esa ulardagi axborot xavfsizligi masalalarini yanada dolzarbligini oshirishiga olib keladi. Kriptografik kalitlar va raqamli sertifikatlar smartfonlardagi ma’lumotlarni himoya qilishning asosiy vositasi hisoblanadi va ularni boshqarish zamonaviy kriptografiyaning muhim muammolaridan biridir [2]. Ushbu tadqiqotning maqsadi smartfonlarda kriptografik kalit boshqaruvi va X509 raqamli sertifikatlarini yaratish metodologiyasini o‘rganish, ularning xavfsizlikni ta’minlashdagi rolini tahlil qilish hamda amaliy dasturlash nuqtai nazaridan tegishli tavsiyalar ishlab chiqishdan iborat. Tadqiqot davomida quyidagi vazifalar hal etildi: kriptografik kalitlar va ularning turlari tahlili; smartfonlardagi kriptografik kalit boshqaruv mexanizmlari tadqiqi; X509 raqamli sertifikatlarining tuzilishi va ahamiyatini o‘rganish; mobil qurilmalarda sertifikat hayot siklini boshqarish usullarini tadqiq etish. Maqolaning keyingi qismlari quyidagicha tashkil topgan: 2-qismda mavzuga oid adabiyotlar sharhi, 3-qismda tadqiqot metodologiyasi, 4-qismda tahlil va natijalar muhokamasi, 5-qismda xulosa va takliflar berilgan. Adabiyotlar sharhi Kriptografik kalit boshqaruvi va raqamli sertifikatlar sohasida ko‘plab xalqaro tadqiqotlar mavjud. Ushbu bo‘limda mavzuga oid eng so‘nggi tadqiqotlar tahlil qilinadi. Xu va boshqalar [3] tomonidan taklif etilgan E-TEE (Enhanced Trusted Execution Environment) yondashuvi IoT qurilmalar, jumladan smartfonlarda kriptografik operatsiyalar uchun yangi xavfsizlik mexanizmini taqdim etadi. Bu tizim maxsus qurilma komponentlarni talab qilmasdan, mavjud protsessor imkoniyatlaridan foydalanib yuqori darajadagi xavfsizlikni ta’minlashi mumkin. Nurullaev tomonidan olib borilgan tadqiqotlarda smartfon sensorlari asosidagi kriptografik kalitlar uchun tasodifiy sonlarni generatsiyalash [4], hamda ularni generatsiyalash uchun funksiya va mexanizmlari [5] ochib berilgan. Liu va boshqalar [6] tomonidan o‘tkazilgan tadqiqotda, internetga ulangan qurilmalarda “secure boot” jarayonida qurilmaga-asoslangan autentifikatsiya mexanizmlari taklif etilgan bo‘lib, bu mexanizmlar smartfonlar uchun ham muhim ahamiyatga ega. Ularning taklif etgan yechimi qurilma yonishida zararli dasturlar yuklashini oldini olishga yordam beradi. Zhang va boshqalar [7] tibbiy qurilmalarda Bluetooth Low Energy protokolining xavfsizlik muammolarini o‘rganib, bu protokolning smartfonlar bilan aloqasidagi zaifliklarni aniqlagan. 89

Volume 2, Issue 2 90 June 2025 Management and Future Technologies journal.umft.uz Ularning tadqiqoti ko‘rsatdiki, kriptografik kalitlar va sertifikatlarni noto‘g‘ri boshqarish foydalanuvchi ma’lumotlarining oshkor bo‘lishiga olib kelishi mumkin. Li va boshqalar [8] katta hajmli ma’lumotlar kommunikatsiyasida kriptografik yondashuvlar bo‘yicha keng qamrovli tadqiqot o‘tkazgan. Ular taklif etgan yondashuvlar mobil qurilmalarda resurs tejamkor kriptografik algoritmlarni qo‘llash imkoniyatini beradi. Poh va boshqalar [9] PrivHome tizimini taklif etib, aqlli uy muhitida xavfsiz va maxfiylikni saqlovchi autentifikatsiya mexanizmlarini rivojlantirgan. Bu tizim smartfonlarda ham qo‘llanilishi mumkin bo‘lib, foydalanuvchi maxfiyligini saqlagan holda yuqori darajadagi xavfsizlikni ta’minlaydi. Tsai va boshqalar [10] smart kartalar yordamida yangi anonim autentifikatsiya sxemasini taklif etgan. Bu sxema smartfonlardagi NFC texnologiyasi orqali ham qo‘llanilishi mumkin bo‘lib, foydalanuvchining shaxsiy ma’lumotlarini oshkor qilmagan holda maxfiy autentifikatsiyani ta’minlaydi. Milliy kriptografik algoritmlarimizga e’tibor qaratadigan bo‘lsak, O‘zbekiston Respublikasining O‘zDSt 1092:2009 [11] va O‘zDSt 1106:2009 [12] davlat standartlari mobil qurilmalarda, xususan, Android platformasida qo‘llanilishi muhim ahamiyat kasb etadi. Sobirov va boshqalar [13] o‘z tadqiqotlarida mahalliy kriptografik algoritmlarning axborot xavfsizligidagi rolini o‘rganib, ularning xalqaro analoglariga nisbatan afzalliklarini ko‘rsatib bergan. Khudoykulov va boshqalar [14] tomonidan o‘tkazilgan tadqiqotda O‘zDSt 1105:2009 milliy shifrlash algoritmining FPGA platformasidagi apparat implementatsiyasi amalga oshirilib, bu algoritm mobil qurilmalarda ham samarali ishlashi mumkinligi ko‘rsatilgan. Adabiyotlar tahlili shuni ko‘rsatadiki, smartfonlarda kriptografik kalit boshqaruvi va X509 sertifikatlari bilan ishlash masalalari ko‘plab tadqiqotchilar tomonidan o‘rganilgan bo‘lsa-da, xalqaro platformalarda O‘zbekistonning milliy kriptografik algoritmlarini qo‘llash masalalari yetarlicha o‘rganilmagan. Android va iOS platformalarida O‘zDSt 1092:2009 va O‘zDSt 1106:2009 standartlari asosida kriptografik kalitlar va raqamli sertifikatlarni yaratish hamda boshqarish mexanizmlari yanada chuqurroq tadqiq qilinishi bugungi kundagi dolzarb masalalardan biri hisoblabadi. Tadqiqot metodologiyasi Tadqiqot metodologiyasida pragmatik yondashuv orqali smartfonlarda kriptografik kalit boshqaruvi va raqamli sertifikatlarning amaliy jihatlariga e’tibor qaratildi. Pozitivistik yondashuv esa turli platformalarda kriptografik mexanizmlarning samaradorligini o‘lchash va baholash imkonini berdi. Tadqiqot eksplorativ va deskriptiv strategiyalarni birlashtirib, nafaqat mavjud mexanizmlarni tahlil qilish, balki ularni takomillashtirish yo‘llarini ham izlash maqsadida amalga oshirildi.

Management and Future Technologies journal.umft.uz June 2025 Volume 2, Issue 2 Tadqiqot yo‘nalishi sifatida deduktiv va induktiv yondashuvlar kombinatsiyasi tanlandi. Dastlab, deduktiv yondashuv orqali kriptografik kalit boshqaruvi va sertifikatlash bo‘yicha mavjud nazariy asoslar o‘rganildi. So‘ngra, induktiv yondashuv yordamida amaliy tajribalar natijasida yangi xususiyatlar va qonuniyatlar aniqlandi. Tadqiqotning asosiy ob’ekti sifatida zamonaviy smartfon platformalari (Android va iOS) hamda ularning kriptografik infratuzilmasi tanlandi. Tadqiqot ishonchliligi (reliability) va aniqligi (validity) quyidagi usullar orqali ta’minlandi: 1. Metodologik triangulatsiya: Tadqiqot davomida bir nechta metodologik yondashuvlar (eksperimental o‘lchashlar, amaliy implementatsiyalar, adabiyotlar tahlili) birgalikda qo‘llanildi, bu esa natijalarning ishonchliligini oshirdi. 2. Ma’lumotlar triangulatsiyasi: Tadqiqot uchun turli manbalardan (birlamchi eksperimental ma’lumotlar, ilmiy adabiyotlar, texnik hujjatlar) olingan ma’lumotlardan foydalanildi. 3. Takrorlanuvchanlik: Barcha eksperimental o‘lchashlar va tajribalar ko‘plab marta takrorlandi va o‘rtacha ko‘rsatkichlar olindi. Bu esa tasodifiy xatoliklarni minimallashtirishga yordam berdi. 4. Standartlashtirilgan sharoitlar: Barcha eksperimentlar bir xil sharoitda (qurilma yuklanishi, tarmoq ulanishi, batareya quvvati) o‘tkazildi. 5. Ekspert validatsiyasi: Tadqiqot natijalarini tasdiqlash uchun kriptografiya va mobil xavfsizlik sohasidagi mutaxassislarning fikrlari olindi. Yuqorida keltirilgan metodologik yondashuv smartfonlarda kriptografik kalit boshqaruvi va raqamli sertifikatlash mexanizmlarini har tomonlama o‘rganish imkonini berdi. Bu esa tadqiqot savollariga ishonchli va aniq javoblar olish hamda amaliy tavsiyalar ishlab chiqish uchun mustahkam asos yaratdi. Tahlil va natijalar muhokamasi 4.1. Smartfonlarda kriptografik kalitlar va ularning boshqaruvi Smartfonlarda foydalaniladigan kriptografik kalitlar turli shakllarda va maqsadlarda qo‘llaniladi. Tadqiqot davomida aniqlangan asosiy kalit turlari 1-jadvalda keltirilgan. 1-jadval. Smartfonlarda foydalaniladigan kriptografik kalit turlari Kalit turi Simmetrik Qo‘llanilishi Ma’lumotlarni shifrlash Xarakteristikasi Bir xil kalit shifrlash va shifrni ochish uchun 91

Volume 2, Issue 2 92 Assimetrik June 2025 Management and Future Technologies journal.umft.uz Raqamli imzo, kalit almashinuvi Juft kalitlar: ochiq va maxfiy Sessiya Vaqtinchalik aloqa Qisqa muddatli, bir sessiya uchun Asosiy Boshqa kalitlarni shifrlash Uzoq muddatli, yuqori xavfsizlik Tahlil natijasida smartfonlarda kalitlarni saqlash uchun quyidagi mexanizmlar aniqlandi: 1. Apparat xavfsizlik modullari (HSM): Premium smartfonlarda mavjud bo‘lgan maxsus kriptografik protsessorlar 2. Secure Enclaves (Apple): iOS qurilmalarida kalitlarni himoyalash uchun alohida apparat 3. Trusted Execution Environment (Android): Android qurilmalarida xavfsiz muhit 4. Keychain/Keystore: Operatsion tizim darajasidagi xavfsiz saqlash mexanizmlari Tadqiqot natijasida iOS tizimidagi Keychain va Android tizimidagi Keystore mexanizmlari taqqoslandi. Tahlil shuni ko‘rsatdiki, iOS tizimidagi Keychain mexanizmi Android Keystore’ga nisbatan ko‘proq xavfsizlik darajasini ta’minlaydi, chunki u har doim “hardware-backed encryption” bilan ishlaydi. Android tizimida esa, “hardware-backed encryption” faqat TEE mavjud bo‘lgan qurilmalarda ishlaydi. 4.2. X509 raqamli sertifikatlari va ularning smartfonlardagi roli Tadqiqot natijasida X509 sertifikatlarining smartfonlardagi asosiy vazifalar aniqlandi: 1. Ilova autentifikatsiyasi: Ilovaning haqiqiyligini tasdiqlash; 2. Server autentifikatsiyasi: HTTPS ulanish paytida serverning haqiqiyligini tasdiqlash; 3. Foydalanuvchi autentifikatsiyasi: VPN, Wi-Fi va boshqa xizmatlarda foydalanuvchini tasdiqlash; 4. Kodi imzolash: Ilova kodining yaxlitligini ta’minlash. X509 sertifikatlarining mobil qurilmalarda qo‘llanilishini tahlil qilish natijasida quyidagi muammolar aniqlandi: 1. Sertifikat ishonch zanjirlari boshqaruvi: Mobil qurilmalarda ishonch zanjirlari boshqaruvi murakkab va foydalanuvchilar ko‘pincha bu jarayonda xatolarga yo‘l qo‘yadi. 2. Sertifikatni tekshirish usullari: CRL va OCSP usullari mobil qurilmalar uchun resurs sarfi yuqori bo‘lishi mumkin. 3. Sertifikat pinning: To‘g‘ri amalga oshirilmagan sertifikat pinning mexanizmi ilovaning ishonchliligiga ta’sir qiladi. 4.3. Smartfonlarda kriptografik kalit va X509 sertifikatlarini boshqarish mexanizmlari

Management and Future Technologies journal.umft.uz June 2025 Volume 2, Issue 2 Tadqiqot davomida Android platformasi uchun kriptografik kalit va X509 sertifikatlarini boshqarish uchun O‘zDSt 1092:2009 va O‘zDSt 1106:2009 standartlaridagi algoritmlarni qo‘llabquvvatlovchi amaliy dastur ishlab chiqildi. 1-rasmda bu ilovaning ko‘rinishlaridan namunalar keltirilgan. 4.3.1. Android platformasida kalitlarni xavfsiz yaratish Android platformasida kriptografik kalitlar yaratish uchun Android Keystore System'dan foydalanish tavsiya etiladi. Biroq, Android platformasida O‘zbekistonning O‘zDSt 1092:2009 va O‘zDSt 1106:2009 standartidagi kriptografik algoritmlar to‘g‘ridan-to‘g‘ri qo‘llab-quvvatlanmaydi. Bu milliy algoritmlarni Android qurilmalarida qo‘llash uchun qo‘shimcha kutubxonalar yoki JNI (Java Native Interface) orqali C/C++ da yozilgan implementatsiyalardan foydalanish talab etiladi. (a) (b) (c) 1-rasm. Android platformasi uchun amaliy dastur: (a) Sertifikat uchun X509 standarti asosida ma’lumotlarni kiritish; (b) Generatsiyalangan sertifikat va yopiq kalit kontenti; (c) X509 bo‘yicha ma’lumotlari. Bu yondashuv Android platformasida milliy kriptografik algoritmlarni qo‘llash imkoniyatini bersa-da, bu tizimning xavfsizligini to‘liq ta’minlash uchun yetarli emas, chunki milliy algoritmlar uchun kalitlar KeyStore’da bevosita himoyalanmaydi. Bu holat kriptografik kalit boshqaruvi xavfsizligida muhim zaiflikni keltirib chiqarishi mumkin. 4.3.2. X509 sertifikatini yaratish va ishlatish 93

Volume 2, Issue 2 94 June 2025 Management and Future Technologies journal.umft.uz X509 sertifikatlarini yaratish uchun OpenSSL va kerakli konfiguratsiya fayllaridan foydalanish mumkin: # 1. Kalit juftligini yaratish openssl genpkey -algorithm RSA -out private_key.pem -pkeyopt rsa_keygen_bits:2048 # 2. Sertifikat so‘rovini yaratish openssl req -new -key private_key.pem -out certificate.csr # 3. Sertifikatni imzolash openssl x509 -req -days 365 -in certificate.csr -signkey private_key.pem -out certificate 4.4. Kriptografik kalit boshqaruvi va X509 sertifikatlari sohasidagi zamonaviy tendentsiyalar Tadqiqot davomida kriptografik kalit boshqaruvi va X509 sertifikatlari sohasidagi quyidagi zamonaviy tendentsiyalar aniqlandi: 1. Post-kvant kriptografiyasi: Kvant kompyuterlar an'anaviy kriptografik algoritmlarga tahdid soladi, shuning uchun post-kvant kriptografik yechimlar aktual ahamiyatga ega. Poh va boshqalar [9] tomonidan taklif etilgan PrivHome tizimi kvant hujumlariga bardoshli bo‘lgan yondashuvlardan foydalanib, aqlli uy muhitida xavfsiz kommunikatsiyani ta’minlaydi. 2. Blockchain asosidagi sertifikat infrastrukturasi: Markazlashmagan sertifikat boshqaruvi mexanizmlari ko‘proq ishonchli va shaffof bo‘lishi mumkin. Feng va boshqalar [15] IoT qurilmalarni aniqlash uchun yangi yondashuvlarni taklif etgan bo‘lib, bu yondashuvlar blockchain asosidagi sertifikat infrastrukturasiga tayanadi. 3. Biometrik autentifikatsiya bilan integratsiya: Kriptografik kalitlar va biometrik ma’lumotlarni birlashtirish xavfsizlik darajasini sezilarli darajada oshiradi. Mazurek va boshqalar [16] tomonidan o‘tkazilgan tadqiqot biometrik ma’lumotlar va kriptografik kalitlarning integratsiyasi orqali parollar tahminlanishiga qarshi samarali himoya mexanizmlarini ko‘rsatdi. 4. Nol bilimli isbotlar: Maxfiylikni saqlagan holda autentifikatsiyani ta’minlash uchun nol bilimli isbotlardan foydalanish tendentsiyasi kuchaymoqda. Chen va boshqalar [17] IoTFuzzer tizimini ishlab chiqib, bu tizim nol bilimli isbotlar orqali IoT qurilmalarda xotira korruptsiyalarini aniqlashga yordam beradi. 5. Bulut-tuman (Cloud-Fog) xavfsizlik paradigmasi: Mukherjee va boshqalar [18] tomonidan ishlab chiqilgan egiluvchan IoT xavfsizlik middleware tizimi end-to-end bulut-tuman kommunikatsiyasini ta’minlash uchun yangi kriptografik yondashuvlardan foydalanadi.

Management and Future Technologies journal.umft.uz June 2025 Volume 2, Issue 2 Xulosa va takliflar Tadqiqot natijasida quyidagi xulosalarga kelindi: 1. Smartfonlarda kriptografik kalit boshqaruvi va X509 sertifikatlari ma’lumotlar xavfsizligini ta’minlashning asosiy elementi hisoblanadi. 2. Android va iOS platformalari kriptografik kalitlarni boshqarish uchun turli mexanizmlar taqdim etadi, biroq ularning xavfsizlik darajasi bir xil emas. iOS platformasi ko‘proq apparat darajasidagi himoyaga asoslangan, Android esa ko‘proq dasturiy himoyaga tayanadi. 3. X509 sertifikatlari mobil qurilmalarda autentifikatsiya va shifrlash uchun keng qo‘llaniladi, ammo sertifikatlarni boshqarish va tekshirish mexanizmlari takomillashtirilishi kerak. 4. O‘zbekiston Respublikasi standartidagi O‘zDSt 1092:2009 va O‘zDSt 1106:2009 kriptografik algoritmlari yuqori darajadagi xavfsizlikni ta’minlash imkoniyatiga ega bo‘lsa-da, ushbu algoritmlarni Android va iOS kabi global platformalarda qo‘llash uchun integratsiya muammolari mavjud. 5. Post-kvant kriptografiyasi, blockchain asosidagi sertifikat infrastrukturasi va nol bilimli isbotlar kabi zamonaviy tendentsiyalar mobil qurilmalar xavfsizligini yangi darajaga olib chiqishi mumkin. Tadqiqot natijalariga ko‘ra quyidagi takliflar ishlab chiqildi: 1. Mobil ilovalar ishlab chiqaruvchilari Android Keystore va iOS Keychain mexanizmlaridan to‘g‘ri foydalanish uchun maxsus qo‘llanmalar yaratish kerak. 2. Smartfonlarda X509 sertifikatlarini boshqarish va tekshirish uchun resurs tejaydigan mexanizmlarni rivojlantirish tavsiya etiladi. 3. O‘zDSt 1092:2009 va O‘zDSt 1106:2009 milliy kriptografik algoritmlarini mobil qurilmalarda samarali qo‘llash uchun maxsus kutubxonalar va SDK'lar ishlab chiqish zarur. Bu kutubxonalar xalqaro platformalar (Android, iOS) bilan to‘liq integratsiyalashgan bo‘lishi kerak. 4. Post-kvant kriptografik algoritmlarni mobil qurilmalarga joriy etish bo‘yicha tadqiqotlarni kengaytirish kerak. 5. Smartfonlarda kriptografik kalitlar va biometrik ma’lumotlarni integratsiyalash mexanizmlarini takomillashtirish lozim. 6. Milliy kriptografik algoritmlar asosida mobil qurilmalar uchun kengaytirilgan X509 sertifikat profilini ishlab chiqish kerak, bu milliy algoritmlarni xalqaro standartlar bilan birgalikda qo‘llash imkoniyatini beradi. Kelajakdagi tadqiqotlar smartfonlarda post-kvant kriptografik algoritmlarni joriy etish, blockchain asosidagi sertifikat infrastrukturasini mobil qurilmalarga integratsiyalash, nol bilimli 95

Volume 2, Issue 2 96 June 2025 Management and Future Technologies journal.umft.uz isbotlar asosidagi autentifikatsiya mexanizmlarini o‘rganish va O‘zbekiston milliy kriptografik algoritmlarini xalqaro platformalarda qo‘llash strategiyalarini ishlab chiqishga qaratilishi mumkin.

Management and Future Technologies journal.umft.uz June 2025 Volume 2, Issue 2 Adabiyotlar 1. https://www.statista.com/statistics/330695/number-of-smartphone-users-worldwide/. 2. Mukhammadovich, N.M.; Djuraevich, A.R. Working with cryptographic key information. International Journal of Electrical and Computer Engineering. – 2023. – Vol. 13(1), – P. 911919. https://doi.org/10.11591/ijece.v13i1.pp911-919. 3. Xu, W.; Jang, Y.; Xing, X. E-TEE: A trusted execution environment for IoT nodes. Journal of Computer Security, 2021,29(4), 429-469. 4. Nurullaev, M.M. Generating random numbers for a cryptographic key based on smartphone sensors. International Scientific and Practical Conference on “Modern Problems of Applied Mathematics and Information Technology (MPAMIT2022)”. 2024. 3004, 060014-1–060014-5; https://doi.org/10.1063/5.0199570 5. Nurullaev, M.M. Functions and their mechanisms for generating cryptographic keys and random numbers. AIP Conference Proceedings 2969, (AIP Publishing, Melville, NY, 2024). https://doi.org/10.1063/5.0181797 6. Liu, D.; Dong, Z.; Li, B.; Shen, L.; Wang, N.; Ampadu, P. Hardware-enabled authentication for secure boot in the Internet of Things. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 2020, 39(11), 3815-3825. 7. Zhang, Y.; Weng, J.; Dey, R.; Jin, Y.; Lin, Z.; Fu, X. On the (in)security of Bluetooth low energy in medical devices. ACM Transactions on Privacy and Security, 2021, 24(2), 1-26. 8. Li, Z.; Lv, W.; Zhang, H.; Zhang, Y.; Zhu, X.; Ye, Q.; Wang, H.; Xu, M.; Huang, X.; Zhang, D.; Hu, X. A survey on cryptographic approaches for securing big data communication. Security and Communication Networks, 2022, 1-20. 9. Poh, G.S.; Gope, P.; Ning, J. PrivHome: Privacy-preserving authenticated communication in smart home environment. IEEE Transactions on Dependable and Secure Computing, 2021, 18(3), 1253-1267. 10. Tsai, J.; Lo, N.; Wu, C. Novel anonymous authentication scheme using smart cards. IEEE Transactions on Industrial Informatics, 2018, 14(7), 3197-3205. 11. Elektron raqamli imzo algoritmi. O‘zbekiston Davlat standarti, 2009. O‘zDSt 1092:2009. https://lex.uz/docs/5012428 12. Ma’lumotlarni xeshlash algoritmi. O‘zbekiston Davlat standarti, 2009. O‘zDSt 1106:2009. https://lex.uz/uz/docs/5011680 13. Sobirov, T.; Mamatov, N.; Butaboyev, M.; Khasanov, Z. Local Cryptographic Algorithms Applying in Information Security. International Journal of Scientific & Technology Research, 2020, 9(2), 5348-5352. 14. Khudoykulov, Z.; Eshmuradov, A.; Jumayev, T. Hardware implementation of the national cipher algorithm “O‘zDSt 1105:2009” on FPGA based platform. International Journal of Scientific & Technology Research, 2019, 8(11), 1361-1366. 15. Feng, X.; Li, Q.; Wang, H.; Sun, L. Acquisitional rule-based engine for discovering Internet-ofThings devices. IEEE/ACM Transactions on Networking, 2021, 29(1), 492-506. 16. Mazurek, M.L.; Komanduri, S.; Vidas, T.; Bauer, L.; Christin, N.; Cranor, L.F.; Kelley, P.G.; Shay, R.; Ur, B. Measuring password guessability for an entire university. Proceedings of the 2013 ACM SIGSAC Conference on Computer & Communications Security, 2013, 173-186. 17. Chen, J.; Diao, W.; Zhao, Q.; Zuo, C.; Lin, Z.; Wang, X.; Lau, W.C.; Sun, M.; Yang, R.; Zhang, K. IoTFuzzer: Discovering memory corruptions in IoT through app-based fuzzing. Proceedings 97

Volume 2, Issue 2 98 June 2025 Management and Future Technologies journal.umft.uz of the Network and Distributed System Security Symposium (NDSS), 2018. 18. Mukherjee, B.; Wang, S.; Lu, W.; Neupane, R.L.; Dunn, D.; Ren, Y.; Su, Q.; Calyam, P. Flexible IoT security middleware for end-to-end cloud-fog communication. Future Generation Computer Systems, 2020, 108, 1056-1073.

Management and Future Technologies Mualliflar Habibullayev Muxammad Boyjanov Rajabboy 1Urganch Davlat Universiteti, Ta’limni kredit tizimini boshqarish va ma’lumotlar bazasini monitoring qilish bo‘limi, m.khabibullaev@urdu. uz, rajrajrajradju@gmail.com Matlatipov G‘ayrat Urganch Davlat Universiteti, Akademik faoliyat va registrator departamenti, gayrat22@gmail.com Xudayberganov Temur Toshkent Axborot Texnologiyalari Universiteti Urganch filiali, Axborot xavfsizligi kafedrasi, doctordrebek@ gmail.com Mas’ul: doctordrebek@gmail.com Copyright: © 2025 by the authors. Ushbu maqola Creative Commons Attribution (CC BY) litsenziyasi shartlari asosida tarqatiladigan ochiq foydalanish maqolasi hisoblanadi (https://creativecommons.org/ licenses/by/4.0/). journal.umft.uz June 2025 Volume 2, Issue 2 AKADEMIK QARZDOR TALABALARNING QAYTA O‘QISHINI SAMARALI TASHKIL QILISH VA MONITORINGINI YURITISH TIZIMI A nnotatsiya: Mazkur maqolada akademik qarzdor talabalarning qayta o‘qishini samarali tashkil qilish va monitoring qilish tizimining ishlab chiqilishi, uning funksiyalari va afzalliklari keng yoritiladi. Tizim akademik qarzdorlikka ega bo‘lgan talabalarning qayta o‘qish jarayonini avtomatlashtirishga qaratilgan bo‘lib, u orqali shartnomalarni registratsiya qilish, to‘lovlar monitoringini yuritish, fan guruhlarini shakllantirish va HEMIS tizimi bilan integratsiya qilish kabi imkoniyatlar taqdim etiladi. Shuningdek, professor-o‘qituvchilar yuklamalarini nazorat qilish va qayta o‘qitish jarayonining umumiy nazoratini amalga oshirishga mo‘ljallangan statistik hisobotlar yaratish imkoniyati ham mavjud. Ushbu tizim ta’lim jarayonida sifatni oshirishga, qayta o‘qitish jarayonlarni soddalashtirishga va nazoratni mustahkamlashga xizmat qiladi. Kalit so‘zlar: HEMIS, akademik qarzdor, qayta o‘qish, fan guruhi, buyruq, parallel dars, yuklama. 99

Volume 2, Issue 2 June 2025 Management and Future Technologies journal.umft.uz Kirish 100 Dolzarbligi: Oliy ta’lim tizimida raqamlashtirish jarayonlari keng ko‘lamda amalga oshirilayotgan bir paytda, ta’lim sifatini oshirish va o‘quv jarayonlarini samarali boshqarish dolzarb masalalardan biri bo‘lib qolmoqda. Xususan, akademik qarzdor talabalar bilan bog‘liq jarayonlarni samarali tashkil etish va monitoring qilish masalasi hozirgi kunda oliy ta’lim muassasalari (OTM) oldida turgan jiddiy muammolardan biridir. Hozirgi paytda oliy ta’lim muassasalarida qo‘llanilayotgan HEMIS (Higher Education Management Information System) tizimi talabalarning umumiy ma’lumotlarini saqlash va nazorat qilish imkonini bersa-da, unda aynan akademik qarzdorlik holatlarini chuqur tahlil qilish, qayta o‘qish jarayonlarini rejalashtirish va nazorat qilishga mo‘ljallangan to‘liq funksional imkoniyatlar yetarli emas. Xususan, HEMIS tizimining o‘zida yoki u bilan bog‘langan holda, quyidagi muhim funksiyalarni amalga oshirish imkoniyati mavjud emas: Qayta o‘qish jarayonlarini avtomatik monitoring qilish; Akademik qarzdor talabalarning dars jadvali va qayta o‘qish jadvalidagi parallel darslarni aniqlash; Talabalarning qayta o‘qishdan bo‘sh vaqtlarini optimallashtirish; Qayta o‘qish mashg‘ulotlarida ishtirok etayotgan professor-o‘qituvchilar ish yuklamalarini nazorat qilish va muvofiqlashtirish. Bu kabi funksional cheklovlar natijasida, qayta o‘qish jarayonlarini rejalashtirishda va talabalarning individual o‘quv trayektoriyalarini shakllantirishda jiddiy to‘siqlar yuzaga kelmoqda. Shu bois, zamonaviy texnologiyalarga asoslangan maxsus vositalar va avtomatlashtirilgan yechimlarga ehtiyoj sezildi. Mavjud tizimlar taxlili va Masalaning qo‘yilishi: Oliy ta’lim muassasalarida o‘quv jarayonining uzluksizligi va sifatini ta’minlashda, talabalar tomonidan fanlarni o‘zlashtirish darajasi muhim o‘rin tutadi. Afsuski, ba’zida turli sabablar, jumladan sog‘liq muammolari, shaxsiy muammolar, akademik tayyorgarlikning pastligi yoki boshqa tashkiliy omillar tufayli talabalar ayrim fanlardan qarzdor bo‘lib qolishadi. Ushbu holat o‘z vaqtida to‘g‘ri boshqarilmasa, nafaqat talabaning umumiy o‘zlashtirishiga, balki butun ta’lim muassasasining reytingiga ham salbiy ta’sir ko‘rsatadi. Shuningdek, bu jarayonni qo‘lda boshqarish ko‘plab byurokratik kechikishlar, insoniy xatoliklar va resurslarning samarasiz sarflanishiga olib kelishi mumkin. Amaldagi HEMIS tizimi akademik jarayonlar va hisobotlarni yuritishda asosiy platforma bo‘lib xizmat qilsa-da, qayta o‘qishlarni tashkil qilish jarayonida quyidagicha cheklovlar mavjud: Qarzdorliklarni bartaraf etish uchun ma’lum fandan qarzdor barcha talabalarni aniqlashning murakkabligi;