the Mathematical Foundations of Asymmetric Algorithms Based on Elliptic Curves and Problems of Their Application
Mathematical Foundations of Asymmetric Algorithms Based on Elliptic Curves and Problems of Their Application
Keywords:
Asimmetrik kriptografiya, Elliptik egri chiziqlar, Diskret logarifm, El-Gamal shifrlash algoritmi, Xavfsizlik, Kalit uzunligi, Matematik murakkablik, Diffie-Hellman, ECC (Elliptik Egri Chiziqlar Kriptografiyasi)Abstract
This paper analyzes the mathematical foundations of the transfer of asymmetric cryptographic algorithms to elliptic curves and their applications. Asymmetric cryptography, such as RSA and Diffie-Hellman algorithms, have long been used in secure communication and data protection. However, due to the large key length and computational complexity, these systems become difficult to apply in resource-constrained environments. Elliptic curve cryptography (ECC) has emerged as an effective solution to these problems. ECC provides a high level of security in a small key length. The article describes in detail the mathematical basis of ECC algorithms, their security advantages and their practical application.
References
Boyquziyev I., Saydullayev E., Rahmatullayev I. ELLIPTIK EGRI CHIZIQLARNING KRIPTOGRAFIYADA QO ‘LLANILISHI //DIGITAL TRANSFORMATION AND ARTIFICIAL INTELLIGENCE. – 2024. – Т. 2. – №. 1. – С. 71-76.
Abdunazar o'g A. O. et al. ELLIPTIK EGRI CHIZIQLARDA NUQTALARNI TOPISH MUAMMOSIGA ASOSLANGAN SHIFRLASH //ОБРАЗОВАНИЕ НАУКА И ИННОВАЦИОННЫЕ ИДЕИ В МИРЕ. – 2023. – Т. 30. – №. 2. – С. 180-188.
Olimov I. S., Ibrohimov X. I. ELEKTRON RAQAMLI IMZO ALGORITMLARI TAHLILI //GOLDEN BRAIN. – 2023. – Т. 1. – №. 18. – С. 211-221.
Khudoykulov Z. T., Rakhmatullayev I. R. A new key stream encryption algorithm and its cryptanalysis //Scientific and technical journal Namangan Institute of Engineering and Technology. – 2023. – Т. 8. – №. 1. – С. 146-157.
Rahmatullayev I. R., Saydullayev E. I., Karimov I. KRIPTOGRAFIYADA ELLIPTIK EGRI CHIZIQLARNING AHAMIYATI //Talqin va tadqiqotlar. – 2024. – №. 28.
Xudoykulov Z., Rahmatullayev I. Yengil vaznli kriptografik algoritmlarda foydalanilgan chiziqsiz akslantirishlash tahlili //Международный Журнал Теоретических и Прикладных Вопросов Цифровых Технологий, 7 (2), 51–58. извлечено от https://ijdt. uz/index. php/ijdt/article/view. – 2024. – Т. 181.
Rakhmatullaevich R. I., Mardanokulovich I. B. Analysis of cryptanalysis methods applied to stream encryption algorithms //Artificial Intelligence, Blockchain, Computing and Security Volume 1. – CRC Press, 2023. – С. 393-401.
Xudoynazarov U., Meliquziyev A. OCHIQ KALITLI RSA SHIFRLASH ALGORITMINI PARAMETRLI ALGEBRA ASOSIDA TAKOMILLASHTIRISH //Research and implementation. – 2023. Xudoynazarov U., Meliquziyev A. OCHIQ KALITLI RSA SHIFRLASH ALGORITMINI PARAMETRLI ALGEBRA ASOSIDA TAKOMILLASHTIRISH //Research and implementation. – 2023.
Мухтаров Ф. Обеспечение более безопасного цифрового будущего, важность образования в области кибербезопасности //Информатика и инженерные технологии. – 2023. – Т. 1. – №. 1. – С. 46-49.
AXBOROT O. Z. R. et al. Kriptografiyaning matematik asoslari. – 2018.
Allanov O. M. et al. ELLIPTIK EGRI CHIZIQLARNING KRIPTOGRAFIYADA QO ‘LLANISHI //Educational Research in Universal Sciences. – 2022. – Т. 1. – №. 7. – С. 22-25.
Тавбоев С., Каршибаев Н. Анализ алгебраических структур, лежащих в основе алгоритмов симметричного шифрования //Информатика и инженерные технологии. – 2023. – Т. 1. – №. 1. – С. 43-46.
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Copyright (c) 2024 Eldorjon Saydullayev, Ilhom Rahmatullayev, Ilxom Boyquziyev, Oybek Umurzakov
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