ELLIPTIK EGRI CHIZIQLAR KRIPTOGRAFIYASIDA DISKRET LOGARIFM MUAMMOSI VA UNI TADQIQ QILISH
Ключевые слова:
Kalit so‘zlar: kriptografiya, DLP(dikret logarifm muammosi), algoritm, Shanks (Baby-Step Giant-Step), Pollard’s Rho, MOV, index hisoblash, protokol, egri chiziq nuqtasi, shifrlash, xavfsizlik, raqamli imzoАннотация
Annotatsiya. Diskret logarifm muammosi ko'plab kriptografik tizimlarning asosini tashkil qiladi.Ushbu maqolada elliptik egri chiziqlar kriptografiyasida DLP va uni samarali hal qilishning bir nechta usullari tadqiq qilinib yoritib berilgan.Shu bilan birga tahliliy natijalar va xulosa keltirilgan.
Библиографические ссылки
1. Koblitz N. (1987). Elliptic Curve Cryptosystems. Mathematics of Computation, 48(177), 203–209.
2. Miller V. S. (1985). Use of Elliptic Curves in Cryptography. In Advances in Cryptology — CRYPTO ’85 (pp. 417–426).
3. Silverman J. H. (2009). The Arithmetic of Elliptic Curves (2nd ed.). Springer.
4. Hankerson D., Menezes A., & Vanstone S. (2004). Guide to Elliptic Curve Cryptography.
5. Pollard J. M. (1978). Monte Carlo Methods for Index Computation (mod p). Mathematics of Computation, 32(143), 918–924.
6. Shanks D. (1971). Class number, a theory of factorization and genera. Proceedings of Symposia in Pure Mathematics, 20, 415–440.
7. Menezes A., Okamoto T., & Vanstone S. A. (1993). Reducing Elliptic Curve Logarithms to Logarithms in a Finite Field. IEEE Transactions on Information Theory, 39(5), 1639–1646.
8. Washington L. C. (2008). Elliptic Curves: Number Theory and Cryptography (2nd ed.). Chapman and Hall/CRC.
9. Bernstein D. J., Lange T. (2007). Faster Addition and Doubling on Elliptic Curves. In Advances in Cryptology — ASIACRYPT 2007, Springer.
10. Galbraith S. D. (2012). Mathematics of Public Key Cryptography. Cambridge University Press.
11. Henri Cohen. A Course in Computational Algebraic Number Theory
12. Crandall & Pomerance. Prime Numbers: A Computational Perspective
13. Шеннон К. Теория и связи в секретных системах. Работы по теории информации и кибернетике. – М.: Иностранная лит. 1963. – 243 б.
14. Washington L. C. (2008). Elliptic Curves: Number Theory and Cryptography.
15. Menezes A. J., Vanstone, S. A., & Oorschot, P. C. (1996). Handbook of Applied Cryptography.
