ELLIPTIK EGRI CHIZIQQA ASOSLANGAN KRIPTOTIZIMLAR

Authors

  • Yusupova S.M., AmonovA.H., Abdullayev I.K., Avazbekov M.A Toshkent axborot texnologiyalari unversiteti abdujabbor.madina.1989@gmail.com

Keywords:

Elliptik egri chiziq, diskerminant, elliptik egri chiziqqa o’tkazilgan urinma, elliptik egri chiziqni kesib o’tuvchi to’g’ri chiziq.

Abstract

Elliptik egri chiziqqa asoslangan Kriptotizimlar ochiq kalitli kriptografiya tizimlari kabi ikkita alohida kalitni birlashtirish uchun matematik jarayondan foydalanadi va keyin ma’lumotlarni shifrlash va shifrini ochish uchun maxfiy kalitdan foydalanadi. Ulardan biri har kimga ma’lum bo’lgan ochiq kalit, ikkinchisi esa faqat ma’lumotni jo’natuvchi va qabul qiluvchiga ma’lum bo’lgan shaxsiy kalitdir.

References

KRIPTOGRAFIYANING MATEMATIK ASOSLARI О’quv qо’llanma D.Y.Akbarov, P.F.Xasanov, X.P.Xasanov, O.P.Axmedova, I.U.Xolimtayeva Toshkent 2018.

Silverman, Joseph H. The arithmetic of elliptic curves. Graduate Texts in Mathematics, 106. Springer-Verlag, New York, 1986. [The number theory of elliptic curves at a level suitable for advanced graduate students.]

Silverman, J.: Advanced Topics in the Arithmetic of Elliptic Curves, Graduate Texts in Mathematics, 155, Springer-Verlag, 1994.

Miller, Victor. Use of elliptic curves in cryptography. Advances in cryptology CRYPTO ‘85 (Santa Barbara, CA, 1985), 417–426, Lecture Notes in Comput. Sci., 218, Springer, Berlin, 1986. [One of the original articles proposing the use of elliptic curves for crypto. The other is by Neal Koblitz.]

Koblitz, Neal. Elliptic curve cryptosystems. Mathematics of Computation 48 (1987), 203-209. [One of the original articles that proposed the use of elliptic curves for cryptography. The other is by Victor Miller.]

https://lib.fbtuit.uz/assets/files/4.-AkbarovD.YXasanovP.FXasanovX.PAxmedovaO.PXolimtayevaI.U.Kriptografiyaningmatematikasoslari.pdf

https://www.ssldragon.com/blog/what-is-openssl/#:~:text=OpenSSL%20is%20an%20all%2Daround,generation%2C%20and%20SSL%20certificate%20installation.

Internet sayti https://mathworld.wolfram.com/EllipticCurve.html

Internet sayti

https://people.math.rochester.edu/faculty/doug/otherpapers/Husemoller.pdf

Internet sayti:

https://www.math.brown.edu/johsilve/Presentations/WyomingEllipticCurve.pdf

https://www.keyfactor.com/blog/elliptic-curve-cryptography-what-is-it-how-does-it-work/

https://xenovation.com/blog/security/pki/creating-elliptic-curve-ecdh-key-with-openssl

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Published

2023-06-01