MATHEMATICAL FOUNDATIONS OF THE TRANSFER OF THE EL-GAMAL ASYMMETRIC ENCRYPTION ALGORITHM TO ELLIPTIC CURVES
Abstract
Today, the stability of modern asymmetric algorithms, unlike the stability of symmetric ciphers, is based on certain mathematical problems,. In particular, the problems of decomposition of the given number into prime multipliers (factorization) and discrete logarithmization in the finite field are recognized as the bases of mathematical complexity.
References
Alguliyev R.M., Imamverdiyev Ya.N. Research of international and national digital signature standards on elliptic curves // Questions of information protection. Moscow, 2005.-№2 (69) – Pp. 2-7.
Bolotov A.A. and others. Elementary introduction to elliptical cryptography: algebraic and algorithmic basics. Moscow, MEI, 2006.-328 p.
Gorbenko I.D., Balagura D.S. Directional encryption schemes in groups of points on an elliptic curve // Bulletin of Kharkiv National University of Radioelectronics 2002, No. 2.
Eremeev M.A., Maksimov Yu.N. Construction of cryptosystems based on the properties of elliptic curves // Information technology security. 1995. No. 2. - pp.52-55.
Kuryazov D.M. Algorithm for ensuring message confidentiality using elliptic curves // International Journal of Advanced Trends in Computer Science and Engineering (IJATCSE) Volume 9. №1, 2020, India, pp.295-298.
Kuryazov D.M. Optimal asymmetric data encryption algorithm // Global Journal of Computer Science and Technology, volume 21 Issue 2, 2021., pp. 29-33.