%A Maleszewski, Wiesław
%D 2019
%T THE APPLICATION OF ISOGENIC ELLIPTIC CURVES AND GRAPHS IN POST-QUANTUM CRYPTOGRAPHY
%K
%X The article presents the properties of elliptic curves and the laws of arithmetic in their structures forming an additive group characterized by relatively low computational costs of performing group operations. The concept of isogens is introduced, the structure of a quotient grid in the body of complex numbers is defined and the properties of group activities in these structures are enumerated. Next, reference was made to the methods of exchanging cryptographic keys based on graph structures. In the next part, the Supersingular Isogeny Key Exchange is introduced, and a comparison of three versions of the Diffie-Hellman key phrase protocol is made – classical, based on elliptic curves and based on isogeny. Finally, research problems were presented in the area where any minimal progress would bring a greater guarantee of secure communication – both now and in the future when quantum computers will be available.
%U http://pjas.pwsip.edu.pl/index.php/pjas/article/view/122
%J Polish Journal of Applied Sciences
%0 Journal Article
%R 10.34668/PJAS.2018.4.3.03
%P 96-101%V 4
%N 3
%@ 2451-1544
%8 2019-08-21