THE APPLICATION OF ISOGENIC ELLIPTIC CURVES AND GRAPHS IN POST-QUANTUM CRYPTOGRAPHY

Abstract

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.