Development of a software and laboratory complex for studying cryptography on elliptic curves

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Abstract

This article presents a software and laboratory suite for studying the mathematical foundations and practical applications of elliptic curve cryptography (ECC). The suite is implemented in Python using the PyQt6 framework and the sympy library for cryptographic computations. The program provides an interactive interface for entering elliptic curve parameters, visualizing points on the curve, constructing Cayley tables for point addition, and checking group properties. Key features of the suite include the implementation of the Tonelli–Shanks algorithm for finding absolute square roots, the ability to work with curves over finite fields of large order, and a bilingual interface (Russian/English). The developed suite can be used in educational settings to teach the fundamentals of elliptic curve cryptography.

About the authors

Rifat R. Sharipov

Kazan National Research Technical University named after A.N. Tupolev – KAI

Author for correspondence.
Email: riphat@mail.ru
ORCID iD: 0000-0002-4957-8132
SPIN-code: 8116-0738
Scopus Author ID: 57191173824

Cand. Sci. (Eng.), associate professor, Department of Information Security Systems

Russian Federation, Kazan

Askar Z. Khalimov

Kazan National Research Technical University named after A.N. Tupolev – KAI

Email: Khalimov20@yandex.ru
SPIN-code: 7563-8145

Department of Information Protection Systems

Russian Federation, Kazan

Marat Y. Perukhin

Kazan National Research Technological University

Email: perukhin@inbox.ru
SPIN-code: 3199-2966
Scopus Author ID: 52564039400

Cand. Sci. (Eng.), Associate Professor, associate professor, Department of Automated Information Collection and Processing Systems

Russian Federation, Kazan

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