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.
Keywords:elliptic curve cryptography, ECC, group operator, Cayley table, Tonelli–Shanks algorithm, software implementation, software laboratory complex, information security.
