Матричний шифр Гілла: математична модель та реалізація в с++

Abstract

The report focuses on the software implementation of the symmetric Hill cipher algorithm in C++ using a 3 X 3 key matrix. The work provides a detailed analysis of the mathematical apparatus of the method, specifically linear algebra operations (matrix multiplication, determinant calculation, and adjugate matrix construction) and their adaptation for the residue ring Z26. Special attention is paid to solving the key invertibility problem by implementing an algorithm to check the determinant for coprimality with the modulus 26, ensuring the correctness of data encryption and decryption processes.