PRACTICAL APPLICATION AND VULNERABILITIES OF HILL CIPHER IN A MODERN CONTEXT

Abstract

The article examines the Hill cipher as a classical example of applying linear algebra and modular arithmetic in cryptography. It elucidates the mathematical foundations of the algorithm, including the formation of the key matrix over finite fields, the conditions for its invertibility, and the implementation of encryption as the multiplication of plaintext vectors by the key matrix. This approach is presented as a distinctive “bridge between theory and practice,” combining formal mathematical constructions with practical data protection mechanisms. Particular attention is given to the vulnerabilities of the Hill cipher. It is shown that the algorithm is insecure in modern contexts due to the linearity of its transformations and the absence of nonlinear components. Examples of cryptanalytic attacks are provided, demonstrating that the cipher can be “broken apart” even with a minimal number of plaintext-ciphertext pairs. This makes it evident that, in the context of 21st-century cybersecurity, the Hill cipher is merely a “shadow of its era” and cannot serve as a fully reliable tool for data protection. At the same time, the educational and methodological value of the cipher is emphasized. It allows one to “see the mechanism from the inside,” clearly illustrating the transition from monoalphabetic ciphers to block transformations. The article highlights that the Hill cipher played the role of a “first step” in the development of structures that later evolved into DES and AES, where the use of block structures and matrix operations became a fundamental element of modern cryptography.