Conventional HILL Algorithm: From Classical Cryptography to Modern Cryptography

Abstract

With the development of modern computer tools using standard character encoding which assigns each graphic character a number, in particular the written characters of human language, HILL’s cipher, which, in its conventional version, uses the alphabet of 26 letters reaches its limits. It has also been demonstrated that the algorithm is fallible at a frequency analysis attack but also to a known plaintext attack.

For this purpose, in order to adapt the HILL’s cipher to modern communication systems and to strengthen its cryptographical security, we are proposing in this article an improvement of the algorithm. The study will mainly focused on an expansion of the alphabet and the secret key. Thus, the standard character-encoding (example of the ASCII code) will be used instead of a 26-letter alphabet and the secret key extended to three parameters with the additional use of two randomly chosen numbers  from the set real numbers .