Generation of Invertible High Order Matrix Keys for the Hill Cipher

Abstract

Developers are often limited to the use of low order matrix keys when the Hill cipher is embraced. This is due to the complexity of determining matrix inverses when high order matrices are involved. Matrix inverses are required during decryption. This paper proposes an approach for generating invertible high order matrix keys for the Hill cipher. The Hill cipher uses a matrix key of order n x n for encryption, and its inverse is required for decryption. Increasing the order of the matrices used as keys in the Hill cipher undoubtedly strengthen the Hill encryption algorithm. When we increase the order of the matrices, the Hill cipher is more complex to decode as it would be hard to find the inverse matrices, hence hard to break. The proposed approach generates invertible high order matrix keys sequentially within a chosen order. However, the choice of an order is flexible. The actual key to be used is dynamically selected from a pool of candidate matrix keys. Our system for generating high order matrix keys was repeatedly run for several times, generating invertible high order matrices that are successfully pooled. The system also successfully randomly selected one matrix key from the pool. This approach eliminates repeated use of the same matrix key over and over. It strengthens the Hill cipher algorithm by complicating obvious brute force attacks. The algorithm's performances are anticipated to outclass those of the original Hill model.