Vectrix: A Proposed Mathematical Structure and Its Application in Cryptography

This paper studies the security of the Hill cipher through its key space and the entropy of the keys, the analysis was extended to a proposed structure called Vectrix (plural, Vectrices). The key space of the existing cipher is defined by the space of non-singular matrices, and for the proposed algorithm it is define by the space of non-sigular Vectrices. In each case, Shannon entropy was used to measure the associated uncertainty. The results show that, the entropy associated with Vectrix key is triple of the entropy of the traditional Hill Cipher key and the key space is cubic power of the key space of the respective Matrix key space.