APPLICATION OF A CERTAIN CLASS OF INFINITE MATRICES TO THE HILL CRYPTOGRAPHIC SYSTEM

Abstract

In this paper, a class of infinite matrices called “R.D.” class is introduced. Each member of this class is an infinite matrix K (over Z/29) which admits the existence of an infinite number of matrices ${\overline {\rm K}}_{\rm i} (i=1,2,3,…) satisfying {\overline {\rm K}}_{\rm i}{\rm K}={\rm I} (\neq {\rm K}{\overline {\rm K}}_{\rm i}), where each ${\overline {\rm K}}_{\rm i} is over Z/29. If P is a plaintext matrix, over Z/29 and P is embedded into an infinite matrix in a way described in this paper, then enciphering (using ${\overline {\rm K}}_{\rm i} for any i) and deciphering (using K) can be carried on in a way similar to that in the Hill system ([2],[3]). Security and freedom are thus increased at no cost since the deciphering algorithm uses the same K while the enciphering algorithm can use any of the ${\overline {\rm K}}_{\rm i} (i=1,2,3,…). To increase security (and other objectives) the entries of each member of this class are required to be functions of several parameters λ μ,,…. Moreover, som...