Counter Mode of the Shannon Block Cipher Based on MPF Defined over a Non-Commuting Group

Abstract

In this paper, we present a counter mode of a Shannon block cipher based on the matrix power function. We make use of the matrix power function to define a single round symmetric cipher. Continuing our previous research, we implement a non-commuting group the order of which is a power of two in order to define a CTR mode in its most classic interpretation. We explore the security of the newly defined scheme, first, by showing that our block cipher is perfectly secure and does not leak any information about the initial plaintext based on the ciphertext. Then, we define a sequence of security games that show how the CTR mode of our cipher can resist all passive attacks.