Group Theoretic Remarks on Cryptographic Systems Based on Two Types of Addition

This paper studies from a group theoretic point of view certain cryptographic systems acting on blocks of n binary digits. The systems in question add to the message block successive blocks of key but the type of addition used alternates between (add mod 2) and + (add mod 2ⁿ). It is proved that the totality of such transformations constitutes a group whose order grows exponentially with n. The order of the group in question is .