Algorithm for the fast generation of Latin squares

Abstract

We introduce an algorithm for the fast generation of Latin squares. Considering Latin squares with n rows and columns, we introduce a map which maps one square to another one of opposite parity. This map is not unique and it is determined by two indices, i.e. two single numbers. These numbers can be used as secret key in cryptographic schemes which are build up on Latin squares. Thus the introduced algorithm can be applied in cryptography. Additionally, we give a theoretical upper bound for the number of Latin squares of order n.