A survey of Latin squares, orthogonal arrays and their applications to cryptography


Latin squares and orthogonal arrays are two of the most studied objects in combinatorial designs theory. Indeed, the study of Latin squares even precedes the development of designs theory during the 20th century, dating back at least to Euler’s 36 officers problem. In this talk, we will survey some basic properties and facts about Latin squares and orthogonal arrays, emphasizing their connection to cryptographic primitives such as perfect authentication codes and secret sharing schemes. We will additionally introduce a new construction of orthogonal Latin squares based on cellular automata.

Room U5-3014, Dipartimento di Matematica e Applicazioni, University of Milano-Bicocca, Italy