Chains of time dependent 3D matrices and Applications to Cryptography

Abstract

 This paper deals with chains of time-dependent 3D matrices and their applications. We introduce the 3D rotation-chain 2×2×2 and describe the properties of each 3D matrix in this chain after identifying it with the non-associative algebra that it defines. To this end, we characterize when the algebra associated with a 3D matrix of dimension 2×2×2  is associative, commutative, has a unit (or a one-sided unit), or is a division algebra, respectively. Based on the properties of the 3D rotation-chain 2×2×2 we develop algorithms for encryption and decryption  processes.