Chains of time-dependent 3D matrices and applications to encryption systems

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.

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