The Perrin R-matrix and more properties with an application

Abstract

In this note, we propose the Perrin R-matrix, study some properties of the Perrin sequences of numbers and derive some identities involving them such as the sum of special terms and extended relations of Perrin and Padovan numbers. Finally we give a model of cryptography based on the Padovan Q-matrix and Perrin R-matrix. This method uses a different encryption and decryption keys of the message matrix which will increase the security of the methods.

Subject Classification:

• 11C20
• 11B50
• 68P30

Keywords:

• Padovan sequence
• Padovan Q-matrix
• Perrin sequence
• Perrin R-matrix