Cryptography utilizing the Affine-Hill cipher and Extended Generalized Fibonacci matrices

We are aware that a major cryptosystem element plays a crucial part in maintainingthe security and robustness of cryptography. Various researchers are focusing on creatingnew forms of cryptography and improving those that already exist using the principles ofnumber theory and linear algebra. In this article, we have proposed a Extended generalizedFibonacci matrix (recursive matrix of higher order) having relation with Extended generalizedFibonacci sequences and established some properties in addition to that usual matrix algebra.Further, we proposed a modified public key cryptography using these matrices as keys inAffine-Hill Cipher and key agreement for encryption-decryption with the combination ofterms of Extended generalized Fibonacci sequences under prime modulo. This system hasa large key space and reduce the time complexity as well as space complexity of the keytransmission by only requiring the exchange of pair of numbers(parameters) as opposed tothe entire key matrix