Cryptography using generalized Fibonacci matrices with Affine-Hill cipher

In this article, we have proposed a public key cryptography using Affine-Hill cipher with a generalized Fibonacci matrix(called multinacci matrix). Also proposed a key establishment(exchange of key matrix $K=Q_{\lambda }^k$ of order $\lambda \times \lambda$ for encryption-decryption) scheme with the help of multinacci sequences under prime modulo. In this scheme, instead of exchanging key matrix, we need to exchange the only pair of numbers $(\lambda ,k)$, which reduces the time complexity as well as space complexity and comes with a large key-space.