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 $K=Q_λ^{k}$ of order $λ\timesλ$ 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 $(λ, k)$, which reduces the time complexity as well as space complexity and comes with a large key-space.