a new public key cryptography using $m_{q}$ matrix

We consider a new class of square fibonacci $(q+1)times(q+1)$-matrices in public key cryptography. this extends previous cryptography using generalized fibonacci matrices. for a given integer $q$, a $(q+1)times(q+1)$ binary matrix $m_{q}$ is a matrix which nonzero entries are located either on the super diagonal or on the last row of the matrix. in this article, we have proposed a modified public key cryptography using such matrices as key in hill cipher and key agreement for encryption-decryption of terms of $m_{q}$-matrix. in this scheme, instead of exchanging the whole key matrix, only a pair of numbers needed to be exchanged, which reduces the time complexity as well as the space complexity of the transmission and has a large key space.