A new public key cryptography using M_{q} matrix

We consider a new class of square Fibonacci (q+۱)\times(q+۱)-matrices in public key cryptography. This extends previous cryptography using generalized Fibonacci matrices. For a given integer q, a (q+۱)\times(q+۱) 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.

Keywords:

Cryptography , Hill cipher , key exchange Elgamal , Fibonacci sequence and M_{q}-matrix