  In this article, we have proposed a generalized Lucas matrix (recursive
matrix of higher order) having relation with generalized Fibonacci sequences
and established many special properties in addition to that usual matrix
algebra. Further, we have proposed a modified public key cryptography using
these matrices as keys in Affine cipher and key agreement for
encryption-decryption with the combination of terms of generalized Lucas
sequences under residue operations. In this scheme, instead of exchanging the
whole key matrix, only a pair of numbers(parameters) need to be exchanged,
which reduces the time complexity as well as space complexity of the key
transmission and has a large key-space.
