A novel public key cryptography based on generalized Lucas matrices
This work addresses efficiency issues in cryptography for secure communication, but it appears incremental as it builds on existing Affine cipher and matrix-based methods.
The authors tackled the problem of reducing time and space complexity in public key cryptography by proposing a modified scheme using generalized Lucas matrices as keys in an Affine cipher and key agreement, resulting in a method that only requires exchanging a pair of numbers instead of whole key matrices and offers a large key-space.
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.