On the role of the Fibonacci matrix as key in modified ECC

Abstract

In this paper, we have proposed a modified cryptographic scheme based on the application of recursive matrices as key in ECC and ElGamal. For encryption, we consider mapping analogous to affine Hill cipher in which a plaintext matrix has been constructed by points corresponding to letters on elliptic curves. In the formation of key-space, the generalized Fibonacci matrices have been taken into account, which is the sequence of matrices. The beauty of considering Fibonacci matrices is their construction where we need only two parameters(integers) in place of n 2 elements. The use of a recursive matrix makes a large keyspace for our proposed scheme and increases its efficiency. Thus, it reduces time as well space complexity, and its security & strength is based on EC-DLP which is a hard problem in number theory.

A novel public key cryptography based on generalized Lucas matrices

“…Here the numerical values equivalent to NOBLE2022 is [13,14,01,11,04,28,26,28,28]. Let us consider the alphabets Σ = Z 37 defined as for letters from A-Z equivalent to 00-25, digits 0-9 are that to 26-35 and 36 for blank/white space.…”

“…Nowadays a lot of research work is going on in the direction of generalizing the existing sequences for higher order as well as generalizing for arbitrary initial values. While some of the authors made generalizations by considering the same relation but with different multipliers(constant/arbitrary functions as coefficients), some of such recent developments and their applications may be seen in [2,7,10,11,21].…”

Cryptography utilizing the Affine-Hill cipher and Extended Generalized Fibonacci matrices

“…There is now a lot of study being done on the generalization of existing sequences for higher order as well as a generalization for arbitrary beginning values. While some authors produced extensions by examining the same connection but with other multipliers(constant/arbitrary functions as coefficients), some of these more recent advances and their applications may be found in [8,9,19].…”