Abstract:

Key exchanging scheme of Diffie-Hellman type (KES-DH) is a fundamental tool which can be employed for encryption algorithms. In this paper, we propose an alternative model of KES-DH as another contribution using the integer Fibonacci matrix of size 2x2 (IFM_{2x2}) which is inspired by Ajeena in \cite{Ajeena3}. In the proposed KES-DH, namely IFM_{2x2}-KES-DH, the private keys are converted into IFMs_{2x2} through the random selections of the Fibonacci numbers over a prime field F_p. The left (right) side power IFMs_{2x2} is computed (LPIFM_{2x2}(RPIFM_{2x2})). The public keys are computed using these matrices. The IFM_{2x2}-KES-DH is proved mathematically based on LPIFM_{2x2} and RPIFM_{2x2}. Users shared secret key (SSK) is calculated. The security issue is determined based on the computations of LPIFM_{2x2} and RPIFM_{2x2} simultaneously. The proposed model is useful in cryptographic applications.