Undirected Complete Graph to Design New Public Key Cryptosystem
Karrar Taher R. Aljamaly, Ruma Kareem K. Ajeena
Abstract
Abstract In this work, the alternative version of the ElGamal public key cryptosystem (EPKC) first is proposed. The revised EPKC depended on an extended discrete logarithm problem over matrices. More secure communications with the revised EPKC in compare to the original one are obtained. Also, a new public key cryptosystem has been designed based on undirected complete graph (UCG). The plaintext data is selected as a subset from the finite fields which is corresponded to undirected complete graph G ( V , E ), where V and E are finite sets of the vertices and edges respectively. The plaintext is encrypted using the matrix power function (MPF) and the minimum spanning tree (MST) problem of undirected complete graph (UCG). The adjacent matrix representation of MST is used to speed up the calculations. More secure on the proposed cryptosystem has been determined in compare to other asymmetric public key cryptosystems. New computational results of the revised EPKC and the UCG-based public key cryptosystem are discussed.