"The aim of this paper is to provide a characterization diagram for a family of B\'{e}zier flexible interpolation curves as well as to present an application of our results in cryptography. In our interpolation scheme, two parameters, $t_1,\ t_2\in (0,1)$ determine the position of the interpolation points on the B\'{e}zier curve. Consequently we obtain a family of B\'{e}zier interpolation curves depending on two parameters. Altering the values of the parameters we modify the intermediary control points and implicitly the shape of the interpolation curve. In order to control the shape of the interpolation curves from this family, we provide a partition of the domain $T=(0,1)\times (0,1)$ where the parameters lie according to the geometric characterization of these curves: with zero, one or two inflexion points; with loop; with cusp and degenerated in quadratic curves. The characterization diagram can be used as a tool for the choice of parameters, with possible applications in different fields. We present one of its application in cryptography, for finding certain subspaces over which particular elliptic sub-curves are defined. Computation, implementation and graphics are made using MATLAB."

Characterization of a cubic interpolation scheme dependent on two parameters and applications

This work presents the employment of graph theory for cryptographic applications. A Cartesian product graph (CPG) is used to propose new symmetric encryption schemes. On proposed encryption schemes, the ciphertexts of the plaintexts are sent to the receiver entity as the CPGs. The CPG is created based on two graphs G and H that are generated depending on the random choices of the plaintext bits. These bits are used as vertices of graphs G and H. The purpose of using the CPG is to increase the security level of the symmetric encryption schemes in comparison with other encryption schemes. Two study cases of the proposed symmetric Cartesian product graphic encryption (SCPGE) schemes are presented as new experimental results. The security issues of the proposed SCPGE schemes are determined. The SCPGE schemes consider as new insights for more secure communications. 

The Cartesian product graph for encryption schemes

A coloring bipartite graph (CBG) is a main point in this work for creating new version of the symmetric encryption (SE) scheme. The security of this version has been increased comparing with other ES schemes, since a shared secret key is generated based on the CBG. The ciphertext of a plaintext reaches to receiver as the CBG. A new experimental result of CBG-SE scheme is presented through study case. The security issue of the CBG-SE scheme is determined. The CBG-SE scheme considers as an alternative insight for symmetric communications with more security.

New Version of Symmetric Encryption Scheme Using the Coloring Bipartite Graph

The intersection of cryptography and number theory has been encapsulated by studying the graph theory. The graphs have an important role in building the cryptographic schemes. In this work, a new contribution has been proposed by using the Mersenne numbers. These numbers are used to define new weighted graphs which named by Mersenne weight graphs (MWG). An efficient symmetric encryption (SE) scheme using MWG has been formed. The implementation results of a proposed algorithm are presented in this study. The security analysis of the proposed MWG-SE algorithm is discussed as well. 

Mersenne Weighted Graph for Increasing the Symmetric Encryption Schemes Security

Mathematical models based on elliptic curves have been intensively studied since their applicability in data security systems was discovered. In this article, the authors describe the optimal way to select particular subspaces over which elliptic curves are defined, showing the applicability of these subspaces in secure data transfer. Access to large databases and analyses of the requests made to these databases are required daily by a variety of users, including legal entities. An attack on these communication systems causes violations in privacy and damage to/theft of data that can be worth EUR tens of billions annually. For requests made between computers, encryption methods can be used as these systems have adequate computing power and energy. For requests made from fixed and mobile systems, if the data are distributed heterogeneously, the computing power required to authenticate both the users and the answering entities determines the efficiency of the proposed solution. To address this limitation, our study proposes a double-authentication method based on particular elliptic-curve systems.

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Optimal Elliptic-Curve Subspaces for Applications in Double-Authenticated Requests in Mobile Distributed Data Mining

Undirected Complete Graph to Design New Public Key Cryptosystem

In this work, a new graph has been defined as a main point to design a new version of an asymmetric encryption scheme. This graph is formed based on the scalar multiplication operation on elliptic ...

Karrar Taher R. Aljamaly

Papers

Undirected Complete Graph to Design New Public Key Cryptosystem

The elliptic scalar multiplication graph and its application in elliptic curve cryptography

The KR-Elliptic Curve Public Key Cryptosystem