On the security of digital signature protocol based on iterated function systems.

A common goal of cryptographic research is to design protocols that provide a confidential and authenticated transmission channel for messages over an insecure network. Hash functions are used within digital signature schemes to provide data integrity for cryptographic applications. In this paper, we take a closer look at the security and efficiency of the digital signature protocol based on fractal maps. This new system can be expected to have at least the same computational security against some known attacks. A Diffie-Hellman algorithm is used to improve the security of the proposed protocol by generating the number of iteration that is used to find the attractor of the iterated function system, which is used to calculate the public key and the signature. The proposed algorithm possesses sufficient security against some known attacks applicable on finite field cryptosystems. They are considered as time consuming to be involved in solving non-linear systems numerically over the defined infinite subfield

Fractal attractor based digital signature

Fractal theories are applied to enhance the efficiency and performance of cryptosystem due to their inherent complexity and mathematical framework. A new digital signature scheme based on Iterated Function System (IFS) is proposed, which can reduce computation cost and increase security of the system. The properties of the proposed system are discussed in detail

About fuzzy fixed point theorem in the generalized fuzzy fractal space.

The Banach fixed point theorem has applications in several branches of science. Many authors prove this theorem in different types of fuzzy metric spaces and fuzzy fractal spaces. The aim of this paper is to prove the Banach fixed point theorem in a new generalized space called multi fuzzy fractal space

Efficiency analysis for public key systems based on fractal functions.

In the last decade, dynamical systems were utilized to develop cryptosystems, which ushered the era of continuous value cryptography that transformed the practical region from finite field to real numbers. Approach: Taking the security threats and privacy issues into consideration, fractals functions were incorporated into public-key cryptosystem due to their complicated mathematical structure and deterministic nature that meet the cryptographic requirements. In this study we propose a new public key cryptosystem based on Iterated Function Systems (IFS). Results: In the proposed protocol, the attractor of the IFS is used to obtain public key from private one, which is then used with the attractor again to encrypt and decrypt the messages. By exchanging the generated public keys using one of the well known key exchange protocols, both parties can calculate a unique shared key. This is used as a number of iteration to generate the fractal attractor and mask the Hutchinson operator, so that, the known attacks will not work anymore. The algorithm is implemented and compared to the classical one, to verify its efficiency and security. We conclude that public key systems based on IFS transformation perform more efficiently than RSA cryptosystems in terms of key size and key space

Generalized π-Armendariz Authentication Cryptosystem

Algebra is one of the important fields of mathematics. It concerns with the study and manipulation of mathematical symbols. It also concerns with the study of abstractions such as groups, rings, and fields. Due to the development of these abstractions, it is extended to consider other structures, such as vectors, matrices, and polynomials, which are non-numerical objects. Computer algebra is the implementation of algebraic methods as algorithms and computer programs. Recently, many algebraic cryptosystem protocols are based on non-commutative algebraic structures, such as authentication, key exchange, and encryption-decryption processes are adopted. Cryptography is the science that aimed at sending the information through public channels in such a way that only an authorized recipient can read it. Ring theory is the most attractive category of algebra in the area of cryptography. In this paper, we employ the algebraic structure called skew -Armendariz rings to design a neoteric algorithm for zero knowledge proof. The proposed protocol is established and illustrated through numerical example, and its soundness and completeness are proved

Discrete Dynamic Model of a Disease-Causing Organism Caused by 2D-Quantum Tsallis Entropy

Many aspects of the asymmetric organ system are controlled by the symmetry model (R&L) of the disease-causing organism pathway, but sensitive matters like somites and limb buds need to be shielded from its influence. Because symmetric and asymmetric structures develop from similar or nearby matters and utilize many of the same signaling pathways, attaining symmetry is made more difficult. On this note, we aim to generalize some important measurements in view of the 2D-quantum calculus (q-calculus, q-analogues or q-disease), including the dimensional of fractals and Tsallis entropy (2D-quantum Tsallis entropy (2D-QTE)). The process is based on producing a generalization of the maximum value of the Tsallis entropy in view of the quantum calculus. Then by considering the maximum 2D-QTE, we design a discrete system. As an application, by using the 2D-QTE, we depict a discrete dynamic system that is afflicted with a disease-causing organism (DCO). We look at the system’s positive and maximum solutions. Studies are done on equilibrium and stability. We will also develop a novel design for the fundamental reproductive ratio based on the 2D-QTE

Dynamics and Complexity of a New 4D Chaotic Laser System

Derived from Lorenz-Haken equations, this paper presents a new 4D chaotic laser system with three equilibria and only two quadratic nonlinearities. Dynamics analysis, including stability of symmetric equilibria and the existence of coexisting multiple Hopf bifurcations on these equilibria, are investigated, and the complex coexisting behaviors of two and three attractors of stable point and chaotic are numerically revealed. Moreover, a conducted research on the complexity of the laser system reveals that the complexity of the system time series can locate and determine the parameters and initial values that show coexisting attractors. To investigate how much a chaotic system with multistability behavior is suitable for cryptographic applications, we generate a pseudo-random number generator (PRNG) based on the complexity results of the laser system. The randomness test results show that the generated PRNG from the multistability regions fail to pass most of the statistical tests

A New Megastable Chaotic Oscillator with Blinking Oscillation terms

Recently, megastable systems have grabbed many researchers’ interests in the area of nonlinear dynamics and chaotic systems. In this paper, the oscillatory terms’ coefficients of the simplest megastable oscillator are forced to blink in time. The forced system can generate an infinitive number of hidden attractors without changing parameters. The behavior of these hidden attractors can be chaotic, tori, and limit cycle. The attractors’ topology of the system seems unique and looks like picture frames. Besides, the existence of different coexisting attractors with different kinds of behaviors reflects the system's high sensitivity. Using the sample entropy algorithm, the system’s complexity for different initial values is assessed. In addition, the circuit of the introduced forced system is designed, and the possibility of implicating the system with analog elements is investigated

An improved information rate of perfect secret sharing scheme based on dominating set of vertices

Due to the fast development in data communication systems and computer networks in recent years, the necessity to protect the secret data is of great demands. Several methods have been arisen to protect the secret data; one of them is the secret sharing scheme. It is a method of distributing a secret K among a finite set of participants, in such a way that only predefined subset of participant is enabled to reconstruct a secret from their shares. A secret sharing scheme realizing uniform access structure described by a graph has received a considerable attention, where each vertex represents a participant and each edge represents a minimum authorized subset. In this paper, an independent dominating set of vertices in a graph $G$ is introduced and applied as a novel idea to construct a secret sharing scheme such that the vertices of the graph represents the participants and the dominating set of vertices in $G$ represents the minimal authorized set. This new scheme is based on principle of non-adjacent vertices, whereas, most of the previous works are based on the principle of adjacent vertices. We prove that the scheme is perfect, and the lower bound of the information rate for this new construction is improved as compared to some well-known previous constructions

Image Encryption Based on Local Fractional Derivative Complex Logistic Map

Local fractional calculus (fractal calculus) plays a crucial role in applications, especially in computer sciences and engineering. One of these applications appears in the theory of chaos. Therefore, this paper studies the dynamics of a fractal complex logistic map and then employs this map to generate chaotic sequences for a new symmetric image encryption algorithm. Firstly, we derive the fractional complex logistic map and investigate its dynamics by determining its equilibria, geometric properties, and chaotic behavior. Secondly, the fractional chaotic sequences of the proposed map are employed to scramble and alter image pixels to increase resistance to decryption attacks. The output findings indicate that the proposed algorithm based on fractional complex logistic maps could effectively encrypt various kinds of images. Furthermore, it has better security performance than several existing algorithms