Ángel Martín del Rey

Mathematical modeling of the propagation of malware: a review

In the present work, we offer a critical review of the mathematical models that have been proposed to date to simulate malware propagation in a network of computers or mobile devices. We analyze the models proposed determining the deficits and possible alternatives for improving them. Copyright

A new secret sharing scheme for images based on additive 2-dimensional cellular automata

A new secret color image sharing scheme based on two-dimensional memory cellular automata, is proposed. Such protocol is of a (n,n)-threshold scheme where the secret image to be shared is considered as one of the initial configurations of the cellular automata. The original idea is to study how a reversible model of computation permits to compute the shares and then using the reverse computation in order to recover the original image. The scheme is proved to be perfect and ideal, and resistant to the most important attacks such as statistical attacks.

Graphic cryptography with pseudorandom bit generators and cellular automata

In this paper we propose a new graphic symmetrical cryptosystem in order to encrypt a colored image defined by pixels and by any number of colors. This cryptosystem is based on a reversible bidimensional cellular automaton and uses a pseudorandom bit generator. As the key of the cryptosystem is the seed of the pseudorandom bit generator, the latter has to be cryptographically secure. Moreover, the recovered image from the ciphered image has not loss of resolution and the ratio between the ciphered image and the original one, i.e., the factor expansion of the cryptosystem, is 1.

A Computer Virus Spread Model Based on Cellular Automata on Graphs

In this paper a new mathematical model to simulate the computer virus spreading on a network is introduced. It based on cellular automata on graphs. Specifically the model proposed is a SEIS model where each node/computer of the network can be in one of three states: susceptible, exposed and infected.

A SCIRS Model for Malware Propagation in Wireless Networks

The main goal of this work is to propose a novel mathematical model to simulate malware spreading in wireless networks considering carrier devices (those devices that malware has reached but it is not able to carry out its malicious purposes for some reasons: incompatibility of the host’s operative system with the operative system targeted by the malware, etc.) Specifically, it is a SCIRS model (Susceptible-Carrier-Infectious-Recovered-Susceptible) where reinfection and vaccination are considered. The dynamic of this model is studied determining the stability of the steady states and the basic reproductive number. The most important control strategies are determined taking into account the explicit expression of the basic reproductive number.

Message Authentication Protocol Based on Cellular Automata

The main goal of this work is to study the design of message authentication protocols by using cellular automata. Specifically, memory cellular automata with linear transition functions are considered. It is shown that the proposed protocol is secure against different cryptanalytic attacks.

How Engineers Deal with Mathematics Solving Differential Equation

Abstract Numerical methods are tools for approximating solutions to problems that may have complicated developments or cannot be solved analytically. In engineering courses, students must address problems related other disciplines such as structural or rock mechanics, biology, chemistry or physics. Prior to solving these problems it is important to define and adopt a rational framework. The students of fourth course out of five, of the bachelors degree in Computer Sciences or Industrial Engineering at the University of Salamanca (Spain), they learn mathematics solving real problems with the help of the already acquired interdisciplinary knowledge. We have proposed the students a term project that summarizes some of the knowledge and competences acquired during the lessons. We will describe in this study the software and specific applications that will be use during the whole course.

A SIR e-Epidemic Model for Computer Worms Based on Cellular Automata

In this work a mathematical model to simulate malware spreading is proposed. Specifically, it is an individual-based model whose dynamic is governed by means of a particular type of finite state machine called cellular automaton. Moreover, it is a SIR compartmental model, i.e. the population of hosts is divided into three classes: susceptible computers, infected computers and recovered computers, and the evolution between these states is ruled according to specific local transition functions involving boolean expressions. Several computer simulations are performed using different initial conditions.

A graph cellular automata model to study the spreading of an infectious disease

A mathematical model based on cellular automata on graphs to simulate a general epidemic spreading is presented in this paper. Specifically, it is a SIR-type model where the population is divided into susceptible, infected and recovered individuals.

On the Security of "Golden" Cryptography

In this paper the security of ”golden” cryptography, which has been proposed recently, is tackled. Specifically, it is shown that the security of such cryptosystem is trivially compromised as it does not pass one of the basic cryptanalytic attacks: the chosen plaintext attack.