Gerardo Rodríguez Sánchez

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 CA Model for Mobile Malware Spreading Based on Bluetooth Connections

There is an unstoppable rise of the number of smartphones worldwide and, as several applications requires an Internet access, these mobile devices are exposed to the malicious effects of malware. Of particular interest is the malware which is propagated using bluetooth connections since it infects devices in its proximity as does biological virus. The main goal of this work is to introduce a new mathematical model to study the spread of a bluetooth mobile malware. Specifically, it is a compartmental model where the mobile devices are classified into four types: susceptibles, carriers, exposed and infectious; its dynamic is governed by means of a couple of two-dimensional cellular automata. Some computer simulations are shown and analyzed in order to determine how a proximity mobile malware might spread under different conditions.

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.

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 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.

Case study: Malware propagation models for undergraduate engineering students

Engineering students learn Mathematics solving real-life problems with the help of mathematical tools and the already acquired competencies and knowledge. Moreover, the use of realistic mathematics education method allows the integration of daily, real and realistic experiences to master Mathematics. The proposed teaching and learning method, is the way to make Mathematics more accessible to engineering students, since they will need to solve mathematical problems in their careers. In particular, everyday we hear news and comments related to the virus propagation in computers and mobile devices. We present in this study the acquisition of mathematical competencies through the use of mathematical models in the specific case of the malware spreading and Internet of Things.

Application to Cybersecurity of the Stability Theory of the Systems of Ordinary Differential Equations

The main goal of this work is to show an application of the stability theory of systems of ordinary differential equations to cybersecurity. Specifically, we will focus our attention on the study of the systems used in the mathematical models to simulate malware spreading on computer networks. Thus, a compartmental SCIRS model for computer worms spreading is proposed and analyzed.

Materials for a course in Calculus on several variables: An example of inter-university collaboration

Universities today offer many courses where the study materials can be obtained online through different mechanisms. The terms e-learning and b-learning are being overshadowed by u-learning (ubiquitous learning), since the learning scenario is any place and any device that can be used to get the materials. The task of preparing the appropriate materials in this new context cannot be addressed individually and, consequently, international collaborative process can be very fruitful. The main goal is to adapt the study materials for using in several Universities, with official recognition for any University involved in the collaborative process and with agreements with other Universities interested in the use of such materials. We will present an ongoing experience which involves the National Technological University (UTN) in Buenos Aires, Argentina, and Spanish universities: Salamanca University (USAL) and Pontificia Comillas University (UPCOMILLAS) in Madrid. The authors of this paper have updated a virtual Multivariable Calculus course, hosted in the virtual learning environment STUDIUM to be used by the students from the three universities.

A Secret Sharing Scheme for Digital Images Based on Cellular Automata and Boolean Functions

In this paper an efficient probabilistic secret sharing scheme for black and white digital images is introduced. It is an extension of the algorithm proposed originally in [11]. Specifically, it is a (m , n )-threshold scheme. It is based on the use of a simple matrix boolean function which involves the Hadamard matrix product modulo 2, and the addition modulo 2 and m . Moreover, an algorithm based on cellular automata is used for the enhancement of the recovered image. The algorithm introduced is shown to be secure and its expansion factor is equal to 1.