Vector Boolean Functions: Applications in Symmetric Cryptography

Esta tesis establece los fundamentos teóricos y diseña una colección abierta de clases C++ denominada VBF (Vector Boolean Functions) para analizar funciones booleanas vectoriales (funciones que asocian un vector booleano a otro vector booleano) desde una perspectiva criptográfica. Esta nueva implementación emplea la librería NTL de Victor Shoup, incorporando nuevos módulos que complementan a las funciones de NTL, adecuándolas para el análisis criptográfico. La clase fundamental que representa una función booleana vectorial se puede inicializar de manera muy flexible mediante diferentes estructuras de datas tales como la Tabla de verdad, la Representación de traza y la Forma algebraica normal entre otras. De esta manera VBF permite evaluar los criterios criptográficos más relevantes de los algoritmos de cifra en bloque y de stream, así como funciones hash: por ejemplo, proporciona la no-linealidad, la distancia lineal, el grado algebraico, las estructuras lineales, la distribución de frecuencias de los valores absolutos del espectro Walsh o del espectro de autocorrelación, entre otros criterios. Adicionalmente, VBF puede llevar a cabo operaciones entre funciones booleanas vectoriales tales como la comprobación de igualdad, la composición, la inversión, la suma, la suma directa, el bricklayering (aplicación paralela de funciones booleanas vectoriales como la empleada en el algoritmo de cifra Rijndael), y la adición de funciones coordenada. La tesis también muestra el empleo de la librería VBF en dos aplicaciones prácticas. Por un lado, se han analizado las características más relevantes de los sistemas de cifra en bloque. Por otro lado, combinando VBF con algoritmos de optimización, se han diseñado funciones booleanas cuyas propiedades criptográficas son las mejores conocidas hasta la fecha. ABSTRACT This thesis develops the theoretical foundations and designs an open collection of C++ classes, called VBF, designed for analyzing vector Boolean functions (functions that map a Boolean vector to another Boolean vector) from a cryptographic perspective. This new implementation uses the NTL library from Victor Shoup, adding new modules which complement the existing ones making VBF better suited for cryptography. The fundamental class representing a vector Boolean function can be initialized in a flexible way via several alternative types of data structures such as Truth Table, Trace Representation, Algebraic Normal Form (ANF) among others. This way, VBF allows the evaluation of the most relevant cryptographic criteria for block and stream ciphers as well as for hash functions: for instance, it provides the nonlinearity, the linearity distance, the algebraic degree, the linear structures, the frequency distribution of the absolute values of the Walsh Spectrum or the Autocorrelation Spectrum, among others. In addition, VBF can perform operations such as equality testing, composition, inversion, sum, direct sum, bricklayering (parallel application of vector Boolean functions as employed in Rijndael cipher), and adding coordinate functions of two vector Boolean functions. This thesis also illustrates the use of VBF in two practical applications. On the one hand, the most relevant properties of the existing block ciphers have been analysed. On the other hand, by combining VBF with optimization algorithms, new Boolean functions have been designed which have the best known cryptographic properties up-to-date.

Cryptographic properties of Boolean functions defining elementary cellular automata

In this work, the algebraic properties of the local transition functions of elementary cellular automata (ECA) were analysed. Specifically, a classification of such cellular automata was done according to their algebraic degree, the balancedness, the resiliency, nonlinearity, the propagation criterion and the existence of non-zero linear structures. It is shown that there is not any ECA satisfying all properties at the same time.

Music and evolutionary computation

This paper presents a brief history of the western music: from its genesis to serialism and the Darmstadt school. Also some mathematical aspects of music are then presented and confronted with music as a form of art. The question is, are these two distinct aspects compatible? Can computers be of real help in automatic composition? The more appealing algorithmic approach is evolutionary computation as it offers creativity potential. Therefore, the Evolutionary Algorithms are then introduced and some results of GAs and GPs application to music generation are analysed.

Combining data mining and evolutionary computation for multi-criteria optimization of earthworks

Earthworks tasks aim at levelling the ground surface at a target construction area and precede any kind of structural construction (e.g., road and railway construction). It is comprised of sequential tasks, such as excavation, transportation, spreading and compaction, and it is strongly based on heavy mechanical equipment and repetitive processes. Under this context, it is essential to optimize the usage of all available resources under two key criteria: the costs and duration of earthwork projects. In this paper, we present an integrated system that uses two artificial intelligence based techniques: data mining and evolutionary multi-objective optimization. The former is used to build data-driven models capable of providing realistic estimates of resource productivity, while the latter is used to optimize resource allocation considering the two main earthwork objectives (duration and cost). Experiments held using real-world data, from a construction site, have shown that the proposed system is competitive when compared with current manual earthwork design.

On some geometry and equivalence classes of normal form games

Equivalence classes of normal form games are defined using the geometryof correspondences of standard equilibiurm concepts like correlated, Nash,and robust equilibrium or risk dominance and rationalizability. Resultingequivalence classes are fully characterized and compared across differentequilibrium concepts for 2 x 2 games. It is argued that the procedure canlead to broad and game-theoretically meaningful distinctions of games aswell as to alternative ways of viewing and testing equilibrium concepts.Larger games are also briefly considered.

Wavelength assignment using a hybrid evolutionary computation to reduce cross-phase modulation

In this paper, we propose a hybrid methodology based on Graph-Coloring and Genetic Algorithm (GA) to solve the Wavelength Assignment (WA) problem in optical networks, impaired by physical layer effects. Our proposal was developed for a static scenario where the physical topology and traffic matrix are known a priori. First, we used fixed shortest-path routing to attend demand requests over the physical topology and the graph-coloring algorithm to minimize the number of necessary wavelengths. Then, we applied the genetic algorithm to solve WA. The GA finds the wavelength activation order on the wavelengths grid with the aim of reducing the Cross-Phase Modulation (XPM) effect; the variance due to the XPM was used as a function of fitness to evaluate the feasibility of the selected WA solution. Its performance is compared with the First-Fit algorithm in two different scenarios, and has shown a reduction in blocking probability up to 37.14% when considered both XPM and residual dispersion effects and up to 71.42% when only considered XPM effect. Moreover, it was possible to reduce by 57.14% the number of wavelengths.

Carbon dioxide and climate impulse response functions for the computation of greenhouse gas metrics: a multi-model analysis

The responses of carbon dioxide (CO2) and other climate variables to an emission pulse of CO2 into the atmosphere are often used to compute the Global Warming Potential (GWP) and Global Temperature change Potential (GTP), to characterize the response timescales of Earth System models, and to build reduced-form models. In this carbon cycle-climate model intercomparison project, which spans the full model hierarchy, we quantify responses to emission pulses of different magnitudes injected under different conditions. The CO2 response shows the known rapid decline in the first few decades followed by a millennium-scale tail. For a 100 Gt-C emission pulse added to a constant CO2 concentration of 389 ppm, 25 ± 9% is still found in the atmosphere after 1000 yr; the ocean has absorbed 59 ± 12% and the land the remainder (16 ± 14%). The response in global mean surface air temperature is an increase by 0.20 ± 0.12 °C within the first twenty years; thereafter and until year 1000, temperature decreases only slightly, whereas ocean heat content and sea level continue to rise. Our best estimate for the Absolute Global Warming Potential, given by the time-integrated response in CO2 at year 100 multiplied by its radiative efficiency, is 92.5 × 10−15 yr W m−2 per kg-CO2. This value very likely (5 to 95% confidence) lies within the range of (68 to 117) × 10−15 yr W m−2 per kg-CO2. Estimates for time-integrated response in CO2 published in the IPCC First, Second, and Fourth Assessment and our multi-model best estimate all agree within 15% during the first 100 yr. The integrated CO2 response, normalized by the pulse size, is lower for pre-industrial conditions, compared to present day, and lower for smaller pulses than larger pulses. In contrast, the response in temperature, sea level and ocean heat content is less sensitive to these choices. Although, choices in pulse size, background concentration, and model lead to uncertainties, the most important and subjective choice to determine AGWP of CO2 and GWP is the time horizon.

Design and Optimization of Power Delivery and Distribution Systems Using Evolutionary Computation Techniques

Nowadays computing platforms consist of a very large number of components that require to be supplied with diferent voltage levels and power requirements. Even a very small platform, like a handheld computer, may contain more than twenty diferent loads and voltage regulators. The power delivery designers of these systems are required to provide, in a very short time, the right power architecture that optimizes the performance, meets electrical specifications plus cost and size targets. The appropriate selection of the architecture and converters directly defines the performance of a given solution. Therefore, the designer needs to be able to evaluate a significant number of options in order to know with good certainty whether the selected solutions meet the size, energy eficiency and cost targets. The design dificulties of selecting the right solution arise due to the wide range of power conversion products provided by diferent manufacturers. These products range from discrete components (to build converters) to complete power conversion modules that employ diferent manufacturing technologies. Consequently, in most cases it is not possible to analyze all the alternatives (combinations of power architectures and converters) that can be built. The designer has to select a limited number of converters in order to simplify the analysis. In this thesis, in order to overcome the mentioned dificulties, a new design methodology for power supply systems is proposed. This methodology integrates evolutionary computation techniques in order to make possible analyzing a large number of possibilities. This exhaustive analysis helps the designer to quickly define a set of feasible solutions and select the best trade-off in performance according to each application. The proposed approach consists of two key steps, one for the automatic generation of architectures and other for the optimized selection of components. In this thesis are detailed the implementation of these two steps. The usefulness of the methodology is corroborated by contrasting the results using real problems and experiments designed to test the limits of the algorithms.

A review on probabilistic graphical models in evolutionary computation

Thanks to their inherent properties, probabilistic graphical models are one of the prime candidates for machine learning and decision making tasks especially in uncertain domains. Their capabilities, like representation, inference and learning, if used effectively, can greatly help to build intelligent systems that are able to act accordingly in different problem domains. Evolutionary algorithms is one such discipline that has employed probabilistic graphical models to improve the search for optimal solutions in complex problems. This paper shows how probabilistic graphical models have been used in evolutionary algorithms to improve their performance in solving complex problems. Specifically, we give a survey of probabilistic model building-based evolutionary algorithms, called estimation of distribution algorithms, and compare different methods for probabilistic modeling in these algorithms.

Evolutionary computation of forests with Degree- and Role-Constrained Minimum Spanning Trees

Finding the degree-constrained minimum spanning tree (DCMST) of a graph is a widely studied NP-hard problem. One of its most important applications is network design. Here we deal with a new variant of the DCMST problem, which consists of finding not only the degree- but also the role-constrained minimum spanning tree (DRCMST), i.e., we add constraints to restrict the role of the nodes in the tree to root, intermediate or leaf node. Furthermore, we do not limit the number of root nodes to one, thereby, generally, building a forest of DRCMSTs. The modeling of network design problems can benefit from the possibility of generating more than one tree and determining the role of the nodes in the network. We propose a novel permutation-based representation to encode these forests. In this new representation, one permutation simultaneously encodes all the trees to be built. We simulate a wide variety of DRCMST problems which we optimize using eight different evolutionary computation algorithms encoding individuals of the population using the proposed representation. The algorithms we use are: estimation of distribution algorithm, generational genetic algorithm, steady-state genetic algorithm, covariance matrix adaptation evolution strategy, differential evolution, elitist evolution strategy, non-elitist evolution strategy and particle swarm optimization. The best results are for the estimation of distribution algorithms and both types of genetic algorithms, although the genetic algorithms are significantly faster.

On the realization of Boolean functions using AND and OR elements /

Thesis (M. S.)--University of Illinois at Urbana-Champaign.