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Networked computers are ubiquitous, and are subject to attack, misuse, and abuse. One method to counteracting this cyber threat is to provide security analysts with better tools to discover patterns, detect anomalies, identify correlations, and communicate their findings. Visualization for computer security (VizSec) researchers and developers are doing just that. VizSec is about putting robust information visualization tools into the hands of human analysts to take advantage of the power of the human perceptual and cognitive processes in solving computer security problems. This volume collects the papers presented at the 4th International Workshop on Computer Security - VizSec 2007.

Computer security --- Computer science. --- Data structures (Computer science). --- Computer graphics. --- Computers. --- Law and legislation. --- Information theory. --- Mathematics. --- Visualization. --- Computer Science. --- Computer Imaging, Vision, Pattern Recognition and Graphics. --- Data Structures, Cryptology and Information Theory. --- Legal Aspects of Computing. --- Information and Communication, Circuits.

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The study of permutation complexity can be envisioned as a new kind of symbolic dynamics whose basic blocks are ordinal patterns, that is, permutations defined by the order relations among points in the orbits of dynamical systems. Since its inception in 2002 the concept of permutation entropy has sparked a new branch of research in particular regarding the time series analysis of dynamical systems that capitalizes on the order structure of the state space. Indeed, on one hand ordinal patterns and periodic points are closely related, yet ordinal patterns are amenable to numerical methods, while periodicity is not. Another interesting feature is that since it can be shown that random (unconstrained) dynamics has no forbidden patterns with probability one, their existence can be used as a fingerprint to identify any deterministic origin of orbit generation. This book is primarily addressed to researchers working in the field of nonlinear dynamics and complex systems, yet will also be suitable for graduate students interested in these subjects. The presentation is a compromise between mathematical rigor and pedagogical approach. Accordingly, some of the more mathematical background needed for more in depth understanding has been shifted into the appendices.

Nonlinear theories. --- Time-series analysis. --- Mathematical statistics. --- Mathematics --- Statistical inference --- Statistics, Mathematical --- Analysis of time series --- Statistical methods --- Physics. --- Data structures (Computer science). --- Applied mathematics. --- Engineering mathematics. --- Statistical physics. --- Dynamical systems. --- Statistical Physics, Dynamical Systems and Complexity. --- Mathematical Methods in Physics. --- Data Structures, Cryptology and Information Theory. --- Applications of Mathematics. --- Statistics --- Probabilities --- Sampling (Statistics) --- Autocorrelation (Statistics) --- Harmonic analysis --- Mathematical statistics --- Time-series analysis

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This volume contains a collection of research and survey papers written by some of the most eminent mathematicians in the international community and is dedicated to Helmut Maier, whose own research has been groundbreaking and deeply influential to the field. Specific emphasis is given to topics regarding exponential and  trigonometric sums and their behavior in short intervals, anatomy of integers and cyclotomic polynomials, small gaps in sequences of sifted prime numbers, oscillation theorems for primes in arithmetic progressions, inequalities related to the distribution of primes in short intervals, the Möbius function, Euler’s totient function, the Riemann zeta function and the Riemann Hypothesis. Graduate students, research mathematicians, as well as computer scientists and engineers who are interested in pure and interdisciplinary research, will find this volume a useful resource. Contributors to this volume: Bill Allombert, Levent Alpoge, Nadine Amersi, Yuri Bilu, Régis de la Bretèche, Christian Elsholtz, John B. Friedlander, Kevin Ford, Daniel A. Goldston, Steven M. Gonek, Andrew Granville, Adam J. Harper, Glyn Harman, D. R. Heath-Brown, Aleksandar Ivić, Geoffrey Iyer, Jerzy Kaczorowski, Daniel M. Kane, Sergei Konyagin, Dimitris Koukoulopoulos, Michel L. Lapidus, Oleg Lazarev, Andrew H. Ledoan, Robert J. Lemke Oliver, Florian Luca, James Maynard, Steven J. Miller, Hugh L. Montgomery, Melvyn B. Nathanson, Ashkan Nikeghbali, Alberto Perelli, Amalia Pizarro-Madariaga, János Pintz, Paul Pollack, Carl Pomerance, Michael Th. Rassias, Maksym Radziwiłł, Joël Rivat, András Sárközy, Jeffrey Shallit, Terence Tao, Gérald Tenenbaum, László Tóth, Tamar Ziegler, Liyang Zhang.

Algebra --- Mathematics --- Physical Sciences & Mathematics --- Numerical analysis. --- Data structures (Computer science) --- Mathematics. --- Math --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Data structures (Computer science). --- Number theory. --- Number Theory. --- Numerical Analysis. --- Data Structures, Cryptology and Information Theory. --- Science --- Mathematical analysis --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Data structures (Computer scienc. --- Data Structures and Information Theory. --- Number study --- Numbers, Theory of

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This textbook provides an introduction to the mathematics on which modern cryptology is based. It covers not only public key cryptography, the glamorous component of modern cryptology, but also pays considerable attention to secret key cryptography, its workhorse in practice. Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines: computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved. Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assumed, corresponding to his or her background in computer science or engineering. Algebra for Cryptologists is a textbook for an introductory course in cryptography or an upper undergraduate course in algebra, or for self-study in preparation for postgraduate study in cryptology.

Mathematics. --- Data structures (Computer science). --- Computer science --- Algebra. --- Data Structures, Cryptology and Information Theory. --- Discrete Mathematics in Computer Science. --- Computer mathematics --- Discrete mathematics --- Electronic data processing --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Math --- Mathematics --- Data structures (Computer scienc. --- Computational complexity. --- Data Structures and Information Theory. --- Mathematical analysis --- Complexity, Computational --- Machine theory --- Data encryption (Computer science) --- Computer science—Mathematics. --- File organization (Computer science) --- Abstract data types (Computer science)

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This book presents the basics of quantum information, e.g., foundation of quantum theory, quantum algorithms, quantum entanglement, quantum entropies, quantum coding, quantum error correction and quantum cryptography. The required knowledge is only elementary calculus and linear algebra. This way the book can be understood by undergraduate students. In order to study quantum information, one usually has to study the foundation of quantum theory. This book describes it from more an operational viewpoint which is suitable for quantum information while traditional textbooks of quantum theory lack this viewpoint. The current  book bases on Shor's algorithm, Grover's algorithm, Deutsch-Jozsa's algorithm as basic algorithms. To treat several topics in quantum information, this book covers several kinds of information quantities in quantum systems including von Neumann entropy. The limits of several kinds of quantum information processing are given. As important quantum protocols,this book contains quantum teleportation, quantum dense coding, quantum data compression. In particular conversion theory of entanglement via local operation and classical communication are treated too. This theory provides the quantification of entanglement, which coincides with von Neumann entropy. The next part treats the quantum hypothesis testing. The  decision problem of two candidates of the unknown state are given. The asymptotic performance of this problem is characterized by information quantities. Using this result, the optimal performance of classical information transmission via noisy quantum channel is derived. Quantum information transmission via noisy quantum channel by quantum error correction are discussed too. Based on this topic, the secure quantum communication is explained. In particular, the quantification of quantum security which has not been treated in existing book is explained.  This book treats quantum cryptography from a more practical viewpoint.

Physics. --- Quantum Information Technology, Spintronics. --- Quantum Computing. --- Theoretical, Mathematical and Computational Physics. --- Data Structures, Cryptology and Information Theory. --- Information and Communication, Circuits. --- Data structures (Computer science). --- Mathematics. --- Physique --- Structures de données (Informatique) --- Mathématiques --- Engineering & Applied Sciences --- Electrical & Computer Engineering --- Computer Science --- Electrical Engineering --- Information theory. --- Quantum computers. --- Spintronics. --- Data structures (Computer scienc. --- Data Structures and Information Theory. --- Math --- Science --- Mathematical physics. --- Communication theory --- Communication --- Cybernetics --- Information structures (Computer science) --- Structures, Data (Computer science) --- Structures, Information (Computer science) --- Electronic data processing --- File organization (Computer science) --- Abstract data types (Computer science) --- Physical mathematics --- Physics --- Fluxtronics --- Magnetoelectronics --- Spin electronics --- Spinelectronics --- Microelectronics --- Nanotechnology --- Computers --- Mathematics