Cybersecurity and Applied Mathematics

 
 
Syngress (Verlag)
  • 1. Auflage
  • |
  • erschienen am 7. Juni 2016
  • |
  • 240 Seiten
 
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
978-0-12-804499-5 (ISBN)
 

Cybersecurity and Applied Mathematics explores the mathematical concepts necessary for effective cybersecurity research and practice, taking an applied approach for practitioners and students entering the field. This book covers methods of statistical exploratory data analysis and visualization as a type of model for driving decisions, also discussing key topics, such as graph theory, topological complexes, and persistent homology.

Defending the Internet is a complex effort, but applying the right techniques from mathematics can make this task more manageable. This book is essential reading for creating useful and replicable methods for analyzing data.


  • Describes mathematical tools for solving cybersecurity problems, enabling analysts to pick the most optimal tool for the task at hand
  • Contains numerous cybersecurity examples and exercises using real world data
  • Written by mathematicians and statisticians with hands-on practitioner experience


Leigh Metcalf research's network security, game theory, formal languages, and dynamical systems. She is Editor in Chief of the Journal on Digital Threats and has a PhD in Mathematics.
  • Englisch
  • Saint Louis
  • |
  • USA
Elsevier Science
  • 5,55 MB
978-0-12-804499-5 (9780128044995)
0128044993 (0128044993)
weitere Ausgaben werden ermittelt
  • Front Cover
  • Cybersecurity and Applied Mathematics
  • Copyright
  • Contents
  • Biography
  • Chapter 1: Introduction
  • Chapter 2: Metrics, similarity, and sets
  • 2.1 Introduction to Set Theory
  • 2.2 Operations on Sets
  • 2.2.1 Complement
  • 2.2.2 Intersection
  • 2.2.3 Union
  • 2.2.4 Difference
  • 2.2.5 Symmetric Difference
  • 2.2.6 Cross Product
  • 2.3 Set Theory Laws
  • 2.4 Functions
  • 2.5 Metrics
  • 2.6 Distance Variations
  • 2.6.1 Pseudometric
  • 2.6.2 Quasimetric
  • 2.6.3 Semimetric
  • 2.7 Similarities
  • 2.8 Metrics and Similarities of Numbers
  • 2.8.1 Lp Metrics
  • 2.8.2 Gaussian Kernel
  • 2.9 Metrics and Similarities of Strings
  • 2.9.1 Levenshtein Distance
  • 2.9.2 Hamming Distance
  • 2.10 Metrics and Similarities of Sets of Sets
  • 2.10.1 Jaccard Index
  • 2.10.2 Tanimoto Distance
  • 2.10.3 Overlap Coefficient
  • 2.10.4 Hausdorff Metric
  • 2.10.5 Kendall's Tau
  • 2.11 Mahalanobis Distance
  • 2.12 Internet Metrics
  • 2.12.1 Great Circle Distance
  • 2.12.2 Hop Distance
  • 2.12.3 Keyword Distance
  • Chapter 3: Probability models
  • 3.1 Basic Probability Review
  • 3.1.1 Language and Axioms of Probability
  • 3.1.2 Combinatorics Aka Parlor Tricks
  • 3.1.3 Joint and Conditional Probability
  • 3.1.4 Independence and Bayes Rule
  • 3.2 From Parlor Tricks to Random Variables
  • 3.2.1 Types of Random Variables
  • 3.2.2 Properties of Random Variables
  • 3.3 The Random Variable as a Model
  • 3.3.1 Bernoulli and Geometric Distributions
  • 3.3.2 Binomial Distribution
  • 3.3.3 Poisson Distribution
  • 3.3.4 Normal Distribution
  • 3.3.5 Pareto Distributions
  • 3.3.6 Uniform Distribution
  • 3.4 Multiple Random Variables
  • 3.5 Using Probability and Random Distributions
  • 3.6 Conclusion
  • Chapter 4: Introduction to data analysis
  • 4.1 The Language of Data Analysis
  • 4.1.1 Producing Data
  • 4.1.2 Exploratory Data Analysis
  • 4.1.3 Inference
  • 4.2 Units, Variables, and Repeated Measures
  • 4.2.1 Measurement Error and Random Variation
  • 4.3 Distributions of Data
  • 4.4 Visualizing Distributions
  • 4.4.1 Bar Plot
  • 4.4.2 Histogram
  • 4.4.3 Box Plots
  • 4.4.4 Density Plot
  • 4.5 Data Outliers
  • 4.6 Log Transformation
  • 4.7 Parametric Families
  • 4.8 Bivariate Analysis
  • 4.8.1 Visualizing Bipartite Variables
  • 4.8.2 Correlation
  • 4.9 Time Series
  • 4.10 Classification
  • 4.11 Generating Hypotheses
  • 4.12 Conclusion
  • Chapter 5: Graph theory
  • 5.1 An Introduction to Graph Theory
  • 5.2 Varieties of Graphs
  • 5.2.1 Undirected Graph
  • 5.2.2 Directed Graph
  • 5.2.3 Multigraph
  • 5.2.4 Bipartite Graph
  • 5.2.5 Subgraph
  • 5.2.6 Graph Complement
  • 5.3 Properties of Graphs
  • 5.3.1 Graph Sizes
  • 5.3.2 Vertices and Their Edges
  • 5.3.3 Degree
  • 5.3.4 Directed Graphs and Degrees
  • 5.3.5 Scale Free Graphs
  • 5.4 Paths, Cycles and Trees
  • 5.4.1 Paths and Cycles
  • 5.4.2 Shortest Paths
  • 5.4.3 Connected and Disconnected Graphs
  • 5.4.4 Trees
  • 5.4.5 Cycles and Their Properties
  • 5.4.6 Spanning Trees
  • 5.5 Varieties of Graphs Revisited
  • 5.5.1 Graph Density, Sparse and Dense Graphs
  • 5.5.2 Complete and Regular Graphs
  • 5.5.3 Weighted Graph
  • 5.5.4 And Yet More Graphs!
  • 5.6 Representing Graphs
  • 5.6.1 Adjacency Matrix
  • 5.6.2 Incidence Matrix
  • 5.7 Triangles, the Smallest Cycle
  • 5.7.1 Introduction and Counting
  • 5.7.2 Triangle Free Graphs
  • 5.7.3 The Local Clustering Coefficient
  • 5.8 Distances on Graphs
  • 5.8.1 Eccentricity
  • 5.8.2 Cycle Length Properties
  • 5.9 More Properties of Graphs
  • 5.9.1 Cut
  • 5.9.2 Bridge
  • 5.9.3 Partitions
  • 5.9.4 Vertex Separators
  • 5.9.5 Cliques
  • 5.10 Centrality
  • 5.10.1 Betweenness
  • 5.10.2 Degree Centrality
  • 5.10.3 Closeness and Farness
  • 5.10.4 Cross-Clique Centrality
  • 5.11 Covering
  • 5.11.1 Vertex Covering
  • 5.11.2 Edge Cover
  • 5.12 Creating New Graphs From Old
  • 5.12.1 Union Graphs
  • 5.12.2 Intersection Graphs
  • 5.12.3 Uniting Graphs
  • 5.12.4 The Intersection Graph
  • 5.12.5 Modifying Existing Graphs
  • 5.13 Conclusion
  • Chapter 6: Game theory
  • 6.1 The Prisoner's Dilemma
  • 6.2 The Mathematical Definition of a Game
  • 6.2.1 Strategies, Payoffs and Normal Form
  • 6.2.2 Normal Form
  • 6.2.3 Extensive Form
  • 6.3 Snowdrift Game
  • 6.4 Stag Hunt Game
  • 6.5 Iterative Prisoner's Dilemma
  • 6.6 Game Solutions
  • 6.6.1 Cooperative and Non-Cooperative Games
  • 6.6.2 Zero Sum Game
  • 6.6.3 Dominant Strategy
  • 6.6.4 Nash Equilibrium
  • 6.6.5 Mixed Strategy Nash Equilibrium
  • 6.7 Partially Informed Games
  • 6.8 Leader-Follower Game
  • 6.8.1 Stackelberg Game
  • 6.8.2 Colonel Blotto
  • 6.9 Signaling Games
  • Chapter 7: Visualizing cybersecurity data
  • 7.1 Why Visualize?
  • 7.2 What We Visualize
  • 7.2.1 Considering the Efficacy of a Visualization
  • 7.2.2 Data Collection and Visualization
  • 7.2.3 Visualizing Malware Features
  • 7.2.4 Existence Plots
  • 7.2.5 Combining Plots
  • 7.3 Visualizing IP Addresses
  • 7.3.1 Hilbert Curve
  • 7.3.2 Heat Map
  • 7.4 Plotting Higher Dimensional Data
  • 7.4.1 Principal Component Analysis
  • 7.4.2 Sammon Mapping
  • 7.5 Graph Plotting
  • 7.6 Visualizing Malware
  • 7.7 Visualizing Strings
  • 7.7.1 Word Cloud
  • 7.7.2 Sammon Mapping for Strings
  • 7.8 Visualization with a Purpose
  • Chapter 8: String analysis for cyber strings
  • 8.1 String analysis and Cyber Data
  • 8.1.1 Cyber Data
  • 8.1.2 Modes of analyzing Cyber Data
  • 8.1.3 Alphabets and Finite Strings
  • 8.1.4 Formal Languages
  • Languages and Regular Expressions
  • 8.2 Discrete String Matching
  • 8.2.1 Hashing
  • Birthday Party and Universal Hash Function Collisions
  • 8.2.2 Applications of Hashing
  • Bag of Hashes, or Bag of Numbers
  • Normalizing Bag of Numbers
  • 8.2.3 Other Methods
  • 8.3 Affine Alignment String Similarity
  • 8.3.1 Optimality and Dynamic Programming
  • 8.3.2 Global Affine Alignment
  • 8.3.3 Example Alignments
  • 8.4 Summary
  • Chapter 9: Persistent homology
  • 9.1 Triangulations
  • 9.2 a Shapes
  • 9.3 Holes
  • 9.4 Homology
  • 9.5 Persistent Homology
  • 9.6 Visualizing Persistent Homology
  • 9.6.1 Comparing Point Clouds
  • 9.7 Conclusions
  • Appendix: Introduction to linear algebra
  • A.1 Vector Algebra
  • A.1.1 Vector Addition
  • A.1.2 Vector Scalar Multiplication
  • A.1.3 Linear Mappings
  • A.1.4 Matrices
  • A.1.5 Matrix Addition
  • A.1.6 Matrix Multiplication
  • A.2 Eigenvalues
  • A.3 Additional Matrix Operations
  • Bibliography
  • Index
  • Back Cover

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