Cybersecurity and Applied Mathematics

Cybersecurity and Applied Mathematics

by Leigh Metcalf, William Casey
Released June 2016
Publisher(s): Syngress
ISBN: 9780128044995

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Book description

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

Table of contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Biography
  6. Chapter 1: Introduction
    1. Abstract
  7. Chapter 2: Metrics, similarity, and sets
    1. Abstract
    2. 2.1 Introduction to Set Theory
    3. 2.2 Operations on Sets
    4. 2.3 Set Theory Laws
    5. 2.4 Functions
    6. 2.5 Metrics
    7. 2.6 Distance Variations
    8. 2.7 Similarities
    9. 2.8 Metrics and Similarities of Numbers
    10. 2.9 Metrics and Similarities of Strings
    11. 2.10 Metrics and Similarities of Sets of Sets
    12. 2.11 Mahalanobis Distance
    13. 2.12 Internet Metrics
  8. Chapter 3: Probability models
    1. Abstract
    2. 3.1 Basic Probability Review
    3. 3.2 From Parlor Tricks to Random Variables
    4. 3.3 The Random Variable as a Model
    5. 3.4 Multiple Random Variables
    6. 3.5 Using Probability and Random Distributions
    7. 3.6 Conclusion
  9. Chapter 4: Introduction to data analysis
    1. Abstract
    2. 4.1 The Language of Data Analysis
    3. 4.2 Units, Variables, and Repeated Measures
    4. 4.3 Distributions of Data
    5. 4.4 Visualizing Distributions
    6. 4.5 Data Outliers
    7. 4.6 Log Transformation
    8. 4.7 Parametric Families
    9. 4.8 Bivariate Analysis
    10. 4.9 Time Series
    11. 4.10 Classification
    12. 4.11 Generating Hypotheses
    13. 4.12 Conclusion
  10. Chapter 5: Graph theory
    1. Abstract
    2. 5.1 An Introduction to Graph Theory
    3. 5.2 Varieties of Graphs
    4. 5.3 Properties of Graphs
    5. 5.4 Paths, Cycles and Trees
    6. 5.5 Varieties of Graphs Revisited
    7. 5.6 Representing Graphs
    8. 5.7 Triangles, the Smallest Cycle
    9. 5.8 Distances on Graphs
    10. 5.9 More properties of graphs
    11. 5.10 Centrality
    12. 5.11 Covering
    13. 5.12 Creating New Graphs from Old
    14. 5.13 Conclusion
  11. Chapter 6: Game theory
    1. Abstract
    2. 6.1 The Prisoner’s Dilemma
    3. 6.2 The Mathematical Definition of a Game
    4. 6.3 Snowdrift Game
    5. 6.4 Stag Hunt Game
    6. 6.5 Iterative Prisoner’s Dilemma
    7. 6.6 Game Solutions
    8. 6.7 Partially Informed Games
    9. 6.8 Leader-Follower Game
    10. 6.9 Signaling Games
  12. Chapter 7: Visualizing cybersecurity data
    1. Abstract
    2. 7.1 Why visualize?
    3. 7.2 What we visualize
    4. 7.3 Visualizing IP addresses
    5. 7.4 Plotting higher dimensional data
    6. 7.5 Graph plotting
    7. 7.6 Visualizing malware
    8. 7.7 Visualizing strings
    9. 7.8 Visualization with a purpose
  13. Chapter 8: String analysis for cyber strings
    1. Abstract
    2. 8.1 String Analysis and Cyber Data
    3. 8.2 Discrete String Matching
    4. 8.3 Affine alignment string similarity
    5. 8.4 Summary
  14. Chapter 9: Persistent homology
    1. Abstract
    2. 9.1 Triangulations
    3. 9.2 α Shapes
    4. 9.3 Holes
    5. 9.4 Homology
    6. 9.5 Persistent homology
    7. 9.6 Visualizing Persistent Homology
    8. 9.7 Conclusions
  15. Appendix: Introduction to linear algebra
    1. A.1 Vector Algebra
    2. A.2 Eigenvalues
    3. A.3 Additional Matrix Operations
  16. Bibliography
  17. Index

Product information

  • Title: Cybersecurity and Applied Mathematics
  • Author(s): Leigh Metcalf, William Casey
  • Release date: June 2016
  • Publisher(s): Syngress
  • ISBN: 9780128044995