Mathematical Approaches to Security Analytics

Mathematical Approaches to Security Analytics

Network Security Fundamentals and Cryptography

Identify a specific application of statistics in identifying an information security related threat.

Visual Analytics (VA) techniques have been explored and put in service to counter cyber security. There are many VA applications related to network analysis. Visualization is often appropriate when human intelligence and domain knowledge must be combined with automated methods. This is certainly the situation with monitoring and exploring network traffic patterns. The sheer number of alerts and the sophistication of attacks require a symbiosis of Intrusion Detection Systems (IDS) algorithms and human analysis to fight new adversaries. The NFlowVis Network visualization tool provides a number of views used to perform large-scale network traffic monitoring, to detect distributed attacks and to analyze intrusion detection events. The design of the Visual assistant for Information Assurance analysis (VIAssist) was informed by cognitive tasks analysis activities. This visual analysis platform provides one view for in-depth event analysis and a dashboard view for global activity. Different kinds of visualizations are provided to enable the analysis of events in network, temporal and geographic contexts. Multiple visualizations are linked together to facilitate exploration and discovery. ManyNets is a network visualization tool with tabular interface designed to visualize up to several thousand network overviews at once. This allows networks to be compared and large networks to be explored using a divide-and-conquer approach. A collection of networks is presented in a table, where each row represents a single network. Columns represent statistics, such as link count, degree distribution or clustering coefficients. Networks can also be subdivided and compared based on motifs (small patterns of connectivity), clusters or network-specific attributes. (Lavigne, Gouin, 2014)

Identify how number theory plays a role in contributing to information security data analytics and encryption algorithms.

Applications of number theory allow the development of mathematical algorithms that can make information (data) unintelligible to everyone except for intended users. In addition, mathematical algorithms can provide real physical security to data—allowing only authorized users to delete or update data. Specialized mathematical derivations of number theory such as theory and equations dealing with elliptical curves are also making an increasing impact on cryptology. Larger keys provide increasing security, applications of number theory and elliptical curves to cryptological algorithms allow the use of easier-to-use smaller keys without any loss of security. Another ramification related to applications of number theory is the development of “nonreputable” transactions. Non-reputable means that parties cannot later deny involvement in authorizing certain transactions. Number theory allowed factoring of large numbers that by hand might take billions of years to procedures that with the use of advanced computing might be accomplished in a matter of months. Further advances in number theory may lead to the discovery of a polynomial time factoring algorithm that can accomplish in hours what now takes months or years of computer time. (


Lavigne, V., & Gouin, D. (2014, April 3). Visual Analytics for cyber security and intelligence. Retrieved January 21, 2018, from

Applications of Number Theory in Cryptography.” Science and Its Times: Understanding the Social Significance of Scientific Discovery. . Retrieved January 21, 2018 from