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The

UMAP

Journal

Publisher

COMAP, Inc.

Vol. 37, No. 2

Executive Publisher

Solomon A. Garfunkel

ILAP Editor

Chris Arney

Dept. of Math’l Sciences

U.S. Military Academy

West Point, NY 10996

david.arney@usma.edu

On Jargon Editor

Yves Nievergelt

Dept. of Mathematics

Eastern Washington Univ.

Cheney, WA 99004

ynievergelt@ewu.edu

Reviews Editor

James M. Cargal

20 Higdon Ct.

Fort Walton Beach,

FL 32547

jmcargal@gmail.com

Chief Operating Ofﬁcer

Laurie W. Arag´on

Production Manager

George Ward

Copy Editor

David R. Heesen

Distribution

John Tomicek

Editor

Paul J. Campbell

Beloit College

700 College St.

Beloit, WI 53511–5595

campbell@beloit.edu

Associate Editors

Don Adolphson

Aaron Archer

Chris Arney

Ron Barnes

Arthur Benjamin

Robert Bosch

James M. Cargal

Murray

K. Clayton

Lisette De Pillis

James P. Fink

Solomon A. Garfunkel

William B. Gearhart

William C. Giauque

Richard Haberman

Jon Jacobsen

Walter Meyer

Yves Nievergelt

Michael O’Leary

Catherine A. Roberts

Philip D. Strafﬁn

J.T. Sutcliffe

Brigham Young Univ.

Google Research

U.S. Military Academy

U. of Houston—Downtn

Harvey Mudd College

Oberlin College

Troy U.— Montgomery

U. of Wisc.—Madison

Harvey Mudd College

Gettysburg College

COMAP, Inc.

Calif. State U., Fullerton

Brigham Young Univ.

Southern Methodist U.

Harvey Mudd College

Adelphi University

Eastern Washington U.

Towson University

College of the Holy Cross

Beloit College

St. Mark’s School, Dallas

Guest Editorial 93

Guest Editorial

Cyber Modeling: Full of Challenges

Chris Arney, ICM Director

Dept. of Mathematical Sciences

U.S. Military Academy

West Point, NY 10996

david.arney@usma.edu

Introduction

What do we do when our computer misbehaves or our information is

harmed? Why is it that the network is slow or drops our connections?

These could be deep, complicated cyber problems that need solving or just

simple repairs to software or hardware. Perhaps the modeling process can

help solve such problems. So we ask:

What roles do mathematical and interdisciplinary modeling

have in cyberspace?

I will try to explain some of these roles, especially as they affect undergrad-

uate interdisciplinary modeling and the ICM.

Cyber Modeling

In a world that is increasingly connected through expanding digital

networks, cyber modeling offers a tool to understand the complex issues

and to solve the challenging problems that this expansion is creating.

Just as in any other domain (politics, business, ﬁnance, science, sports,

psychology, warfare, etc.), modeling is a valuable tool in cyberspace to

enable understanding of issues and solving problems. Yet, in every do-

main there are differences in how modeling is used. That is deﬁnitely the

case in cyberspace. Cyberspace is complex, dynamic, interdisciplinary, and

chaotic, where modeling structures and processes are challenged to repre-

sent and conceptualize elements of cyberspace and capture the dynamic

The UMAP Journal 37 (2) (2016) 93–97.

Permission to make digital or hard copies of part or all of this work for personal or classroom use

is granted without fee provided that copies are not made or distributed for proﬁt or commercial

advantage and that copies bear this notice. Abstracting with credit is permitted, but copyrights

for components of this work owned by others than COMAP must be honored. To copy otherwise,

to republish, to post on servers, or to redistribute to lists requires prior permission from COMAP.

94 The UMAP Journal 37.2 (2016)

of the attacker-defender interface. Cyberspace itself is the combination

of many digital-related components that store, process, transmit, and use

information. Modeling, while based on assumptions that simplify the com-

plexity of real problems, must develop ways to enable cyber modelers to

contribute to the fast-paced world of digital computing. Cyber modeling

is highly interdisciplinary because its elements involve human interactions

as well as many forms of science relevant to cyber goals, perspectives, and

principles. Computing and networking are important, as are ethics and

social issues. Data science, human psychology, and many other disciplines

are all parts of this virtual and digital cyber world.

Understanding the Problem

One element of the complexity of cyber space is just understanding the

problem to be solved or the issue to be confronted. Often the issues that

need to be addressed are hidden and only the symptoms are visible. The

cause of the problem—a bug, an innocent human error, bad hardware, or a

malicious attack—is often undetectable. The balances between security and

performance, privacy, and information availability are delicate and critical.

Cyber modeling is needed for fast, time-sensitive problem solutions and

robust network designs that are not as common in other domains. We need

to ask continually—sincethe cyber worldis developing at an incredible rate:

Can our modeling keep pace with the computing and artiﬁcial intelligence

that are often component parts of the issues and problems?

Hackers vs. Defenders

Another element of the cyber complexity is the underlying competi-

tive nature of the attacker-defender dynamic. Hackers and malicious sys-

tems are pitted against defenders of information and systems’ performance.

There is much more to cyber security than a formidable ﬁrewall and virus

protection.

In addition, these attacking elements often try to hide their true identity.

This game-theoretic setting takes modelingto new heights of what-if, cause-

effect, and who-did-it questions.

Cyber problem solving is an unstructured process that often requires

high-dimensional nonlinear models, yet still needing dynamic modiﬁca-

tion to adapt to constantly changing situations. Game theory plays a role,

especially when you abstract away all the computers,

networks, cables and

bits of information, and only the human users remain.

Another role for cyber modeling is in war-gaming the basic elements of

the cyber competition. Models that can test capabilities, probe for vulner-

abilities, ﬁx performance degradation, and exercise the cyber systems, are

needed to enhance cyber security. Artiﬁcial intelligence techniques such as

Guest Editorial 95

machine learning and reinforcement learning are valuable to many cyber

modelers.

Information Security

On a larger scale, cyber modeling is a component of the science of in-

formation security, which has a goal of building effective systems for infor-

mation assurance.

A major challenge is that the same elements of the information network

that create itspositiveattributes(effectivenessand freedom) alsoproduceits

negative elements (vulnerability and lack of privacy and security). What

makes a network robust, survivable, and hard to kill, paradoxically also

makes it inefﬁcient, difﬁcult to manage, and vulnerable to penetration.

The Importance of Diversity

Evolutionary biology shows that inherent diversity provides reliabil-

ity at a price of some inefﬁciency, yet with still-acceptable performance.

Evolutionary biology also teaches that change (adaptation) is needed in

order to survive. Today’s cyber systems are vulnerable, dangerous, and

unpredictable—a place where actions and events happen fast. So to sur-

vive on the network, you have to be able to model quickly and effectively—

sometimes proactively, sometimes reactively. Diversity is the model at-

tribute that best provides the potential for resilience to vulnerabilities and

yet the agility to change fast.

The Uses of Randomness

One natural way to create diversity in cyber systems is through random-

ness (explicitly-designed random processes). Nature provides diversity in

its DNA and cells; cyber modelers need explicitly to build diversity and

randomness into their systems.

There is a well-deﬁned and useful deﬁnition of what it means for in-

formation (numbers, words, symbols) to be random: an impossibility to

compress its information content. To build smart systems, cyber modelers

need to include that kind of randomness and its consequential diversity.

Where to Put the Diversity?

Designing diversity into a network can make it robust, secure, inefﬁcient

and impossible to control. Where do cyber modelers need to put diversity

in their models? The goal is to have it nearly everywhere:

• Authentication Procedures

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