The Inside Scoop On Mathematics At The Nsa Pdf

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The Inside Scoop on Mathematics at the NSA

Michelle Wagner

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2004

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The Inside Scoop on Mathematics at the NSA Author(s): Michelle Wagner Source: Math Horizons, Vol. 13, No. 4 (April 2006), pp. 20-23 Published by: Mathematical Association of America Stable URL: http://www.jstor.org/stable/25678621 Accessed: 10-12-2015 23:38 UTC Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://www.jstor.org/page/ info/about/policies/terms.jsp JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Mathematical Association of America is collaborating with JSTOR to digitize, preserve and extend access to Math Horizons. http://www.jstor.org This content downloaded from 139.80.123.50 on Thu, 10 Dec 2015 23:38:02 UTC All use subject to JSTOR Terms and Conditions Organizational Profile "While cryptology is certainlythe bread-and-butterof theAgency's business, out themissionrequiresthe talentofmanydifferent kindsof carrying employees: intelligence analysts, linguists,computer scientists, engineers, human resources specialists, and yes,mathematicians." The Inside Mathematics on Scoop at the NSA Michelle Wagner NationalSecurity Agency Whatdo themovies Enemy of the State, Good Will Hunting, and Die Another Day all have in com mon? If you've seen any of these films you know that the plot features an associate from a fictional "National Security Agency" who is involved in some sort of nefarious activity.Curious to get the4-1-1 on the place and sortout fact fromfiction? If so, sitback and settle in for the inside scoop on what it's like towork as a mathematician inside the halls of one of themost secretive agencies in theUnited States intelli gence community. First a littlebit of history and an overview of theNational Secur; ity Agency (NSA). Prior to the creation of theNSA, the nation's cryptologic requirements fell to a collection of dedi cated units within the U.S. Army and Navy. These units expanded at the outbreak ofWorld War II and, with help from Allied forces, resulted in such well-known successes as the exploits of theGerman cipher system known as Enigma and the Japanese cipher system Purple. During the interimperiod between World War II and theKorean War, itbecame increas ingly apparent thata centralized authoritywas needed toman age the cryptologic needs of the nation; thus,with a stroke of his pen, President Harry Truman established the National Security Agency for this purpose in 1952. The NSA is part of theDepartment ofDefense and itsmain function is to provide signals intelligence or SIGINT, to customers such as theWhite House, the State Department, military departments, and U.S. is twofold: (1) to produce foreign signals and (2) to protect information infrastructurescrit intelligence, While cryptology is cer ical toU.S. national security interests. allies. Our mission tainly the bread-and-butter of theAgency's business, carrying out themission requires the talent of many differentkinds of employees: intelligence analysts, linguists, computer scien tists, engineers, human resources specialists, and yes, mathe maticians. So just what is it like working as a mathematician at the NSA? Well firstof all, thereare lots of us and we're spread out all over theAgency?they say that theNSA is the largest sin in theUnited States, ifnot the mathematicians of gle employer world (whoever "they" are).While the actual number ofmath ematicians working at theAgency is classified, it iswell into the hundreds, and we come in all sizes, shapes, and pedigrees. Over the last five or six years, roughly 50-60% of themathe maticians we've hired hold a PhD and the remaining 40-50% are roughly split between bachelors and masters degrees, the point being thatyou do not have to have a PhD to get hired as a mathematician at theNSA. It's sometimes surprising for people on the outside?the classified nature of our business tends tomake NS Aers refer to lifebeyond NSA walls as the "outside"?to learn thatalthough it is certainly nice if a new hire has specific training in cryp tology,we do not require any particular fluency in the subject. In fact, our mathematicians come to us with training in spe cialties across a broad spectrum of areas that runs the gamut from dynamical systems to statistics to topology and many other subjects.What we reallywant are problem solvers, indi viduals who are willing to learn new techniques and who will approach technical challenges from a variety of perspectives (more later on exactly what these technical challenges are). Newly hired mathematicians acquire the specialized knowl edge needed to perform their jobs by participating in one of threemathematics development programs: theApplied Math ematics Program (AMP), the Cryptologic Mathematics Pro gram (CMP), and the Information Assurance Directorate and Education Program (IDEP). These pro Development are which all three years in duration and are adminis grams, tered throughdifferentdirectorates at theNSA, require partic ipants to take a sequence of courses while simultaneously working in different offices for 6-8 months at a time. The intentof these programs is to allow mathematicians to solve a diverse set of mission critical problems while working under the guidance of experienced mathematicians and cryptana lysts,and also to become a part of a network of peers they can rely on forprofessional and technical support throughout their careers at theAgency. Now to the good stuff?the problems we get towork on. Most of our work is classified and we even maintain our own 20 APRIL 2006 This content downloaded from 139.80.123.50 on Thu, 10 Dec 2015 23:38:02 UTC All use subject to JSTOR Terms and Conditions MATH internal database of classified mathematics HORIZONS and technical papers that never see the light of day. But unlike old times when we were once known as "No Such Agency," it's possible for us to talk about what we do with more openness than ever before. As you would probably expect, mathematicians have played a central role in advancing the theory and practice of cryptology,which can be defined as thedesign and analysis of encryption techniques. But mathematicians do much more than sit around all day cracking secret codes. Mathematicians are scattered throughout theNSA working on problems as wide-ranging as signals analysis, coding theory,network secu rity,biometrics, supercomputing, data mining, speech pro cessing, and data compression. Some of theproblems are very well defined while others are vague at the outset and require the language and structureof mathematics to bring more for malism to the problem statement. Similarly, some projects require only a shortamount of time to solve while others need more long-term investment and research. The mathematics that is brought to bear on these problems includes abstract algebra, number theory,graph theory, combinatorics, proba bility, statistics, and much more. Virtually all the problems generated by NSA's mission require the use of a computer, and although new mathematics hires are not required to possess any prior computer experi ence, it is necessary forNSA mathematicians to learn to use a computer effectively.This could mean writing a shortcomput er program to quickly testout an idea, or using a commercial or in-house software package to display a large collection of data. It could also involve themore complicated process of coding an intricate algorithm that has been streamlined for efficiency and memory usage. Indeed, themathematical com munity at NSA has been so successful because of the combi nation of the analytic abilities of our mathematicians with the power ofmodern computers. to sign up? The application process can be quite lengthy, so it is recommended that applicants submit their materials at least six to ninemonths in advance of their intend Put Your Math Intelligence toWork you join NSA, you join a highly talented group of Mathematicians who deduce structurewhere it is not apparent, find patterns When in seemingly random sets, and create order out of chaos. They apply Number Theory, Group Theory, Finite Field Theory, Linear Algebra, Probability Theory, Mathematical Statistics, Combinatorics, and more to a world of challenges. They exchange ideas and work with some of the finest minds and most powerful computers in the country.And you can too, when you put your math intelligence to work at NSA. Ready ed startdate. Applicants must be able to obtain a security clear ance, must be U.S. citizens, and are subject to random drug testing. Preliminary hurdles in the process include an initial phone screening and the submission of background or "long forms" (when we say long,we're not kidding folks, so make sure you keep copies of these forms after you fill them out). these hurdles are cleared and if you are invited toNSA for an interview by theMathematics Hiring Authority, then you get to spend a couple of days in theBaltimore-Washing ton,D.C. area on the government's dime going through secu Formore informationand to apply online, visit our Web site. ^==?^ Once rity and mathematics screening. In preparation for being put through thepaces of securityday, I sometimes recommend that applicants watch themovie Meet theParents. You know, the one where Ben Stiller gets polygraphed by his soon-to-be www.niSA.gov/Careers WHERE INTELLIGENCE GOES TO WORK U.S.citizenship isrequired. NSAisan equalopportunity foremployment Allapplicants employer. areconsidered torace,color,religion, withoutregard sex,national age,maritalstatus, origin, or as a sexual status orientation, disability, parent. WWW.MAA.ORG/MATHHORIZONS 21 This content downloaded from 139.80.123.50 on Thu, 10 Dec 2015 23:38:02 UTC All use subject to JSTOR Terms and Conditions MATH father-in-lawRobert DeNiro. (Enough said.) In all seriousness, the security processing is tolerable and has been successfully navigated bymany a meek soul (including yours truly) so my best advice is just tomaintain a sense of humor about it,be as relaxed as possible, and give it a shot. One full day of processing includes a Mathematics Profi ciency Test thatevery applicant must take, a set of interviews with NSA mathematicians and, as an option, theopportunity to give a mathematics talk on a topic of your choice (PhDs are expected to give a talk). The interviews are crucial?here, the interviewers are looking for a sense of enthusiasm in how the applicants describe their experiences and goals inmathemat ics, theywant to know how open applicants are toworking on problems thatare not necessarily in theircomfort zone or par ticular area of interest,and theywant to get a sense of the cre ativity and depth of knowledge the applicant possesses in mathematics. This part of the process also gives the applicant a chance to learn more about theNSA culture. If you ever apply toNSA, thiswill be the time to ask as many questions as you like about the place (keep inmind the interviewersmay not be able to answer every question you ask). Speaking of "NSA culture," our work environment and location offer a number of attractive features that one might not expect of such a job. Many offices allow theiremployees towork a flexible work schedule to suit thepersonal or family needs of employees. Also, dress is generally casual inmost offices. Benefits include a certain number of days of annual and sick leave per year as well as federal holidays, health and other types of insurance options, and savings and retirement plans. Salaries for federally employed mathematicians are competitive and livable within theWashington, D.C.-Balti more, MD metropolitan area. The surrounding urban areas of Washington, D.C. and Baltimore, MD offer a variety of cul tural activities and professional sporting events, while beach es and mountains are within two hours driving distance. NSA is located halfway inbetweenWashington, D.C. and Baltimore so living in either city is an option, as is living in the outlying suburbs or rural areas. Of course, there are many satisfying careers that involve mathematics and no doubt therewill be readers who pick up this article and decide that theNSA is just not the rightfit.But if this article has piqued your interesteven the slightest bit, I would encourage you to pursue the option further.On a per sonal note, working at theNSA was never on my radar screen until a chance meeting I had with an Agency mathematician at the JointMathematics Meetings in 2001. Had I not chosen to open myself to thepossibility of a career outside of academia, I never would have had the chance to experience what it's like towork in a place where advanced mathematics meets such high stakes problems. It has enriched my experiences as a mathematician, broadened my training and knowledge, and made all those years of study in abstract algebra, probability, HORIZONS and other subjects seem much more relevant. But don't just take it fromme: NSA mathematicians Paul Iezzi, Valerie Nelson, and Megan Waterman talk about how they ended up at theNSA in theCareer Profiles at the end of this article. Also, have a read through the next article in this issue by Aaron Magid and Sage Briscoe on the Director's Summer Program, a 12-week research experience for under graduates that is NSA's premier outreach program to the nation's most talented students inmathematics and computer science. And last but not least, have a look at our website where you'll find information on http://www.nsa.gov careers, summer internprograms formathematics majors, and other interestingfacts about theNational Security Agency. Career Profiles Paul Iezzi is currently employed as a mathematician at the NSA and is an intern inone of the 3-year trainingprograms for new mathematicians, theApplied Mathematics Program. He in the summer of 2004 and was previously an in firm inAtlanta. He received his bach actuarial employed elor's degree inmathematics from Southern Polytechnic State started at theNSA University inMarietta, Georgia and also attended theUniver sityof Georgia. "I remember flipping through a textbook as a senior inhigh school, coming across the recursion for the Fibonacci sequence, and wanting to learnmore about it.As I tookmore advanced courses in college I was amazed at themathematics I was being exposed to and had a desire to learnmore. That's why I decided to become a math major and also why I enjoy my work at theNSA somuch. I firstheard about theNSA in a cryptology class as a sophomore at theUniversity of Georgia. Shortly after graduating, I applied for a position at theNSA and considered going to graduate school. Unbeknownst tome at the time, I would actually be able to do both [work at the NSA and go to graduate school] via the educational programs available tomathematicians at theNSA. Currently I'm work ing on my master's degree in Computational and Applied Mathematics at JohnsHopkins University [inBaltimore]. Next year, I'll be able to complete my degree as a full time student while earning my full [NSA] salary. The educational benefits, flexibilityofmy work schedule, and an opportunity towork on challenging problems that don't exist anywhere else in the world made my decision towork at theNSA an easy one. At the NSA, your mathematical education never stops. I've worked on problems whose solutions have involved statistical methods to graph theory to abstract algebra, and in all instances I have had excellent mentors to help me through the process. I can't think of another career I could have chosen thatwould have offeredme the same opportunities, or the feel ing I have when I go home every night knowing that I've done important work." 22 APRIL 2006 This content downloaded from 139.80.123.50 on Thu, 10 Dec 2015 23:38:02 UTC All use subject to JSTOR Terms and Conditions MATH Valerie Nelson has worked mathematician at theNSA HORIZONS as a 'working to live and not living to work' and NSA gives me the opportunity tomaintain a personal life as well as develop myself pro for five years and inbetween work and car ing forher daughter, also finds time to teach at Prince George's Com munity College as an Adjunct Pro fessionally. I have been able to go back to school on a part-time as fessor. After graduating from the Applied Mathematics trainingpro well as a full-time basis while gram in 2004, she chose as her per manent office one thatfocuses pri working here, participate in out reach activities, and work with on nontechnical organizations signals analysis and coding theory.Valerie received her Bachelor's Degree atMorgan State The atmosphere often reminds me of a college campus due to theper marily on University inmathematics and has begun her graduate work inmathe other mission-related Applied ResearchMathematicians Valerie Nelson (sig nals analysis and coding theory)and MichelleWagner (Directorof the NSAMathematical Sciences Program). matics at theUniversity ofMary land-College Park using the supportofNSA's educational ben efits. "My decision tomajor inmathematics actually originated from having a wide range of interests inother fields. Growing up, my father often repeated 'mathematics is at the root of everything.' Therefore, when it came time to choose what to study, I decided to choose math to give myself the flexibility to do whatever Iwanted to do at any time,without having to start from scratch.No matter what I am doing, my education never goes to waste. Math is about problem solving and problem solving never goes out of style. If there is one way I have ben efited frommy mathematics background, it is learning how to analyze an unfamiliar situation through critical analysis and questioning so that the situation is no longer unfamiliar. This is the key to learning anything new and being successful at it. "At NSA, I have been able to combine lots of skills, old and new, to a variety of problems in all types of settings.Cur rently, I am combining abstract algebra and linear algebra, computer science, and engineering to solve problems related to signals analysis and coding theory.At the same time, I have been able to use my business skills toward building and strengtheningour customer base, as well as with networking with other groups [at theNSA] to achieve mutual goals. I have also taught classes at theAgency, mentored summer students, and have been actively involved in thediversity awareness and recruitmentefforts in academia and on the professional front. The work I do is a nice blend of application, theory,and per sonal interaction,which ismy preferred chemistry.My other [past] employers could not offerme that, and I don't believe many others could do that today. "As a mother, theNSA work lifehas also been a significant factor inmy decision towork here. The flexibility ofmy work schedule and the benefits offered here have enabled me to actually have a personal life more easily than any other employer I've ever had. I strongly believe in the ideal of activities. sonal climate it has. I get work done, make friends, and have fun at the same time.This mix iswhat makes the big difference tome and iswhy I am here today." Megan Waterman has been working at theNSA as a mathe matician since June 2002. She has a Bachelor's Degree in mathematics and economics in from Nazareth College Rochester, NY and holds aMaster's and PhD in statistics from Virginia Polytechnic University, where she worked with advi sorsDr. JeffreyBirch and Dr. Oliver Schabenberger. "I have an interesting connection between Math Horizons and NSA. When I was an undergraduate at Nazareth College, I came across an article inMath Horizons about mathemati cians at theNSA. At the time, I decided to go ahead to gradu ate school immediately after finishing my bachelor's degree, but made a mental note that theNSA might be a fun place to work at some point. Some ofmy favorite classes as an under graduate were statisticalmethods and mathematical modeling, so I knew Iwanted to go to graduate school for either Statistics or applied mathematics. I ended up doing a PhD in statistics, focusing on semi-parametric mixed models formy disserta tion. "I was intrigued by working for the government, and applied to three or four different agencies after finishingmy PhD, including theNSA. I decided to take the job at theNSA and was hired into theApplied Mathematics Program. While in theprogram, I spent threeyears working on a variety of dif ferentprojects, including informationprocessing, evaluations of new technologies, and computer security. I've programmed and taken classes in a number of programming and scripting languages, and have also taken classes in cryptomathematic techniques, coding theory, and algorithm/stack development. Some of these classes were required as part ofmy trainingpro gram and some were optional courses that I took to enhance my professional development here at theAgency. I really enjoy the flexibility of working for the government and find thework atNSA challenging and important." WWW.MAA.ORG/MATHHORIZONS 23 This content downloaded from 139.80.123.50 on Thu, 10 Dec 2015 23:38:02 UTC All use subject to JSTOR Terms and Conditions