Syllabus Math
133
Dr. R. Beezer Spring
2013
Course Description
Math 133. The Art and Science of Secret Writing. This freshman seminar will study the mathematics
of encryption, a science known as cryptology. Considerable attention will be given to the military and
social history of cryptology and the publicpolicy questions raised by its increasing use in conjunction
with the Internet. However, the focus will be on the use of mathematics to create and analyze
encryption algorithms, so the student will need the equivalent of four years of high school
mathematics. A variety of practical exercises will require the use of specialized software and
email programs, so the student should be willing to use unpolished programs on the Windows
platform.
Aims
Students in this course will make a sustained, focused and indepth exploration of cryptology — its
history, its practice and its future. They will gain an appreciation of the exacting nature of mathematics;
the power of mathematics, especially when combined with advances in computing power; and they will
wrestle with the larger societal questions wrought by advances in technology. The seminar
format will allow for customized assignments and spirited discussions. Substantive written
work in mathematics and in position papers will develop and demonstrate their intellectual
independence.
Beyond the general purposes of freshman seminars, this course will have several more specific
goals.

 To introduce the student to the power of discrete mathematics and to become comfortable with
learning new modes of mathematical thought.

 To become familiar with the twothousand year history of cryptology, and to therefore more fully
appreciate the revolutionary nature of the debut of publickey cryptography in the 1970’s.

 To consider critically the societal implications created by the convergence of strong encryption,
cheap computers and ubiquitous computers.

 To become a more informed consumer of encryption technologies, and a more savvy user of
electronic communications.
Prerequisites
This mathematics employed in this course is accessible to any student with four years of high school
mathematics. Practicums will use a variety of software, so students should be willing to learn new tools
and techniques.
Texts
Five books will be required reading. The first is The Code Book, by Simon Singh. This is written for a
general audience and describes the major events in the history of cryptology, along with very readable
accounts of the underlying technical aspects of these events. It begins with Mary Queen of Scots’ trial for
treason on October 15, 1586 and concludes with a presentation on quantum cryptography. Along the way
are discussions of historical ciphers, the German Enigma machine in World War II, the US Federal Data
Encryption Standard (DES), publickey cryptography, and Pretty Good Privacy (PGP). This book is one
of the best popular accounts I have ever read dealing with mathematics and computer science, since the
examples are both nontrivial and accurate, yet are written so that they are understandable by an
educated nonspecialist.
Mathematics and Crytography, by Robert A. Beezer, is a collection of notes about the
relevant mathematics needed to understand classical crytogrpahy and the basics of modern
cryptography.
Cryptonomicon, by Neal Stephenson, is an historical, and futuristic, novel that features
encryption and networks prominently. I will provide notes to accompany your reading of this
novel.
Crypto, by Steven Levy, is a fascinating account of the origins of modern cryptography. James
Bamford’s Shadow Factory is an excellent discussion of recent events involving the US National Security
Agency.
Course Outline

Unit 1 History, Classical Cryptography


Singh, The Code Book


Chapter 1
 The Cipher of Mary Queen of Scots

Chapter 2
 Le Chiffre Indechiffrable

Chapter 3
 The Mechanisation of Secrecy

Chapter 4
 Cracking the Enigma

Chapter 5
 The Language Barrier

Beezer, Mathematics and Cryptography


Chapter MA
 Modular Arithmetic

Chapter B
 Bases

Chapter BA
 Binary Arithmetic

Chapter SS
 Sharing a Secret

Unit 2 Revolution, Modern Ciphers


Beezer, Mathematics and Cryptography


Chapter DHKE
 DiffieHellman Key Exchange

Chapter DL
 Discrete Logarithms

Chapter DHKS
 DiffieHellman Knapsack Encryption

Chapter NT
 Number Theory

Chapter RSA
 RSA (Rivest–Shamir–Adelman) Cryptography

Singh, The Code Book


Chapter 6
 Alice and Bob Go Public

Chapter 7
 Pretty Good Privacy

Unit 3 The Future, Public Policy, Computer Security


Singh, The Code Book


Chapter 8
 A Quantum Leap into the Future

Levy, Crypto


Bamford, Shadow Factory
Practicums
This course will include a variety of practical examples for students to work themselves. Some aspects
of cryptography sound simple when explained, but seem harder when performed, while other aspects never
seem very clear until practiced.

EM Email
 Set up addresses for electronic communication. Experiment with HushMail’s encrypted
email.

STEG Steganography
 Hide an encrypted message in an image, using a software tool designed
for this purpose.

MONO Monoalphabetic Substitution Cipher
 Decode a classic text that is encrypted using
a classical monoalphabetic substitution cipher, using software tools to make the task more
manageable.

VIG Vigenère Cipher
 Decode a classic text that is encrypted using a classical Vigenère cipher,
using software tools to make the task more manageable.

PONT Pontifex
 Practice the Solitaire (Pontifex) algorithm, as described in the novel
Cryptonomicon.

SDES Simplified DES
 Encode and decode messages by hand using an educational version of the
Data Encryption Standard (DES). Participate in a mock distributed bruteforce attack.

PGP13 Pretty Good Privacy
 Become proficient in using the encryption program Pretty Good
Privacy (PGP) for publickey encryption and digital signatures. Understand the basics of key
management. Three separate practicums (key generation, encryption, digital signatures).

TIME Digital Time Stamping
 Learn to use Stamper to digitally timestamp a message.

ANON Anonymous Remailers
 Learn to frustrate traffic analysis by using anonymous remailers
and mixmasters to camaflougue message traffic.
Evaluation
Student achievement and progress will be evaluated by a variety of instruments. Practicums will be
graded on a pass/fail basis. There will be two inclass exams where students will write to display their
understanding of the readings, and the mathematics and protocols of encryption. Some questions will be
computational, some will be short answer or essay questions. The final material on social and public policy
material will require students to craft a research paper on a topic of their choosing, which at
that point they can study with the requisite technical understandings. These papers will be
the basis for inclass presentations, which will lend themselves to further debates among the
students.
Bibliography
The vast majority of the books listed in the following annotated bibliography are available in the UPS
Library.
History
 Alvarez, David J. Secret messages : codebreaking and American diplomacy, 19301945.
Lawrence, KS, University Press of Kansas. 2000. A good history, especially for its coverage
of the preWWII time period.
 Benson, Robert Louis and Michael Warner, Eds. Venona: Soviet espionage and the American
response, 1939–1957. Washington, D.C., National Security Agency, Central Intelligence
Agency. 1996. Cold War era cryptanalysis.
 Calvocoressi, Peter. Top secret ultra. New York, Pantheon Books. 1980. A memoir of
WWIIera cryptanalysis in Europe.
 Clark, Ronald William. The man who broke Purple : the life of Colonel William F. Friedman,
who deciphered the Japanese code in World War II. Boston, Little, Brown. 1977.
 Farago, Ladislas. The broken seal; the story of Operation Magic and the Pearl Harbor disaster.
New York, Random House. 1967. WWIIera cryptanalysis in the Pacific.
 Garlinski, Jozef. The Enigma war. New York, Scribner. 1980. WWIIera cryptanalysis in
Europe.
 Hinsley, F.H. and Alan Stripp, eds. Codebreakers : the inside story of Bletchley Park. Oxford,
New York, Oxford University Press. 1993. The history of Bletchley Park, where English and
American codebreakers helped win WWII.
 Kahn, David. The codebreakers; the story of secret writing. London, Weidenfeld and Nicolson.
1967. The most comprehensive history of cryptology, though insufficient for modern topics.
 Kozaczuk, Wadysaw. Enigma : how the German machine cipher was broken, and how it was
read by the Allies in World War Two. Frederick, Md., University Publications of America.
1984. An account of the Polish efforts to break Enigma, which laid the groundwork for
Bletchley Park to eventually succeed.
 Kippenhahn, Rudolf. Code breaking : a history and exploration. Woodstock, N.Y., Overlook
Press. 1999. The runnerup (to Singh’s The Code Book) as best choice for a history that
also contains some simplified technical explanations.
 Singh, Simon. The code book : the evolution of secrecy from Mary Queen of Scots to quantum
cryptography. New York, Doubleday. 1999. A wellwritten popular account of the history of
cryptology, with excellent technical descriptions.
 Thompson, James Westfall. Secret diplomacy; espionage and cryptography, 15001815. New
York, F. Ungar Pub. Co. 1963. A good account of classical cryptology in Europe.
 United States Army Air Forces. ULTRA and the history of the United States Strategic Air
Force in Europe vs. the German Air Force. Frederick, MD, University Publications of America.
1980. An official report on WWIIera cryptanalysis in Europe.
 Van Der Rhoer, Edward. Deadly magic : a personal account of communications intelligence
in World War II in the Pacific. New York, Scribner. 1978. WWIIera cryptanalysis in the
Pacific.
 Winterbotham, F. W. The Ultra secret. New York, Harper & Row. 1974. Revelation of the
success cracking Enigma at Bletchley Park.
 Yardley, Herbert O. The American Black Chamber. Indianapolis, BobbsMerrill. 1931. A
classic. Yardley was the first cryptologist officially in the employ of the United States.
Texts — Elementary
 Barr, Thomas H. Invitation to Cryptology. Upper Saddle River, NJ, Prentice Hall. 2002.
Advertised for use at the freshman level for students with normal high school preparation in
mathematics.
 Buchmann, Johannes. Introduction to cryptography. New York, SpringerVerlag. 2001.
 Beutelspacher, Albrecht. Cryptology. Washington, DC, Mathematical Association of America.
1994. An entertaining elementary treatment.
 Caloyannides, Michael A. Privacy protection and computer forensics. Norwood, MA, Artech
House. 2004. A howto on protecting your electronic information (and thereby telling you
how to discover others). Practical uses of encryption. Legal issues.
 Churchhouse, Robert. Codes and Ciphers: Julius Caesar, the Enigma, and the Internet.
Cambridge University Press. 2002. Historical exposition of preRSA ciphers and devices,
with associated mathematics. Some brief discussion of DiffieHellman key exchange and RSA.
 Davis, Donald M. The nature and power of mathematics. Princeton, N.J., Princeton University
Press. 1993. Contains a short, elementary section on cryptology.
 Klugerman, Ira H. and Dan Rose. Cracking the code. Lexington, Mass., COMAP. 1993.
Instructional videotape.
 Garfinkel, Simson PGP: pretty good privacy. Sebastopol, CA, O’Reilly & Associates. 1995.
Howto book on how to use the most popular personal encryption software available.
 Lewand, Robert. Cryptological mathematics. Washington, DC, Mathematical Society of
America. 2000. Written for an audience of high school students, this might be the runnerup
for the mathematical text for this course.
 Sinkov, Abraham. Elementary cryptanalysis : a mathematical approach. Washington, D.C.,
Mathematical Association of America. 1980. Highschool level, classical techniques only.
 Smith, Laurence Dwight. Cryptography, the science of secret writing. New York, W. W.
Norton. 1943. Dated. Only covers techniques for classical methods.
Texts — Advanced
 Bauer, Friedrich Ludwig. Decrypted secrets: methods and maxims of cryptology New York,
Springer. 2000. An advanced textbook. Lots of detail on classical methods, and good photos.
 Biham, Eli. Differential cryptanalysis of the data encryption standard. New York,
SpringerVerlag. 1993. Detailed mathematical treatment of the first successful application of
differential cryptanalysis.
 Bouwmeester, Dirk and Artur Ekert and Anton Zeilinger, Eds. The physics of quantum
information : quantum cryptography, quantum teleportation, quantum computation. New
York, Springer. 2000. Good account of possibilities for quantum computing in cryptographic
applications.
 Brassard, Gilles. Modern cryptology: a tutorial. New York, SpringerVerlag. 1988. Very short,
very advanced.
 Electronic Frontier Foundation. Cracking DES : secrets of encryption research, wiretap
politics & chip design. Sebastopal, CA, O’Reilly & Associates, Inc. 1998. Fantastic break of
DES with cheap hardware, with this report prepared for distribution simultaneous with the
announcement of the break.
 Friedman, William F. The Riverbank publications. Laguna Hills, Calif., Aegean Park Press.
1979. A bit odd, but written by one of the key figures in the history of American
cryptanalysis.
 Garrett, Paul. Making, breaking codes: an introduction to cryptography Upper Saddle River,
NJ, Prentice Hall. 2001. An upperdivision textbook.
 Goldreich, Oded. Foundations of cryptography: basic tools. Cambridge University Press. 2001.
 Koblitz, Neal. Algebraic aspects of cryptography. New York, Springer. 1998. Beginning
graduate level text.
 Koblitz, Neal. A course in number theory and cryptography. New York , SpringerVerlag.
1994. An advanced textbook, with heavy doses of number theory.
 Kullback, Solomon. Statistical methods in cryptanalysis. Laguna Hills, Calif., Aegean Park
Press. 1976. Serious applications of statistics in the service of cryptanalysis.
 Menezes, A. J. and Paul van Oorschot and Scott Vanstone. Handbook of applied cryptography.
Boca Raton, FL, CRC Press. 1997. Reference work of choice for professionals.
 Patterson, Wayne, 1945 Mathematical cryptology for computer scientists
and mathematicians. Totowa, N.J., Rowman & Littlefield. 1987. A very nice upperdivision
text, but quickly becoming outdated.
 Schneier, Bruce. Applied cryptography : protocols, algorithms, and source code in C. New
York, Wiley. 1996. The most popular technical reference on the topic. Includes mathematics,
algorithms and protocols.
 Stallings, William. Cryptography and network security: principles and practice. Upper Saddle
River, N.J., Prentice Hall. 1999. Very good textbook for an upperdivision audience.
 Stinson, Douglas R. Cryptography: theory and practice. Boca Raton, CRC Press. 1995. A
good choice for an upperdivision text.
 Wayner, Peter. Disappearing Cryptography. Morgan Kaufmann. 2002. Howto on
steganography, watermarking, mimicry, etc.
 Williams, Colin P. Explorations in quantum computing. Santa Clara, Calif., TELOS. 1998.
Public Policy

Agre, Philip E. and Marc Rotenberg, Eds. Technology and privacy: the new landscape.
Cambridge, Mass., MIT Press. 1997. Essays from a variety of perspectives about privacy
with regard to technological changes (such as progress in cryptology).
 Bamford, James. The puzzle palace : a report on America’s most secret agency. Boston,
Houghton Mifflin. 1982. A classic history of the National Security Agency.
 Bamford, James. Body of secrets: anatomy of the ultrasecret National Security Agency. New
York, Doubleday. 2001. An updated critique of the National Security Agency.
 Dam, Kenneth W. and Herbert S. Lin, eds. Cryptography’s role in securing the information
society. Washington, DC, National Academy Press. 1996. A report of the National Research
Council’s Computer Science and Telecommunications Board’s Committee to Study National
Cryptography Policy.
 Diffie, Whitfield and Susan Landau. Privacy on the line: the politics of wiretapping and
encryption. Boston, MIT Press. 1998. Public policy, as viewed by one of the pioneers of
publickey cryptography (Diffie), and one of today’s leading industrial cryptologists (Landau).
 Hoffman, Lance J., ed. Building in big brother: the cryptographic policy debate. New York,
SpringerVerlag. 1995. Fiftyfour essays on a variety of topics. An excellent source of a wide
range of opinions, though some of it is now out of date.
 Lessig, Lawrence. Code and other laws of cyberspace. Basic Books. 2000. Lessig writes on
the interplay of networks, encryption, copyrights and the law.
 Lessig, Lawrence. The future of ideas : the fate of the commons in a connected world. Vintage.
2002. Lessig writes on the interplay of networks, encryption, copyrights and the law.
 Lessig, Lawrence. Free culture: how big media uses technology and the law to lock down culture
and control creativity. Penguin Books. 2000. Lessig writes on the interplay of networks,
encryption, copyrights and the law.
Cryptologic Puzzle Books
 Chronicle Books. Mensa Secret Codes for Kids Chronicle Books. 2001.
 Fowler, Mark and Sarah Dixon and Radhi Parekh. The Usborne Book of Superpuzzles Usborne
Publishing Limited, London. 1994. A collection containing Codes and Ciphers by Mark
Fowler, with numerous puzzles based on historical codes and ciphers.
Miscellaneous
 Brown, Dan. Digital Fortress: A Thriller. St. Martin’s Griffin, 2000. A novel about the NSA’s
head cryptographer, Susan Fletcher, “a brilliant, beautiful mathematician.”
 Brown, Dan. The Da Vinci Code. Doubleday, 2003. Bestseller with a main character (Sophie
Neveu) who is a cryptanalyst. Contains a few simple puzzles of a cryptographic nature.
 Budd, Louis J. and Edwin H. Cady, Eds. On Poe. Durham, Duke University Press. 1993.
Essay on pages 4054 by Friedman details Poe as a cryptologist.
 Sarah Flannery In Code: A Mathematical Journey. Mathematical Association of America.
2000. True story of a 16yearold female cryptographer.
 Friedman, William F. The Shakespearean ciphers examined. Cambridge, Cambridge
University Press. 1957. A hobby of one of the key figures in the history of American
cryptanalysis.
 Harris, Robert Enigma Ivy Books. 1996. A novel set at Bletchly Park in 1943.
 Stephenson, Neal. Cryptonomicon. New York, Avon Press. 1999. A novel whose settings
alternate between WWII cryptography and modernday Internet cryptography. Includes the
Solitaire algorithm, which uses a deck of playing cards for its keystream.