MCS 150

Cryptanalysis

January Term 2003

This is a course in making and breaking codes. Students will be engaged in learning how to ``crack'' enciphered messages without knowing, at the outset, the enciphering keys. Beginning with cryptograms of the sort found in newspapers and puzzle books, we shall work our way through successively more complicated enciphering schemes and learn methods of attack based on exhaustive search, computer programs, statistics, and mathematics. This course will also survey the history of cryptography and modern developments, including public-key cryptography and data encryption techniques.

Instructor: John Holte

Office: Olin 307
Telephone: x7465
E-mail: holte@gustavus.edu
Homepage: http://www.gac.edu/~holte
Schedule

Textbooks

Elementary Cryptanalysis: A Mathematical Approach by Abraham Sinkov, Mathematical Association of America, c1966
Cryptological Mathematics by Robert Edward Lewand, Mathematical Association of America, c2000

The Codebreakers: the Story of Secet Writing by David Kahn, 1967. This is probably the most complete and accurate encyclopedic history of cryptography up to the 1960s.
The Code Book: The Evolution of Secrecy from Mary Queen of Scots to Quantum Cryptography by Simon Singh, 1999. This is a lively, readable survey of cryptography, but according the American Mathematical Society review, its telling of history is flawed.

Class meetings

12:30-3:20 MTWRF
Olin 320
Faithful attendance and participation are required.

Course web site

http://www.gac.edu/~holte/courses/mcs150-J03/

Work outside class

January Term is ideally suited for learning by immersion in a single course, and you will learn Cryptanalysis best through the experience of concentrating at length on the problems and theory of "code breaking." It is recommended that you spend time out of class in Olin, where you will be able to work with your team on solving ciphers, to consult with the prof, and to make use of MAPLE and other computer resources.
Official Gustavus January Term policy: "Student workload, including class time, outside reading, and other course-related work, will not be less than 40 hours per week."

Course content

Cryptography	Math/stats/computing	Cryptanalysis
Shift ciphers Decimation Affine ciphers	Modular arithmetic Histograms	Brute force solutions Solving affine ciphers
Monoalphabetic substitution: Aristocrats & Patristocrats	Frequency distributions Combinatorics	Using frequency data Probable word method Pattern words
Polyalphabetic substitution Vigenere cipher	Index of coincidence Prime factorization Periods of sequences	Use of I.C. and Kasiski analysis Reduction to a monoalphabet
Polygraphic systems Playfair cipher Hill's system	Matrix operations Digraph frequencies Solving a x = b (mod m)	Known plaintext attack Solving Hill ciphers by algebra
Transposition ciphers	Permutations Division algorithm	Paper and scissors methods
Public key encryption	Fermat's Little Theorem Chinese Remainder Theorem	Factorization attacks

Academic honesty

Gustavus Guide

Grading

Team solutions of cryptograms (best 5 of 6 @8% each)	40%
Individual problem solutions	16%
Tests (3 @8%)	24%
Report/project	20%
Total	100%
Extra credit	TBA

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