MCS 150

Cryptanalysis

January Term 2007

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 (Note that there is no "j" in it.)
Homepage: http://www.gac.edu/~holte
Schedule Office hours: 1:30-2:20 MTWRF

Textbooks

Elementary Cryptanalysis: A Mathematical Approach by Abraham Sinkov, Mathematical Association of America, c1966
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

10:30-12:20	MTWRF	Olin 321
2:30-3:20	MTWRF	Olin 329/326

Faithful attendance and participation are required.

Course web site

http://www.gac.edu/~holte/courses/mcs150-J07/

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 Solving a x = b (mod m) 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

Syllabus

Dates	Reading: Sinkov	Reading: Singh	Class/lab topics
Jan. 3-4	Ch. 1	Introduction	Direct standard alphabets Modular arithmetic & affine transformations
Jan. 5	2.1-2.2	Ch. 1	Aristocrats: Monoalphabets with word divisions
Jan. 8	2.3-2.4		Patristocrats: Monoalphabets without word divisions Monoalphabets with symbols as cipher equivalents
Jan. 9			Exam 1
Jan. 10-12	Ch. 3	Chs. 2-4	Polyalphabetic substitution
Jan. 15			Exam 2
Jan. 16-17	Ch. 4		Polygraphic systems
Jan. 18-19		Ch. 6	Public-key cryptography
Jan. 22			Exam 3
Jan. 23-24	Ch. 5		Transpositions
Jan. 25-26			Student reports and presentations

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

Academic honesty

"The faculty of Gustavus Adolphus College expects all students to adhere to the highest standards of academic honesty... In all academic exercises, examinations, papers, and reports, students shall submit their own work. Footnotes or some other acceptable form of citation must accompany any use of another's words or ideas."
"The following code will be written in full and signed on every examination and graded paper:
'On my honor, I pledge that I have not given, received, or tolerated others' use of unauthorized aid in completing this work.'"
The complete statement of the honor policy may be found at: http://www.gac.edu/oncampus/academics/general_catalog/current/acainfo.cfm.
"By enrolling classes at Gustavus, you have taken up membership in a worldwide community of scholars, and like any community, Academia has ethical standards to which you are expected to adhere. You are expected to learn and follow the principles of honesty and integrity that apply in academic life. Among those standards are that you faithfully represent your own work, acknowledge any borrowing from the work of others, avoid falsifying data or sources, be respectful of other scholars' efforts and not interfere with their access to resources (e.g., by misappropriating or damaging library materials), do a fair share of the work in group efforts, give others the benefit of your informed opinions and observations in discussion, and be respectful of others' values, knowledge, and feelings while developing your own.... Regrettably, serious and deliberate violations of ethics may incur serious penalties.... If you are in doubt about whether your work conforms to ethical standards, please inquire--you are, after all, a learner." --John Rezmerski, Advising and Registration Manual 1995-96, pp. 60-61.
A first violation of the academic honesty policy will result in a zero grade on the paper in question and a report to the office of the Dean of the Faculty. A second case will result in a failing grade for the course.

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