Course meets: MW 11:30-1 in 427 Dennison, and F 11-12 in B737 East Hall (computer lab in the basement).
Instructor: Sergey Fomin, 2858 East Hall, 764-6297, email@example.com
Office hours: MW 1-2 and F 12-1 in 2858 East Hall, and by appointment.
Course homepage: http://www.math.lsa.umich.edu/~fomin/175.html
Invitation to cryptology, by Thomas H. Barr, Prentice Hall, 2002.
Supplementary texts (none required):
The mathematics of ciphers, by S.C.Coutinho, AK Peters, 1998.
Cryptological mathematics, by R.E.Lewand, Mathematical Association of America, 2000.
Introduction to cryptography, by J.A.Buchmann, Springer-Verlag, 2001.
An Introduction to Cryptology and Discrete Math - The Math 175 Coursepack, by C.Greene, P.Hanlon, T.Hsu, and J.Hutchinson.
Prerequisites: Math 115 or equivalent (single-variable calculus) recommended.
Description: This course gives a historical introduction to Cryptology, the science of secret codes. It begins with the oldest recorded codes, taken from hieroglyphic engravings, and ends with the encryption schemes used to maintain privacy during Internet credit card transactions. Since secret codes are based on mathematical ideas, each new kind of encryption method leads in this course to the study of new mathematical ideas and results.
The first part of the course deals with permutation-based codes: substitutional ciphers, transpositional codes, Vigenere ciphers and more complex polyalphabetic substitutions including those created by rotor machines such as the WWII Enigma. The mathematical subjects treated in this section include permutations, modular arithmetic and some elementary statistics.
In the second part of the course, the subject moves to bit stream encryption methods. These include block cipher schemes such as the Data Encryption Standard (DES). The mathematical concepts introduced here are recurrence relations and some more advanced statistical results.
Public key encryption is the subject of the final part of the course. We learn the mathematical underpinnings of Diffie-Hellman key exchange, RSA and Knapsack codes. A substantial number of results from elementary number theory are needed and proved in this section of the course.
There is considerable development of problem-solving skills in Math 175. So, students taking the course should have significant mathematical experience and sophistication.
Grading: There are no quizzes and no exams in the course. The grade will be based on homework together with weekly computer labs.
This course will not be graded on a curve, i.e., there are not a set number of each grade to be given out. Every student with the total score of 90% (resp., 80%, 70%, 60%) is guaranteed the final grade of A (resp., B or higher, C or higher, D or higher).
Homework: There will be four types of homework assignments:
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