MCS 150

Cryptanalysis

January Term 2001

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.

MCS 150: Cryptanalysis--January 2001

	Monday	Tuesday	Wednesday	Thursday	Friday
Jan. 3-5			4 Sinkov ch. 1	5 Modular arithmetic	6 Sinkov ch. 2
Jan. 8-12	8 RSA	9 TEST 1	10 Sinkov. ch. 3	11 Decoding Nazi Secrets*	12 Work on project
Jan. 15-19	15 Matrices	16 TEST 2	17 Sinkov ch. 4 Maple + ...	18	19 Edgar Allan Poe's birthday Deadline for withdrawing
Jan. 22-26	22 TEST 3	23 Sinkov ch. 5	24	25	26 Student project presentations

* http://www.pbs.org/wgbh/nova/decoding/

Textbooks

Elementary Cryptanalysis: A Mathematical Approach by Abraham Sinkov, Mathematical Association of America, c1966
Cryptology by Albrecht Beutelspacher, Mathematical Association of America, c 1994

Course content

Cryptography	Math/stats/computing	Cryptanalysis
Shift ciphers Decimation Affine ciphers	Modular arithmetic Histograms	Solving affine ciphers Brute force solutions
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 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