# Math 5248: Cryptology and number theory

## Fall 2006

Homework/exam schedule and assignments (tentative)
Assignment or Exam Due date Problems
Homework 1 Wed Sept. 20 1.1 Shift cipher: 04, 12, 15
1.2 Reduction/division algorithm: 04, 13, 15
1.5 Multiplicative inverses: 06, 09
1.6 The integers mod m: 10, 18, 20, 22
6.2 Euclidean algorithm: 03, 04, 09
6.3 Computing inverses: 04
Homework 2 Wed Oct. 4 1.7 The affine cipher: 11, 18, 21
3.1 Cryptograms- substitutions: 04
3.2 Anagrams- transposition: 09
4.2 LCM's and GCD's: 03, 07
4.1 The Vigenere cipher: 03, 05, 07, 09
4.4 Expected values: 01
4.5 Friedman attack: 02
Midterm exam 1 Wed. Oct. 11 The exam is here, in PDF, PostScript,
Homework 3 Wed Oct. 25 7.2 RSA cipher: 03, 06
7.3 Primitive roots, discrete logs: 03, 07, 13
7.5 ElGamal cipher: 01, 02, 03
9.1 Fermat's little theorem: 01, 07
9.5 Exponentiation algorithm: 01, 07
23.1 Groups: 02, 04
23.2 Subgroups: 06, 07
23.3 Lagrange's Theorem: 03
23.6 Finite cyclic groups: 02
Homework 4 Wed Nov. 8 15.5 Primitive roots mod p: 04
10.1 Sun Ze's theorem: 01, 02
10.2 Special systems: 03
10.3 Composite moduli: 02, 03
9.6 Square roots mod p: 08
10.8 Euler's criterion: 02, 03, 04
(Removed, for inclusion on Exam 2 -- 10.4 Hensel's lemma)
Midterm exam 2 Wed. Nov. 15 The exam is here, in PDF, PostScript
Homework 5 Wed Dec. 6 13.1 Fermat pseudoprimes: 04, 08
13.6 Miller-Rabin test: 02, 08
12.5 Fast computation of quadratic symbols: 01, 03, 06, 08, 11, 12
18.1 Pollard's rho method: 02
18.2 Pollard's p-1 method: 03
Final exam Wed. Dec. 13 The exam is here, in PDF, PostScript