# Math 5248: Cryptology and number theory

## Fall 2005

Homework/exam schedule and assignments (tentative)
Assignment or Exam Due date Problems
Homework 1 Wed Sept. 21 1.1 Shift cipher: 05, 13, 15
1.2 Reduction/division algorithm: 05, 10, 12, 15
1.5 Multiplicative inverses: 07, 10
1.6 The integers mod m: 11, 16, 20, 21
6.2 Euclidean algorithm: 01, 06, 08
6.3 Computing inverses: 08
Homework 2 Wed Oct. 5 1.7 The affine cipher: 07, 11, 14
3.2 Anagrams- transposition: 07, 09
4.2 LCM's and GCD's: 04, 05
4.1 The Vigenere cipher: 01, 06, 05, 07, 09
4.4 Expected values: 01
4.5 Friedman attack: 02
Midterm exam 1 Wed. Oct. 12 Take-home exam in PDF, PostScript,
Homework 3 Wed Oct. 26 7.2 RSA cipher: 01, 04
7.3 Primitive roots, discrete logs: 04, 09, 13
7.5 ElGamal cipher: 01, 02, 03
9.1 Fermat's little theorem: 03, 05, 07
9.5 Exponentiation algorithm: 03, 05
23.1 Groups: 04, 07
23.2 Subgroups: 02, 05, 07
23.3 Lagrange's Theorem: 02
23.6 Finite cyclic groups: 04
Homework 4 Wed Nov. 9 10.7 Facts about primitive roots: 01, 02
15.5 Primitive roots mod p: 04
10.1 Sun Ze's theorem: 01, 02
10.2 Special systems: 01, 07
10.3 Composite moduli: 02, 03
9.6 Square roots mod p: 03, 05
10.8 Euler's criterion: 01, 02, 03
(Removed, for inclusion on Exam 2 -- 10.4 Hensel's lemma)
Midterm exam 2 Wed. Nov. 16 Take-home exam in PDF, PostScript,
Homework 5 Wed Dec. 7 13.1 Fermat pseudoprimes: 01, 08
13.6 Miller-Rabin test: 01, 08
12.5 Fast computation of quadratic symbols: 01, 03, 05, 07, 08, 11, 12
18.1 Pollard's rho method: 01
18.2 Pollard's p-1 method: 02
Final exam Wed. Dec. 14 Take-home final exam in PDF, PostScript.