1 |
Jan 8 |
Introduction; Caesar Cipher |
1.1 |
- |
- |
- |
2 |
Jan 10 |
Substitution Ciphers |
1.{1,2} |
pdf |
pdf |
Quiz 0 in class; HW1 available. |
3 |
Jan 13 |
Divisibility |
1.2 |
- |
- |
- |
4 |
Jan 15 |
Greatest Common Divisor; Euclidean Algorithm |
1.2 |
- |
- |
- |
5 |
Jan 17 |
Algorithm Analysis |
1.2 |
pdf |
pdf |
Quiz 1 in class; HW2 available. |
6 |
Jan 22 |
Modular Arithmetic I |
1.3 |
- |
- |
Note: HW2 has been modified. |
7 |
Jan 24 |
Modular Arithmetic II |
1.3 |
pdf |
pdf |
Quiz 2 in class; HW3 available. |
8 |
Jan 27 |
Group of Units; Caeser Cipher and Modular Arithmetic |
1.3 |
- |
- |
- |
9 |
Jan 29 |
Fast Powering Algorithm; Primes; Fun. Thm. of Arith. |
1.4 |
- |
- |
- |
10 |
Jan 31 |
Test 1 in class |
1.{1-3} |
pdf |
pdf |
HW4 available. |
11 |
Feb 3 |
Order of primes in integers |
1.4 |
- |
- |
- |
12 |
Feb 5 |
Finite Fields; Modular Exponentiation |
1.{4-5} |
- |
- |
- |
13 |
Feb 7 |
Fermat's Little Theorem |
1.5 |
pdf |
pdf |
Quiz 4 in class. |
14 |
Feb 10 |
Applications of FLT; Order of elts. in finite fields |
1.5 |
- |
- |
HW5 available. |
15 |
Feb 12 |
Primitive Roots |
1.5 |
- |
- |
- |
16 |
Feb 14 |
History of Cryptography; Formal Cryptosystems |
1.{6-7} |
pdf |
pdf |
Quiz 5 in class; HW6 available. |
17 |
Feb 17 |
Properties of ciphers |
1.7 |
- |
- |
- |
18 |
Feb 19 |
Examples: multiplicative cipher; affine cipher |
1.7 |
- |
- |
- |
19 |
Feb 21 |
Exclusive-or; Pseudorandom generators |
1.7 |
pdf |
pdf |
Quiz 6 in class; HW7 available. |
20 |
Feb 24 |
Asymetric ciphers; Discrete Logarithm; Diffe-Hellman |
1.7,2.2,2.3 |
- |
- |
HW7 updated. |
21 |
Feb 26 |
ElGamal 1 |
2.4 |
- |
- |
- |
22 |
Feb 28 |
Test 2 |
1.4-1.7, 2.2, 2.3 |
pdf |
pdf |
- |
23 |
Mar 3 |
Snow Day: No Class |
- |
- |
- |
- |
24 |
Mar 5 |
ElGamal vs. Discrete Log Problem |
2.4 |
- |
- |
- |
25 |
Mar 7 |
Class canceled due to jury duty |
- |
- |
- |
No quiz today. |
26 |
Mar 17 |
Big-Oh notation; algorithm analysis |
2.6 |
- |
- |
HW8 assigned. |
27 |
Mar 19 |
Shanks's Algorithm for DLP |
2.7 |
- |
- |
- |
28 |
Mar 21 |
Chinese Remainder Theorem I |
2.8 |
pdf |
pdf |
Quiz 8 in class |
29 |
Mar 24 |
Chinese Remainder Thm II; Choice of p and g |
2.8,2.9 |
- |
- |
HW9 assigned. |
30 |
Mar 26 |
Euler's formula for pq |
3.1 |
- |
- |
- |
31 |
Mar 28 |
Euler's formula for pq |
3.1 |
pdf |
pdf |
Quiz 9 in class |
32 |
Mar 31 |
Euler's formula for pq; RSA |
3.1,3.2 |
- |
- |
HW10 assigned. |
33 |
Apr 2 |
RSA; Equivalence of factoring N and computing N' |
3.2 |
- |
- |
- |
34 |
Apr 4 |
Test 3 |
2.4-3.1 |
pdf |
pdf |
HW10 due. |
35 |
Apr 7 |
Factoring N vs computing N'; Man-in-the-middle |
3.2, 3.3 |
- |
- |
HW11 assigned. |
36 |
Apr 9 |
Other Implementation Concerns |
3.3 |
- |
- |
- |
37 |
Apr 11 |
Miller--Rabin Primality Testing I |
3.4 |
pdf |
pdf |
HW11 due; Quiz 11 in class |
38 |
Apr 14 |
Miller--Rabin Primality Testing II |
3.4 |
- |
- |
- |
39 |
Apr 16 |
Elliptic Curves |
5.1 |
pdf |
pdf |
HW12 due; Quiz 12 in class |
40 |
Apr 21 |
Elliptic Curves II |
5.1 |
- |
- |
HW13 assigned. |
41 |
Apr 23 |
Elliptic Curve Cryptography |
5.2,5.4 |
- |
- |
- |
42 |
Apr 25 |
Other topics: Quantum Computers, Lattice Based Cryptography, Digital Signatures |
- |
- |
- |
HW13 due. |
- |
Apr 30 |
Final Exam: 11am-1pm |
- |
- |
- |
- |