| 1 |
Jan 9 |
Introduction; Caesar cyhpers |
1.1 |
- |
- |
- |
| 2 |
Jan 11 |
Intro to Python; Substitution cyphers |
1.1 |
- |
- |
HW1 posted. |
| 3 |
Jan 13 |
Divisibility |
1.2 |
quiz0.pdf |
quiz0-soln.pdf |
Quiz 0 in class. |
| 4 |
Jan 18 |
Integer division: quotient and remainders |
1.2 |
- |
- |
HW1 due. HW2 posted. |
| 5 |
Jan 20 |
GCDs; Integer Linear Combinations |
1.2 |
quiz1.pdf |
quiz1-soln.pdf |
Quiz 1 in class. |
| 6 |
Jan 23 |
Extended Euclidean Algorithm |
1.2 |
- |
- |
- |
| 7 |
Jan 25 |
Algorithm analysis; EEA runtime analysis |
1.2 |
- |
- |
HW2 due. HW3 posted. |
| 8 |
Jan 27 |
Modular Arithmetic |
1.3 |
quiz2.pdf |
quiz2-soln.pdf |
Quiz 2 in class. |
| 9 |
Jan 30 |
Ring of integers modulo m; Addition, Mult. tables; Inverses |
1.3 |
- |
- |
- |
| 10 |
Feb 1 |
Group of units; Euler phi function; mod. arithmetic as a shift cipher |
1.3,1.3.1 |
- |
- |
HW3 due. HW4 posted. |
| 11 |
Feb 3 |
Test 1: Lects 1-9; Secns 1.1-1.3 (not including 1.3.1 or 1.3.2) |
- |
test1.pdf |
test1-soln.pdf |
Test 1 in class |
| 12 |
Feb 6 |
Modular Exponentiation |
1.3.2 |
- |
- |
- |
| 13 |
Feb 8 |
Fundamental Theorem of Arithmetic; Finite Fields |
1.4,1.5 |
- |
- |
HW4 due. HW5 posted. |
| 14 |
Feb 10 |
Fermat's Little Theorem |
1.5 |
quiz4.pdf |
quiz4-soln.pdf |
Quiz 4 in class. |
| 15 |
Feb 13 |
Fermat's Little Theorem applications; Fermat Primality Test; Primitive roots |
1.5 |
- |
- |
- |
| 16 |
Feb 15 |
Brief history; Simple ciphers: Definitions, Theory |
1.6,1.7 |
- |
- |
HW5 due. HW6 posted. |
| 17 |
Feb 17 |
Encodings |
1.7 |
quiz5.pdf |
quiz5-soln.pdf |
Quiz 5 in class. |
| 18 |
Feb 20 |
Multiplicative and shift ciphers; Exclusive-OR cipher |
1.7 |
- |
- |
- |
| 19 |
Feb 22 |
Discrete Logarithm |
2.2 |
- |
- |
HW6 due. HW7 posted. |
| 20 |
Feb 24 |
Diffie--Hellman Key Exchange |
2.3 |
quiz6.pdf |
quiz6-soln.pdf |
Quiz 6 in class. |
| 21 |
Feb 27 |
ElGamal Cryptosystem |
2.4 |
- |
- |
- |
| 22 |
Mar 1 |
Order notation, Shank's Algorithm |
2.6,2.7 |
- |
- |
HW7 due. HW8 posted. |
| 23 |
Mar 3 |
Shank's Algorithm |
2.7 |
quiz7.pdf |
quiz7-soln.pdf |
Quiz 7 in class. |
| 24 |
Mar 6 |
Chinese Remainder Theorem |
2.8 |
- |
- |
- |
| 25 |
Mar 8 |
CRT II; Discrete root problem |
2.8,3.1 |
- |
- |
- |
| 26 |
Mar 10 |
Test 2: Classes 10-23; Sections 1.3.1,1.3.2,1.4--1.7, 2.2-2.4, 2.6-2.7 |
- |
test2.pdf |
test2-soln.pdf |
- |
| 27 |
Mar 20 |
Discrete Roots |
3.1 |
- |
- |
- |
| 28 |
Mar 22 |
RSA Cryptosystem |
3.2 |
- |
- |
HW9 posted. |
| 29 |
Mar 24 |
Equivalance of computing N' and factoring |
3.2 |
quiz8.pdf |
quiz8-soln.pdf |
Quiz 8 in class. |
| 30 |
Mar 27 |
Implementation/Security Concerns |
3.3 |
- |
- |
- |
| 31 |
Mar 29 |
Prime Number Theorem; Carmichael numbers |
3.4 |
- |
- |
HW9 due. HW10 posted. |
| 32 |
Mar 31 |
Primality testing: Fermat Witnesses and Miller--Rabin Witnesses |
3.4 |
quiz9.pdf |
quiz9-soln.pdf
| Quiz 9 in class. |
| 33 |
Apr 3 |
RSA Digital Signatures |
4.1,4.2 |
- |
- |
- |
| 34 |
Apr 5 |
ElGamal Digital Signatures; Primality Test Pseudocode |
4.3,3.4 |
- |
- |
HW10 due. HW11 posted. |
| - |
Apr 7 |
Holiday--- no class |
- |
- |
- |
- |
| 35 |
Apr 10 |
Elliptic Curves |
6.1 |
- |
- |
- |
| 36 |
Apr 12 |
Elliptic Curves over Finite Fields |
6.2 |
- |
- |
HW11 due. HW12 posted. |
| 37 |
Apr 14 |
Test 3: Classes 24--35; Sections 2.8, 3.1-3.4, 4.1-4.3, 6.1 |
- |
test3.pdf |
test3-soln.pdf |
Test 3 in class. |
| 38 |
Apr 17 |
Elliptic Curve Discrete Logarithm Problem (ECDLP); Elliptic Curve Diffie-Hellman (ECDH) |
6.3,6.4 |
- |
- |
- |
| 39 |
Apr 19 |
Elliptic Curve ElGamal; Hash Functions |
6.4,8.1 |
- |
- |
HW12 due. HW13 posted. |
| 40 |
Apr 21 |
Pseudorandom Number Generators (PRNGs) |
8.2 |
quiz12.pdf |
quiz12-soln.pdf |
Quiz 12 in class |
| 41 |
Apr 24 |
Zero-knowledge Proofs |
8.3 |
- |
- |
- |
| 42 |
Apr 26 |
Secret Sharing; Lagrange interpolation |
8.4 |
- |
- |
HW13 due. |
| 43 |
Apr 28 |
Review |
- |
- |
- |
- |
| - |
May 4 |
Final Exam: Thursday May 4, 2pm-4pm |
- |
- |
- |
- |