Math 418

Index of Hand-outs



Date No. Title
11 Sep 17 01 Course Information
* Public Key Cryptography (2pp.)
* The Dancing Men
13 Sep 17 * The Big-O Notation
* The Number of Digits
* Bit Operations
* Polynomial Time Algorithms
14 Sep 17 * The Division Algorithm
* The Euclidean Algorithm
* The Euclidean Algorithm II
18 Sep 17 * Implementing the gcd in Maple (2pp)
* The Euclidean Algorithm (Maple pgm - 2pp)
* The Extended Euclidean Algorithm
* The Extended Euclidean Algorithm: Examples 1 and 2 (2pp.)
20 Sep 11 * MAPLE homework instructions
* MAPLE hints
* Basic MAPLE Commands (4pp.)
* The Extended Euclidean Algorithm (Matrix Method) (2pp.)
* The Euclidean Algorithm (Maple Program - 2pp.)
* Solving mx + ny = c
21 Sep 17 * Modular Arithmetic
* Solving mx + ny = c and ax = b (mod m)
25 Sep 17 * The Euler phi-function (2pp.)
27 Sep 17 * The Chinese Remainder Theorem (4pp.)
28 Sep 17 * The Binary Power Method (3pp.)
* Review of time estimates for algorithms
02 Oct 17 * The Definition of Cryptosystems
* Classical Cryptosystems (2pp.)
04 Oct 17 * Tasks for Public Key Cryptography
* The RSA Method (4pp.)
05 Oct 17 * Design Features of RSA Keys
* The RSA Challenge (2pp.)
* The Discrete Log Problem (2pp.)
11 Oct 17 * The Order of a Group Element (2pp.)
12 Oct 17 * Orders of elements mod 11
16 Oct 17 * The existence of generators
* DL-Cryptosystems
* History of DL-Cryptosystems
18 Oct 17 * DL-Cryptosystems: Examples (5pp.)
19 Oct 17 * Hashfunctions
23 Oct 17 * The Log Table Method (2pp.)
* Realistic Time/Space Estimates (2pp.)
* The SPH Method
25 Oct 17 * The SPH Method: An Example (Maple - 2pp.)
* DL-Attacks and their consequences (3pp.)
26 Oct 17 * Generators of F_p (2pp.)
29 Oct 17 * Primality Tests
* Pseudoprimes and the Fermat Test (3pp.)
01 Nov 17 * Subgroups and Lagrange's Theorem
02 Nov 17 * Quadratic Residues
* Euler Pseudoprimes and the Euler Test (2pp,)
06 Nov 17 * Strong Pseudoprimes and the Miller-Rabin Test
08 Nov 17 * The Miller-Rabin Primality Test (2pp.)
* Primality Tests: Overview (2pp.)
* Elliptic Curves (2pp.)
09 Nov 17 * Elliptic Curves (Graphs)
13 Nov 17 * Complex Elliptic Curves (2pp.)
* Torsion Points (2pp.)
15 Nov 17 * Elliptic Curves over Q (2pp.)
* Comments and Hints for Term Project
* Elliptic Curves over Finite Fields
20 Nov 17 * Subgroups of Z/NZ x Z/NZ
* Elliptic Curve Cryptosystems (2pp.)
* The Embedding of Plaintexts in E(F_p)
22 Nov 17 * Digital Signature (ECDSA)
* Choosing E and P (2pp.)
23 Nov 17 * Pollard's p - 1 Method
* Lenstra's Factorization Method (2pp.)
27 Nov 17 * Pocklington's Primality Test
* The Goldwasser/Kilian EC Primality Test (2pp.)
29 Nov 17 * Schoof's Algorithm (Basic Ideas) (2pp.)
30 Nov 17 CM Elliptic Curves (2pp.)
* Cornacchia's Algorithm (1918)