Date 
No. 
Title 
11 Sep 17  01

Course Information

 *

Public Key Cryptography (2pp.)

 *

The Dancing Men

13 Sep 17  *

The BigO 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 phifunction (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

 *

DLCryptosystems

 *

History of DLCryptosystems

18 Oct 17  *

DLCryptosystems: 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.)

 *

DLAttacks 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 MillerRabin Test

08 Nov 17  *

The MillerRabin 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)
