1.0 Introduction

2.0 Elliptic Curve Groups Over Real Numbers

2.1 Elliptic Curve Addition: A Geometric Approach

2.1.1 Adding distinct points P and Q

2.1.2 Adding the points P and -P

2.1.3 Doubling the point P

2.1.4 Doubling P if y P = 0

2.2 Elliptic Curve Addition: An Algebraic Approach

2.2.1 Adding distinct points P and Q

2.2.2 Doubling the point P

2.3 Experiment: An Elliptic Curve Model (real numbers)

2.4 Quiz 1 Elliptic curve groups over real numbers

3.0 Elliptic Curve Groups Over

3.1 An Example of an Elliptic Curve Group over Fp

3.2 Arithmetic in an Elliptic Curve Group over Fp

3.2.1 Adding distinct points P and Q

3.2.2 Doubling the point P

3.3 Experiment: An Elliptic Curve Model (over Fp)

3.4 Quiz 2 Elliptic curve groups over Fp

4.0 Elliptic Curve Groups Over F 2 m

4.1 An Example of an Elliptic Curve Group over F 2 m

4.2 Arithmetic in an Elliptic Curve Group over F 2 m

4.2.1 Adding the distinct points P and Q

4.2.2 Doubling the point P

4.3 Experiment: An Elliptic Curve Model (over F 2 m )

4.4 Quiz 3 Elliptic curve groups over F 2 m

5.0 EC Groups and the Discrete Log Problem

5.1 Scalar Multiplication

5.2 The Elliptic Curve Discrete Logarithm Problem

5.3 An Example of the Elliptic Curve Discrete Logarithm Problem

5.3.1 An ECDLP Solution