ECC Classroom CONTENTS

notes an interactive, Java enabled EC experiment,
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_{ECC Classroom CONTENTS}
_{INTRODUCTION 1.0}

_{ELLIPTIC CURVE GROUPS OVER REAL NUMBERS 2.0}
_{Elliptic Curve Addition: A Geometric Approach 2.1}
_{Adding distinct points P and Q 2.1.1}
_{Adding the points P and -P 2.1.2}
_{Doubling the point P 2.1.3}
_{Doubling P if yP = 0 2.1.4}
_{Elliptic Curve Addition: An Algebraic Approach 2.2}
_{Adding distinct points P and Q 2.2.1}
_{Doubling the point P 2.2.2}
_{Experiment: An Elliptic Curve Model (real numbers) 2.3}
_{Quiz 1 Elliptic curve groups over real numbers 2.4}

_{ELLIPTIC CURVE GROUPS OVER Fp 3.0}
_{An Example of an Elliptic Curve Group over Fp 3.1}
_{Arithmetic in an Elliptic Curve Group over Fp 3.2}
_{Adding distinct pints P and Q 3.2.1}
_{Doubling the point P 3.2.2}
_{Experiment: An Elliptic Curve Model (over Fp) 3.3}
_{Quiz 2 Elliptic curve groups over Fp 3.4}

_{ELLIPTIC CURVE GROUPS OVER}F₂m4.0
_{An Example of an Elliptic Curve Group over} F₂m_4.1
_{Arithmetic in an Elliptic Curve Group over}F₂m_4.2
_{Adding the distinct points P and Q 4.2.1}
_{Doubling the point P 4.2.2}
_{Experiment: An Elliptic Curve Model (over}F₂m_{) 4.3}
_{Quiz 3 Elliptic curve groups over}F₂m_4.4

_{EC GROUPS AND THE DISCRETE LOGARITHM PROBLEM 5.0}
_{Scalar Multiplication 5.1}
_{The Elliptic Curve Discrete Logarithm Problem 5.2}
_{An Elliptic Curve Discrete Logarithm Problem Challenge 5.3}
_{ECDLP Challenge Solution 5.3.1}

_{INTRODUCTION TO THE ELLIPTIC CURVE ENCRYPTION SCHEME 6.0}
_{ECES ~ Key Agreement 6.1}
_{ECES ~ The Masking Function 6.2}
_{ECES ~ The Exclusive-OR Function 6.3}
_{ECES ~ Putting it All Together 6.4}
_{ECES ~ A Simple Example 6.5}
_{Comments 6.6}

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