Practical Cryptography

9ELLIPTIC CURVE CRYPTOGRAPHY

HAFIZUR RAHMAN AND SAIFUL AZAD

Contents

Keywords

9.1 Introduction

9.2 Elliptic Curves over R

9.3 Elliptic Curves over Z_P

9.3.1 Adding Points in Elliptic Curves over Z_P

9.3.2 Scalar Multiplication

9.4 Discrete Logarithm Problem

9.5 Elliptic Curve Cryptography

9.5.1 Elliptic Curve Diffie–Hellman Key Exchange

9.5.2 Key Exchange Example

9.5.3 Elliptic Curve Encryption/Decryption

9.5.4 Encryption/Decryption Example

9.6 Implementation 1

9.7 Implementation 2

References

Keywords

Asymmetric key algorithm

Diffie–Hellman key exchange

Elliptic curve cryptography

Private key

Public key

9.1 Introduction

Although the RSA algorithm resolves the problem of a secret key, it experiences higher computational cost because of utilizing ...