p 74 3.3.4.2 The Generalized Discrete Logarithm Problem 75 3.3.4.3 Attacks Against DLPs 76 3.4 Hash Functions 77 3.4.1 Introduction 77 3.4.2 Properties of Hash Functions 78 3.4.3 Security of Hash Functions and the Birthday Attack 80 3.4.4 Real Hash Functions 84 3.4.4.1 Classification of Hash Functions 84 3.4.4.2 The Merkle–Damgård Construction 84 3.4.4.3 Structural Weakness 88 3.4.4.4 Security of Real-Life Dedicated Hash Functions 89 3.5 Merkle Trees 91 3.6 Elliptic Curve Cryptography 92 3.6.1 Weierstrass Equations 93 3.6.2 Elliptic Curves 95 3.6.2.1 Definition 95 3.6.2.2 The j -Invariant 95 3.6.2.3 Group Law 96 3.6.3 Elliptic Curves over Finite Fields 102 3.6.3.1椭圆形曲线的示例P 103 3.6.3.2添加点105