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Handbook of Elliptic and Hyperelliptic Curve Cryptography

Table of Contents

 Introduction to Public-Key Cryptography
MATHEMATICAL BACKGROUND
Algebraic Background
Background on p-adic Numbers
Background on Curves and Jacobians
Varieties Over Special Fields
Background on Pairings
Background on Weil Descent
Cohomological Background on Point Counting
ELEMENTARY ARITHMETIC
Exponentiation
Integer Arithmetic
Finite Field Arithmetic
Arithmetic of p-adic Numbers
ARITHMETIC OF CURVES
Arithmetic of Elliptic Curves
Arithmetic of Hyperelliptic Curves
Arithmetic of Special Curves
Implementation of Pairings
POINT COUNTING
Point Counting on Elliptic and Hyperelliptic Curves
Complex Multiplication
COMPUTATION OF DISCRETE LOGARITHMS
Generic Algorithms for Computing Discrete Logarithms
Index Calculus
Index Calculus for Hyperelliptic Curves
Transfer of Discrete Logarithms
APPLICATIONS
Algebraic Realizations of DL Systems
Pairing-Based Cryptography
Compositeness and Primality Testing-Factoring
REALIZATIONS OF DL SYSTEMS
Fast Arithmetic Hardware
Smart Cards
Practical Attacks on Smart Cards
Mathematical Countermeasures Against Side-Channel Attacks
Random Numbers-Generation and Testing
REFERENCES

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