Table of Contents

Cover

Title page

Copyright

List of Figures

Preface

Chapter 1: Introduction

1.1 Multiple Precision Arithmetic

1.2 Purpose of This Text

1.3 Discussion and Notation

1.4 Exercises

1.5 Introduction to LibTomMath

1.6 Choice of LibTomMath

Chapter 2: Getting Started

2.1 Library Basics

2.2 What Is a Multiple Precision Integer?

2.3 Argument Passing

2.4 Return Values

2.5 Initialization and Clearing

2.6 Maintenance Algorithms

2.6.1 Augmenting an mp_int’s Precision

2.6.2 Initializing Variable Precision mp_ints

Chapter 3: Basic Operations

3.1 Introduction

3.2 Assigning Values to mp_int Structures

3.3 Zeroing an Integer

3.4 Sign Manipulation

3.5 Small Constants

3.6 Comparisons

Chapter 4: Basic Arithmetic

4.1 Introduction

4.2 Addition and Subtraction

4.3 Bit and Digit Shifting

4.4 Polynomial Basis Operations

4.5 Powers of Two

Chapter 5: Multiplication and Squaring

5.1 The Multipliers

5.2 Multiplication

5.3 Squaring

Chapter 6: Modular Reduction

6.1 Basics of Modular Reduction

6.3 The Montgomery Reduction

6.4 The Diminished Radix Algorithm

6.5 Algorithm Comparison

Chapter 7: Exponentiation

7.1 Exponentiation Basics

7.2 k–ary Exponentiation

7.3 Modular Exponentiation

7.4 Quick Power of Two

Chapter 8: Higher Level Algorithms

8.1 Integer Division with Remainder

1.1 Single Digit Helpers

8.3 Random Number Generation

8.4 Formatted Representations

Chapter 9: Number Theoretic Algorithms

9.1 Greatest Common Divisor

9.1.1 Complete Greatest Common Divisor

9.2 Least Common Multiple

9.3 Jacobi Symbol Computation

9.4 Modular Inverse

9.5 Primality Tests

Bibliography

Index

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