Big: Num Math. Implementing Cryptographic Multiple Precision Arithmetic

Implementing cryptography requires integers of significant magnitude to resist cryptanalytic attacks. Modern programming languages only provide support for integers which are relatively small and single precision. The purpose of this text is to instruct the reader regarding how to implement efficient multiple precision algorithms. Bignum math is the backbone of modern computer security algorithms. It is the ability to work with hundred-digit numbers efficiently using techniques that are both elegant and occasionally bizarre. This book introduces the reader to the concept of bignum algorithms and proceeds to build an entire library of functionality from the ground up. Through the use of theory, pseudo-code and actual fielded C source code the book explains each and every algorithm that goes into a modern bignum library. Excellent for the student as a learning tool and practitioner as a reference alike BigNum Math is for anyone with a background in computer science who has taken introductory level mathematic courses. The text is for students learning mathematics and cryptography as well as the practioner who needs a reference for any of the algorithms documented within. * Complete coverage of Karatsuba Multiplication, the Barrett Algorithm, Toom-Cook 3-Way Multiplication, and More * Tom St Denis is the developer of the industry standard cryptographic suite of tools called LibTom. * This book provides step-by-step exercises to enforce concepts Implementing cryptography requires integers of significant magnitude to resist cryptanalytic attacks. Modern programming languages only provide support for integers which are relatively small and single precision. The purpose of this text is to instruct the reader regarding how to implement efficient multiple precision algorithms. Bignum math is the backbone of modern computer security algorithms. It is the ability to work with hundred-digit numbers efficiently using techniques that are both elegant and occasionally bizarre. This book introduces the reader to the concept of bignum algorithms and proceeds to build an entire library of functionality from the ground up. Through the use of theory, pseudo-code and actual fielded C source code the book explains each and every algorithm that goes into a modern bignum library. Excellent for the student as a learning tool and practitioner as a reference alike BigNum Math is for anyone with a background in computer science who has taken introductory level mathematic courses. The text is for students learning mathematics and cryptography as well as the practitioner who needs a reference for any of the algorithms documented within. * Complete coverage of Karatsuba Multiplication, the Barrett Algorithm, Toom-Cook 3-Way Multiplication, and More * Tom St Denis is the developer of the industry standard cryptographic suite of tools called LibTom. * This book provides step-by-step exercises to enforce concepts Content: List of Figures , Pages xi-xiv Preface , Pages xv-xviii Chapter 1 - Introduction , Pages 1-12 Chapter 2 - Getting Started , Pages 13-33 Chapter 3 - Basic Operations , Pages 35-52 Chapter 4 - Basic Arithmetic , Pages 53-90 Chapter 5 - Multiplication and Squaring , Pages 91-146 Chapter 6 - Modular Reduction , Pages 147-190 Chapter 7 - Exponentiation , Pages 191-216 Chapter 8 - Higher Level Algorithms , Pages 217-254 Chapter 9 - Number Theoretic Algorithms , Pages 255-288 Bibliography , Pages 289-290 Index , Pages 291-296 Implementing cryptography requires integers of significant magnitude to resist cryptanalytic attacks. Modern programming languages only provide support for integers which are relatively small. Introducing the reader to the concept of bignum algorithms, this book shows how efficient multiple precision algorithms can be implemented.