Topics in Computational Number Theory Inspired by Peter L. Montgomery

Joppe W. Bos, Arjen K. Lenstra

• Publisher: Cambridge University Press
• Year: 2017
• Print ISBN:
  9781107109353
• eBook ISBN:
  9781108548236
• Topic: Mathematics
• Subtopic: Number Theory
• Index: Mathematics

Peter L. Montgomery has made significant contributions to computational number theory, introducing many basic tools such as Montgomery multiplication, Montgomery simultaneous inversion, Montgomery curves, and the Montgomery ladder. This book features state-of-the-art research in computational number theory related to Montgomery's work and its impact on computational efficiency and cryptography. Topics cover a wide range of topics such as Montgomery multiplication for both hardware and software implementations; Montgomery curves and twisted Edwards curves as proposed in the latest standards for elliptic curve cryptography; and cryptographic pairings. This book provides a comprehensive overview of integer factorization techniques, including dedicated chapters on polynomial selection, the block Lanczos method, and the FFT extension for algebraic-group factorization algorithms. Graduate students and researchers in applied number theory and cryptography will benefit from this survey of Montgomery's work.

Table of contents

• Cover
• Half title
• Title
• Copyright
• Contents
• List of Contributors
• Preface
• 1 Introduction
• 2 Montgomery Arithmetic from a Software Perspective
• 3 Hardware Aspects of Montgomery Modular Multiplication
• 4 Montgomery Curves and the Montgomery Ladder
• 5 General Purpose Integer Factoring
• 6 Polynomial Selection for the Number Field Sieve
• 7 The Block Lanczos Algorithm
• 8 FFT Extension for Algebraic-Group Factorization Algorithms
• 9 Cryptographic Pairings
• Bibliography
• Subject Index