Topics in Computational Number Theory Inspired by Peter L. Montgomery

ISBN-13: 9781107109353 / Angielski / Twarda / 2017 / 276 str.

Joppe W. Bos; Arjen K. Lenstra

Opis

This book highlights the many ideas and algorithms that Peter L. Montgomery has contributed to computational number theory and cryptography.

Spis treści

1. Introduction Joppe W. Bos, Arjen K. Lenstra, Herman te Riele and Daniel Shumow; 2. Montgomery arithmetic from a software perspective Joppe W. Bos and Peter L. Montgomery; 3. Hardware aspects of Montgomery modular multiplication Colin D. Walter; 4. Montgomery curves and the Montgomery ladder Daniel J. Bernstein and Tanja Lange; 5. General purpose integer factoring Arjen K. Lenstra; 6. Polynomial selection for the number field sieve Thorsten Kleinjung; 7. The block lanczos algorithm Emmanuel Thomé; 8. FFT extension for algebraic-group factorization algorithms Richard P. Brent, Alexander Kruppa and Paul Zimmermann; 9. Cryptographic pairings Kristin Lauter and Michael Naehrig.