8 - Efficient Modular Arithmetic
from Part II - Implementations
Published online by Cambridge University Press: 11 November 2021
Summary
In Chapter 8, Efficient Modular Arithmetic, Joppe W. Bos, Thorsten Kleinjung and Dan Page discuss how to realise efficient modular arithmetic in practice on a range of platforms. They cover generic modular multiplication routines such as the popular Montgomery multiplication as well as special routines for primes of a specific shape. Moreover, especially fast methods are outlined that might produce errors with a very small probability. Such faster 'sloppy reduction' techniques are especially beneficial in cryptanalytic settings. Bos, Kleinjung and Page have all been involved in various cryptographic and cryptanalytic record-setting software implementations. In Chapter 8 they explain how to select the most efficient modular arithmetic routines for the cryptologic implementation task at hand.
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- Computational CryptographyAlgorithmic Aspects of Cryptology, pp. 223 - 250Publisher: Cambridge University PressPrint publication year: 2021