Integer arithmetic

Christophe Doche*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

In most of the cases, the integer ring ℤ is the fundamental mathematical layer of many cryptosystems. Once it is possible to compute with integers, one can build on top of them finite fields, then curves and even more complicated objects. More generally, rational, real, complex, and p-adic numbers, but also polynomials with coefficients in these sets, rely on integers and their arithmetic is greatly influenced by the underlying integer algorithms. That is why integer arithmetic is so important and should be performed as efficiently as possible.

Original languageEnglish
Title of host publicationHandbook of elliptic and hyperelliptic curve cryptography
Place of PublicationBoca Raton, Florida, USA
PublisherCRC Press, Taylor & Francis Group
Pages169-199
Number of pages31
ISBN (Electronic)9781420034981
ISBN (Print)9781584885184
Publication statusPublished - 2006

Publication series

NameDiscrete mathematics and its applications
PublisherChapman & Hall/CRC
Volume34

Keywords

  • multiprecision intergers
  • addition
  • subtraction
  • multiplication
  • modular reduction
  • division
  • greatest common divisor
  • square root

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