@inbook{c37092b977814bb792b38183e7b2e8d1,

title = "Integer arithmetic",

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.",

keywords = "multiprecision intergers, addition, subtraction, multiplication, modular reduction, division, greatest common divisor, square root",

author = "Christophe Doche",

year = "2006",

language = "English",

isbn = "9781584885184",

series = "Discrete mathematics and its applications",

publisher = "CRC Press, Taylor & Francis Group",

pages = "169--199",

booktitle = "Handbook of elliptic and hyperelliptic curve cryptography",

address = "United States",

}