@comment{ generated by }
@Unpublished{ALGO-STUDENT-2007-008,
abstract = {Since the discovery of the utility of the numbers, the
human being tried to differentiate them. We decide
between them according to whether they are even or odd.
Or, according to the fact that they are prime or
composite. A natural number n >1 is called a prime number
if it has no positive divisors other than 1 and n.
Therefore, other numbers that are not prime have other
divisors. That is why we call them composite numbers
because we can write them : n = p*q with {p,q} =ΜΈ {1,n}.
The problem has always been to decide whether a number is
prime or not. To answer this problem, many algorithms
have been created like the Trial Division. It uses the
property which says that the biggest divisor of n is
smaller or equal to the square root of n. But for numbers
that exceed 30 digits, it will take more than 10^13 years
to know the answer. So, the interest would be to create
an algorithm using mathematical bases which would answer
to this question as fast as possible. This is what we
will see in this project. The study of prime numbers
became really important to code texts. Cryptography is
one of the most important application of prime numbers
theory. At the beginning, it was only used to code texts
during the wars and more recently it was used for other
applications, like the security of an account. Fist of
all, I will focus on randomized algorithms for primality
testing. Then, I will focus on a deterministic algorithm
that I have implemented.},
affiliation = {EPFL},
author = {TAHIRI JOUTI, Kamal},
details = {http://infoscience.epfl.ch/record/101087},
documenturl = {https://infoscience.epfl.ch/record/101087/files/Kamal_TAHIRI.pdf},
oai-id = {oai:infoscience.epfl.ch:101087},
oai-set = {IC},
status = {PUBLISHED},
title = {Primality {T}esting},
unit = {ALGO},
url = { },
year = 2006
}