Primality in polynomial time

François Morain

Séminaire Bourbaki (2002-2003)

  • Volume: 45, page 205-230
  • ISSN: 0303-1179

Abstract

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Primality is one of the simplest and oldest problems in number theory. At the end of the seventies, Adleman, Pomerance and Rumely have designed the first deterministic primality proving algorithm, whose running time was quasi polynomial. Twenty years later, Agrawal, Kayal and Saxena gave the first algorithm running in polynomial time. The talk will present all these works, and will also include the description of some of the primality algorithms invented during this period.

How to cite

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Morain, François. "La primalité en temps polynomial." Séminaire Bourbaki 45 (2002-2003): 205-230. <http://eudml.org/doc/252132>.

@article{Morain2002-2003,
abstract = {Le problème de la primalité est l’un des problèmes les plus simples et les plus anciens de la théorie des nombres. À la fin des années 1970, Adleman, Pomerance et Rumely ont donné le premier algorithme de primalité déterministe, dont le temps de calcul était presque polynomial. Il a fallu 20 années supplémentaires pour qu’Agrawal, Kayal et Saxena donnent un algorithme déterministe de temps de calcul polynomial. L’exposé présentera ces travaux, et il fera également le point sur les différents autres algorithmes inventés dans cette période.},
author = {Morain, François},
journal = {Séminaire Bourbaki},
keywords = {primality proving; Jacobi sums; elliptic curves; hyperelliptic curves; complex multiplication; finite fields},
language = {fre},
pages = {205-230},
publisher = {Association des amis de Nicolas Bourbaki, Société mathématique de France},
title = {La primalité en temps polynomial},
url = {http://eudml.org/doc/252132},
volume = {45},
year = {2002-2003},
}

TY - JOUR
AU - Morain, François
TI - La primalité en temps polynomial
JO - Séminaire Bourbaki
PY - 2002-2003
PB - Association des amis de Nicolas Bourbaki, Société mathématique de France
VL - 45
SP - 205
EP - 230
AB - Le problème de la primalité est l’un des problèmes les plus simples et les plus anciens de la théorie des nombres. À la fin des années 1970, Adleman, Pomerance et Rumely ont donné le premier algorithme de primalité déterministe, dont le temps de calcul était presque polynomial. Il a fallu 20 années supplémentaires pour qu’Agrawal, Kayal et Saxena donnent un algorithme déterministe de temps de calcul polynomial. L’exposé présentera ces travaux, et il fera également le point sur les différents autres algorithmes inventés dans cette période.
LA - fre
KW - primality proving; Jacobi sums; elliptic curves; hyperelliptic curves; complex multiplication; finite fields
UR - http://eudml.org/doc/252132
ER -

References

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