Enjeux Et Avancées De La Théorie Algorithmique Des Nombres

Enjeux Et Avancées De La Théorie Algorithmique Des Nombres (1992)

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[lix.polytechnique.fr]

by François Morain

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@MISC{Morain92enjeuxet,
    author = {François Morain},
    title = {Enjeux Et Avancées De La Théorie Algorithmique Des Nombres},
    year = {1992}
}

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Abstract

Introduction L'apparition des syst`emes de chiffrement `a clefs publiques de fa¸con g'en'erale [DH76], et du syst`eme de chiffrement RSA en particulier [ARS78], a caus'e un regain d'int'eret pour la th'eorie des nombres et en particulier l'arithm'etique dans ses aspects calculatoires. Pour r'epondre `a des questions aussi simples que celles concernant la d'ecomposition des nombres en facteurs premiers, il a fallu donner des r'eponses algorithmiques prenant en compte la faisabilit'e des calculs ainsi que le temps imparti pour donner une r'eponse satisfaisante. Cela a provoqu'e l'essor de la th'eorie algorithmique des nombres. Cet expos'e est destin'e `a mettre en lumi`ere les progr`es accomplis depuis une dizaine d'ann'ees dans les domaines de la primalit'e des entiers (comment peut-on prouver qu'un entier de quelques centaines de chiffres d'ecimaux est premier) ; factorisation des entiers (quels sont les facteurs d'un nombre qui n'est pas premier) ; logarithme

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