Algorithmic Number Theory

The frontiers between computable objects, algorithms (above section), computational number theory and applications to security of cryptographic systems are very porous. This union of research fields is mainly driven by the algorithmic improvement to solve presumably hard problems relevant to cryptography, such as computation of discrete logarithms, resolution of hard subset-sum problems, decoding of random binary codes and search for close and short vectors in lattices. While factorization and discrete logarithm problems have a long history in cryptography, the recent post-quantum cryptosystems introduce a new variety of presumably hard problems/objects/algorithms with cryptographic relevance: the shortest vector problem (SVP), the closest vector problem (CVP) or the computation of isogenies between elliptic curves, especially in the supersingular case.

Related Publications

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[bibtex file=https://who.rocq.inria.fr/Fabrice.Rouillier/Biblio/ouragan_hal.bib key=”barbulescu:hal-01822144″]
[bibtex file=https://who.rocq.inria.fr/Fabrice.Rouillier/Biblio/ouragan_hal.bib key=”biasse:hal-01518438″]
[bibtex file=https://who.rocq.inria.fr/Fabrice.Rouillier/Biblio/ouragan_hal.bib key=”barbulescu:hal-01534101″]
[bibtex file=https://who.rocq.inria.fr/Fabrice.Rouillier/Biblio/ouragan_hal.bib key=”gelin:hal-01362144″]
[bibtex file=https://who.rocq.inria.fr/Fabrice.Rouillier/Biblio/ouragan_hal.bib key=”barbulescu:hal-01363444″]
[bibtex file=https://who.rocq.inria.fr/Fabrice.Rouillier/Biblio/ouragan_hal.bib key=”barbulescu:hal-01155635″]
[bibtex file=https://who.rocq.inria.fr/Fabrice.Rouillier/Biblio/ouragan_hal.bib key=”barbulescu:hal-01112879″]
[bibtex file=https://who.rocq.inria.fr/Fabrice.Rouillier/Biblio/ouragan_ref.bib key=”barbulescu:hal-00835446″]
[bibtex file=https://who.rocq.inria.fr/Fabrice.Rouillier/Biblio/ouragan_ref.bib key=”joux:hal-01213649″]
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[bibtex file=https://who.rocq.inria.fr/Fabrice.Rouillier/Biblio/ouragan_ref.bib key=”JouxTDH”]
[bibtex file=https://who.rocq.inria.fr/Fabrice.Rouillier/Biblio/ouragan_ref.bib key=”DBLP:journals/moc/JouxL03″]

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