Certificates for triangular equivalence and rank profiles

Abstract : In this paper, we give novel certificates for triangular equivalence and rank profiles. These certificates enable to verify the row or column rank profiles or the whole rank profile matrix faster than recomputing them, with a negligible overall overhead. We first provide quadratic time and space non-interactive certificates saving the logarithmic factors of previously known ones. Then we propose interactive certificates for the same problems whose Monte Carlo verification complexity requires a small constant number of matrix-vector multiplications, a linear space, and a linear number of extra field operations. As an application we also give an interactive protocol , certifying the determinant of dense matrices, faster than the best previously known one.
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Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01466093
Contributeur : Clément Pernet <>
Soumis le : lundi 13 février 2017 - 13:04:20
Dernière modification le : mercredi 15 février 2017 - 19:09:08
Document(s) archivé(s) le : dimanche 14 mai 2017 - 13:57:35

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  • HAL Id : hal-01466093, version 1
  • ARXIV : 1702.03755

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Jean-Guillaume Dumas, David Lucas, Clement Pernet. Certificates for triangular equivalence and rank profiles. 2017. 〈hal-01466093〉

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