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X-WR-CALNAME:GREYC UMR CNRS 6072 - Groupe de Recherche en Informatique, Image, et Instrumentation de Caen
X-ORIGINAL-URL:https://www.greyc.fr
X-WR-CALDESC:évènements pour GREYC UMR CNRS 6072 - Groupe de Recherche en Informatique, Image, et Instrumentation de Caen
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TZID:Europe/Paris
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DTSTART:20250330T010000
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DTSTART;VALUE=DATE:20250616
DTEND;VALUE=DATE:20250621
DTSTAMP:20260419T092842
CREATED:20250604T100324Z
LAST-MODIFIED:20250604T100324Z
UID:11878-1750032000-1750463999@www.greyc.fr
SUMMARY:EJCIFM2025 : Ecole Jeunes Chercheureuses en Informatique Fondamentale et ses Mathématiques
DESCRIPTION:L’objectif principal de cette école est de participer à une éducation de haut niveau pour les jeunes doctorants\, complémentaire de celle de leurs universités. Cela peut être une mise à jour dans certains domaines de leurs recherches\, ou aussi une ouverture vers de nouveaux sujets. En leur présentant l’état de la technique sur des sujets proches de leur spécialité\, nous leur apportons des outils pour mieux s’adapter à divers environnements (utile par exemple avant de passer en postdoc)\, et contribuons à favoriser leur mobilité. \nPour plus d’informations : https://ejcifm2025.sciencesconf.org/
URL:https://www.greyc.fr/event/ejcifm2025-ecole-jeunes-chercheureuses-en-informatique-fondamentale-et-ses-mathematiques/
LOCATION:Sciences 3\, Université\, Caen\, Bâtiment Sciences 3\, Caen\, France
CATEGORIES:Amacc,General,Mad,News
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DTSTART;TZID=Europe/Paris:20250618T140000
DTEND;TZID=Europe/Paris:20250618T150000
DTSTAMP:20260419T092842
CREATED:20250611T114554Z
LAST-MODIFIED:20250611T114554Z
UID:11889-1750255200-1750258800@www.greyc.fr
SUMMARY:Alban Gilard - Computation of the Hilbert Series for the Support-Minors Modeling of the MinRank Problem
DESCRIPTION:The MinRank problem is a simple linear algebra problem: given matrices with coefficients in a field\, find a non trivial linear combina- tion of the matrices that has a small rank. There are several algebraic modeling of the problem. The main ones are: the Kipnis-Shamir modeling\, the Minors modeling and the Support-Minors modeling. The Minors modeling has already been studied a lot\, we know a precise analysis of the complexity of computing a Gröbner basis of the modeling\, through the computation of the exact Hilbert Series for a generic instance. For the Support-Minors modeling\, the first terms of the Hilbert Series were known since 2020\, based on an heuristic and experimental work. Here\, we provide a formula and a proof for the complete Hilbert Series of the Support Minors modeling for generic instances. This is done by adapting well known results on determinantal ideals to an ideal generated by a particular subset of the set of all minors of a matrix of variables. We then show that this ideal is generated by standard monomials having a particular shape\, and derive the Hilbert Series by counting the number of such standard monomials. Following the work done for the Minors Modeling\, we then transfer the properties of this particular determinantal ideal to ideals generated by the Support Minors system\, by adding generic forms. This work allows to make a precise comparison between the Minors and Support Minors modeling\, and a precise estimate of the complex- ity of solving MinRank instances for the parameters of the Mirath signature scheme that is currently at the second round of the NIST standardization process for Additional Digital Signature Schemes.
URL:https://www.greyc.fr/event/alban-gilard-computation-of-the-hilbert-series-for-the-support-minors-modeling-of-the-minrank-problem/
LOCATION:Sciences 3- S3 351
CATEGORIES:General,News,Safe,Séminaire Cryptologie et sécurité
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