2020 • In Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV), edited by Steven Galbraith, Open Book Series 4, Mathematical Sciences Publishers, Berkeley, 2020
[en] We consider the problem of recovering the entries of diagonal matrices {U_a}_a for a = 1, . . . , t from multiple “incomplete” samples {W_a}_a of the form W_a = P U_a Q, where P and Q are unknown matrices of low rank.
We devise practical algorithms for this problem depending on the ranks of P and Q. This problem finds its motivation in cryptanalysis: we show how to significantly improve previous algorithms for solving the approximate common divisor problem and breaking CLT13 cryptographic multilinear maps.
Disciplines :
Mathématiques
Auteur, co-auteur :
CORON, Jean-Sébastien ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
NOTARNICOLA, Luca ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Computer Science and Communications Research Unit (CSC)
WIESE, Gabor ; University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Co-auteurs externes :
no
Langue du document :
Anglais
Titre :
Simultaneous Diagonalization of Incomplete Matrices and Applications
Date de publication/diffusion :
décembre 2020
Manifestation à portée :
International
Titre de l'ouvrage principal :
Proceedings of the Fourteenth Algorithmic Number Theory Symposium (ANTS-XIV), edited by Steven Galbraith, Open Book Series 4, Mathematical Sciences Publishers, Berkeley, 2020
Pagination :
127-142
Peer reviewed :
Peer reviewed
Projet FnR :
FNR10621687 - Security And Privacy For System Protection, 2015 (01/01/2017-30/06/2023) - Sjouke Mauw
