[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 :
NOTARNICOLA, Luca ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Langue du document :
Anglais
Titre :
Simultaneous Diagonalization of Incomplete Matrices and Applications
Date de publication/diffusion :
2020
Nom de la manifestation :
Fourteenth Algorithmic Number Theory Symposium 2020, ANTS-XIV
