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Simultaneous Diagonalization of Incomplete Matrices and Applications
Notarnicola, Luca
2020
 

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Abstract :
[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 :
Mathematics
Author, co-author :
Notarnicola, Luca ;  University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH)
Language :
English
Title :
Simultaneous Diagonalization of Incomplete Matrices and Applications
Publication date :
2020
Event name :
Fourteenth Algorithmic Number Theory Symposium 2020, ANTS-XIV
Event date :
June 29 - July 4, 2020
Audience :
International
Focus Area :
Computational Sciences
Available on ORBilu :
since 22 January 2021

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