Reference : Simultaneous Diagonalization of Incomplete Matrices and Applications
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Simultaneous Diagonalization of Incomplete Matrices and Applications
Notarnicola, Luca mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Fourteenth Algorithmic Number Theory Symposium 2020, ANTS-XIV
June 29 - July 4, 2020
New Zealand (online)
[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.

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