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arXiv · 2005.13629

Simultaneous Diagonalization of Incomplete Matrices and Applications

Jean-Sébastien Coron·Luca Notarnicola·Gabor Wiese
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Abstract

We consider the problem of recovering the entries of diagonal matrices $\{U_a\}_a$ for $a = 1,\ldots,t$ from multiple "incomplete" samples $\{W_a\}_a$ of the form $W_a=PU_aQ$, 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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Jean-Sébastien Coron, Luca Notarnicola, Gabor Wiese. 2020-05-27. Simultaneous Diagonalization of Incomplete Matrices and Applications. https://arxiv.org/abs/2005.13629

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