Simultaneous Diagonalization of Incomplete Matrices and Applications

05/27/2020

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by   Jean-Sébastien Coron, et al.

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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=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.