3 research outputs found

    Simultaneous Diagonalization of Incomplete Matrices and Applications

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    We consider the problem of recovering the entries of diagonal matrices {Ua}a\{U_a\}_a for a=1,…,ta = 1,\ldots,t from multiple "incomplete" samples {Wa}a\{W_a\}_a of the form Wa=PUaQW_a=PU_aQ, where PP and QQ are unknown matrices of low rank. We devise practical algorithms for this problem depending on the ranks of PP and QQ. 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.Comment: 16 page

    Simultaneous Diagonalization of Incomplete Matrices and Applications

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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 = 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

    Simultaneous Diagonalization of Incomplete Matrices and Applications

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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 = 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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