3 research outputs found
Simultaneous Diagonalization of Incomplete Matrices and Applications
We consider the problem of recovering the entries of diagonal matrices
for from multiple "incomplete" samples
of the form , where and are unknown matrices of low rank. We
devise practical algorithms for this problem depending on the ranks of and
. 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
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
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