Simultaneous diagonalization of incomplete matrices and applications

Abstract

We consider the problem of recovering the entries of diagonal matrices {Ua}a for a = 1,. .. , t from multiple "incomplete" samples {Wa}a of the form Wa = P UaQ, 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.