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=PUaQ, 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.
@article{arxiv.2005.13629,
title = {Simultaneous Diagonalization of Incomplete Matrices and Applications},
author = {Jean-Sébastien Coron and Luca Notarnicola and Gabor Wiese},
journal= {arXiv preprint arXiv:2005.13629},
year = {2020}
}