Paper 2020/631
Simultaneous Diagonalization of Incomplete Matrices and Applications
Jean-Sébastien Coron, Luca Notarnicola, and Gabor Wiese
Abstract
We consider the problem of recovering the entries of diagonal matrices $\{U_a\}_a$ for $a = 1,\ldots,t$ 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.
Metadata
- Available format(s)
-
PDF
- Category
- Public-key cryptography
- Publication info
- Published elsewhere. Fourteenth Algorithmic Number Theory Symposium ANTS-XIV
- Keywords
- Linear AlgebraCryptanalysisApproximate Common Divisor ProblemMultilinear Maps
- Contact author(s)
-
jean-sebastien coron @ uni lu
luca notarnicola @ uni lu
gabor wiese @ uni lu - History
- 2021-06-24: revised
- 2020-06-03: received
- See all versions
- Short URL
- https://ia.cr/2020/631
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2020/631,
author = {Jean-Sébastien Coron and Luca Notarnicola and Gabor Wiese},
title = {Simultaneous Diagonalization of Incomplete Matrices and Applications},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/631},
year = {2020},
url = {https://eprint.iacr.org/2020/631}
}
