Vol. 4, No. 1, 2020

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Simultaneous diagonalization of incomplete matrices and applications

Jean-Sébastien Coron, Luca Notarnicola and Gabor Wiese

Vol. 4 (2020), No. 1, 127–142
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 = 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.

Keywords
simultaneous diagonalization, cryptanalysis, linear algebra, multilinear maps in cryptography, approximate common divisor problem
Mathematical Subject Classification 2010
Primary: 15A06, 94A60
Milestones
Received: 27 February 2020
Accepted: 29 April 2020
Published: 29 December 2020
Authors
Jean-Sébastien Coron
Faculté des Sciences, de la Technologie et de la Communication
University of Luxembourg
Esch-sur-Alzette
Luxembourg
Luca Notarnicola
Faculté des Sciences, de la Technologie et de la Communication
Université du Luxembourg
Esch-sur-Alzette
Luxembourg
Gabor Wiese
Faculté des Sciences, de la Technologie et de la Communication
University of Luxembourg
Esch-sur-Alzette
Luxembourg