Reference : The Hidden Lattice Problem
E-prints/Working papers : First made available on ORBilu
Physical, chemical, mathematical & earth Sciences : Mathematics
Computational Sciences
http://hdl.handle.net/10993/48541
The Hidden Lattice Problem
English
Notarnicola, Luca mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
Wiese, Gabor mailto [University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Mathematics (DMATH) >]
2021
No
[en] Euclidean Lattices ; Lattice Reduction ; Cryptanalysis
[en] We consider the problem of revealing a small hidden lattice from the knowledge of a low-rank sublattice modulo a given sufficiently large integer -- the {\em Hidden Lattice Problem}.
A central motivation of study for this problem is the Hidden Subset Sum Problem,
whose hardness is essentially determined by that of the hidden lattice problem.
We describe and compare two algorithms for the hidden lattice problem:
we first adapt the algorithm by Nguyen and Stern for the hidden subset sum problem, based on orthogonal lattices,
and propose a new variant, which we explain to be related by duality in lattice theory.
Following heuristic, rigorous and practical analyses,
we find that our new algorithm brings some advantages
as well as a competitive alternative for algorithms for problems with cryptographic interest,
such as Approximate Common Divisor Problems,
and the Hidden Subset Sum Problem.
Finally, we study variations of the problem and highlight its relevance to cryptanalysis.
http://hdl.handle.net/10993/48541

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