  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.
