  A lattice reduction is an algorithm that transforms the given basis of the
lattice to another lattice basis such that problems like finding a shortest
vector and closest vector become easier to solve. We define a class of bases
called obtuse bases and show that any lattice basis can be transformed to an
obtuse basis. A shortest vector $\mathbf{s}$ can be written as
$\mathbf{s}=v_1\mathbf{b}_1+\dots+v_n\mathbf{b}_n$ where
$\mathbf{b}_1,\dots,\mathbf{b}_n$ are the input basis vectors and
$v_1,\dots,v_n$ are integers. When the input basis is obtuse, all these
integers can be chosen to be positive for a shortest vector. This property of
obtuse bases makes the lattice enumeration algorithm for finding a shortest
vector exponentially faster. We have implemented the algorithm for making bases
obtuse, and tested it some small bases.
