Faster Lattice Enumeration
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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. Some of the famous lattice reduction algorithms are LLL and BKZ reductions. We define a class of bases called obtuse bases and show that any lattice basis can be transformed to an obtuse basis in O(n^4) time. A shortest vector s can be written as v_1b_1+...+v_nb_n where b_1,...,b_n are the input basis vectors and v_1,...,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 the obtuse basis makes lattice enumeration algorithm for finding a shortest vector exponentially faster. Moreover, extreme pruning, the current fastest algorithm for lattice enumeration, can be run on an obtuse basis.
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