Abstract. Lattice basis reduction is the problem of finding short vectors in lattices. The security of lattice based cryptosystems is based on the hardness of lattice reduction. Fu...
We present reductions from lattice problems in the 2 norm to the corresponding problems in other norms such as 1, (and in fact in any other p norm where 1 p ). We consider latt...
We show that finding small solutions to random modular linear equations is at least as hard as approximating several lattice problems in the worst case within a factor almost line...
Given a lattice L with the i-th successive minimum λi, its i-th gap λi λ1 often provides useful information for analyzing the security of cryptographic schemes related to L. The...
We construct public-key cryptosystems that are secure assuming the worst-case hardness of approximating the minimum distance on n-dimensional lattices to within small poly(n) fact...