Applications of a new transference theorem to Ajtai's connection factor

We apply a new transference theorem from the geometry of numbers to Ajtai's connection of average-case to worst-case complexity of lattice problems. We also derive stronger bounds for the special class of lattices which possess n/sup /spl epsiv//-unique shortest lattice vectors. This class of lattices plays a significant role in Ajtai's connection of average-case to worst-case complexity of the shortest lattice vector problem, and in the Ajtai-Dwork public-key cryptosystem. Our proofs are non-constructive, based on methods from harmonic analysis. They yield currently the best Ajtai connection factors.