Welcome to the resource topic for 2012/293
Title:
New Transference Theorems on Lattices Possessing n^\epsilon-unique Shortest Vectors
Authors: Wei Wei, Chengliang Tian, Xiaoyun Wang
Abstract:We prove three optimal transference theorems on lattices possessing n^{\epsilon}-unique shortest vectors which relate to the successive minima, the covering radius and the minimal length of generating vectors respectively. The theorems result in reductions between GapSVP${\gamma’} and GapSIVP\gamma$ for this class of lattices. Furthermore, we prove a new transference theorem giving an optimal lower bound relating the successive minima of a lattice with its dual. As an application, we compare the respective advantages of current upper bounds on the smoothing parameter of discrete Gaussian measures over lattices and show a more appropriate bound for lattices whose duals possess \sqrt{n}-unique shortest vectors.
ePrint: https://eprint.iacr.org/2012/293
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