New Transference Theorems on Lattices Possessing n^\epsilon-unique Shortest Vectors

Wei Wei; Chengliang Tian; Xiaoyun Wang

Paper 2012/293

New Transference Theorems on Lattices Possessing n^\epsilon-unique Shortest Vectors

Wei Wei, Chengliang Tian, and Xiaoyun Wang

Abstract

We prove three optimal transference theorems on lattices possessing $n^{ϵ}$ -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 $_{γ^{'}}$ and GapSIVP $_{γ}$ 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 -unique shortest vectors.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Published elsewhere. This paper hasn't been published anywhere.
Keywords: Transference theorem Reduction Gaussian measures Smoothing parameter
Contact author(s): wei-wei08 @ mails tsinghua edu cn
History: 2012-06-03: received
Short URL: https://ia.cr/2012/293
License: CC BY

BibTeX

@misc{cryptoeprint:2012/293,
      author = {Wei Wei and Chengliang Tian and Xiaoyun Wang},
      title = {New Transference Theorems on Lattices Possessing n^\epsilon-unique Shortest Vectors},
      howpublished = {Cryptology {ePrint} Archive, Paper 2012/293},
      year = {2012},
      url = {https://eprint.iacr.org/2012/293}
}