Cryptology ePrint Archive: Report 2012/293

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

Wei Wei and Chengliang Tian and 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.

Category / Keywords: foundations / Transference theorem, Reduction, Gaussian measures, Smoothing parameter

Publication Info: This paper hasn't been published anywhere.

Date: received 28 May 2012

Contact author: wei-wei08 at mails tsinghua edu cn

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Version: 20120603:192543 (All versions of this report)

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