Welcome to the resource topic for 2011/139
Title:
Shortest Lattice Vectors in the Presence of Gaps
Authors: Mingjie Liu, Xiaoyun Wang, Guangwu Xu, Xuexin Zheng
Abstract:Given a lattice {\mathcal L} with the i-th successive minimum \lambda_i, its i-th gap \frac{\lambda_i}{\lambda_1} often provides useful information for analyzing the security of cryptographic scheme related to {\mathcal L}. This paper concerns short vectors for lattices with gaps. In the first part, a \lambda_2-gap estimation of LWE lattices with cryptographic significance is given. For some \gamma', a better reduction from BDD_{\gamma'} to uSVP_{\gamma} is obtained in the presence of larger \lambda_2-gap. The second part of the paper shows that gaps among the successive minima lead to a more efficient SVP search algorithm. As far as we know, it is the first SVP algorithm exploiting lattices with gaps.
ePrint: https://eprint.iacr.org/2011/139
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