Shortest Lattice Vectors in the Presence of Gaps

Given a lattice L with the i-th successive minimum λi, its i-th gap λi λ1 often provides useful information for analyzing the security of cryptographic schemes related to L. The paper concerns short vectors for lattices with gaps. In the first part, a λ2-gap estimation of LWE lattices with cryptographic significance is given. Under some conditions, a better reduction from BDDγ to uSV Pγ is obtained in the presence of larger λ2-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 in allusion to lattices with gaps. Key words: lattice, successive minima, approximate SVP, gap, LWE problem,

• Type: Journal
• Year: 2011
• Where: IACR
• Authors: Mingjie Liu, Xiaoyun Wang, Guangwu Xu, Xuexin Zheng
• Keywords: Cryptographic Schemes, IACR 2011, Lattices, Search Algorithm