[Resource Topic] 2016/852: Faster LLL-type Reduction of Lattice Bases

Welcome to the resource topic for 2016/852

Title:
Faster LLL-type Reduction of Lattice Bases

Authors: Arnold Neumaier, Damien Stehle

Abstract:

We describe an asymptotically fast variant of the LLL lattice reduction algorithm. It takes as input a basis \mathbf B \in \mathbb Z^{n \times n} and returns a (reduced) basis \mathbf C of the Euclidean lattice L spanned by \mathbf B, whose first vector satisfies ||\mathbf c_1|| \leq (1+c)(4/3)^{(n-1)/4} \cdot (\det L)^{1/n} for any fixed c>0. It terminates within O(n^{4+\epsilon} \beta^{1+\epsilon}) bit operations for any \epsilon >0, with \beta = \log \max_i ||\mathbf b_i||. It does rely on fast integer arithmetic but does not make use of fast matrix multiplication.

ePrint: https://eprint.iacr.org/2016/852

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