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A Complete Analysis of the BKZ Lattice Reduction Algorithm
Authors: Jianwei Li, Phong Q. NguyenAbstract:
We present the first rigorous dynamic analysis of BKZ, the most widely used lattice reduction algorithm besides LLL. Previous analyses were either heuristic or only applied to variants of BKZ. Namely, we provide guarantees on the quality of the current lattice basis during execution. Our analysis extends to a generic BKZ algorithm where the SVP-oracle is replaced by an approximate oracle and/or the basis update is not necessarily performed by LLL. Interestingly, it also provides currently the best and simplest bounds for both the output quality and the running time. As an application, we observe that in certain approximation regimes, it is more efficient to use BKZ with an approximate rather than exact SVP-oracle.
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