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• W3111265533 abstract "Abstract We revisit the approximate Voronoi cells approach for solving the closest vector problem with preprocessing (CVPP) on high-dimensional lattices, and settle the open problem of Doulgerakis–Laarhoven–De Weger [PQCrypto, 2019] of determining exact asymptotics on the volume of these Voronoi cells under the Gaussian heuristic. As a result, we obtain improved upper bounds on the time complexity of the randomized iterative slicer when using less than <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mn>2</m:mn> <m:mrow class=MJX-TeXAtom-ORD> <m:mn>0.076</m:mn> <m:mi>d</m:mi> <m:mo>+</m:mo> <m:mi>o</m:mi> <m:mo stretchy=false>(</m:mo> <m:mi>d</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:msup> </m:math> $2^{0.076d + o(d)}$ memory, and we show how to obtain time–memory trade-offs even when using less than <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mn>2</m:mn> <m:mrow class=MJX-TeXAtom-ORD> <m:mn>0.048</m:mn> <m:mi>d</m:mi> <m:mo>+</m:mo> <m:mi>o</m:mi> <m:mo stretchy=false>(</m:mo> <m:mi>d</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:msup> </m:math> $2^{0.048d + o(d)}$ memory. We also settle the open problem of obtaining a continuous trade-off between the size of the advice and the query time complexity, as the time complexity with subexponential advice in our approach scales as <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:msup> <m:mi>d</m:mi> <m:mrow class=MJX-TeXAtom-ORD> <m:mi>d</m:mi> <m:mrow class=MJX-TeXAtom-ORD> <m:mo>/</m:mo> </m:mrow> <m:mn>2</m:mn> <m:mo>+</m:mo> <m:mi>o</m:mi> <m:mo stretchy=false>(</m:mo> <m:mi>d</m:mi> <m:mo stretchy=false>)</m:mo> </m:mrow> </m:msup> </m:math> $d^{d/2 + o(d)}$ matching worst-case enumeration bounds, and achieving the same asymptotic scaling as average-case enumeration algorithms for the closest vector problem." @default.
• W3111265533 created "2020-12-21" @default.
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• W3111265533 date "2020-11-17" @default.
• W3111265533 modified "2023-09-26" @default.
• W3111265533 title "Approximate Voronoi cells for lattices, revisited" @default.
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• W3111265533 doi "https://doi.org/10.1515/jmc-2020-0074" @default.
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