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In "Efficient reductions among lattice problems" by Micciancio (2007) it is said, that

SVP reduces to SIVP in their exact versions.

I did not found anything about this fact, is a reduction that trivial? Does the same hold for their approximation versions?

user108492
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1 Answers1

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It is non-trivial, You need to see the Corollary 7 in Mic07, Micciancio proved that a series of problems (including CVP and SIVP) in the Euclidean norm are equivalent in their exact version under polynomial time rank-preserving reductions. And in GMSS99, Goldreich et al showed a reduction from SVP to CVP, So, combination of both, you got a reduction from SVP to SIVP. As for the approximation versions, you could see Noah Stephens-Davidowitz's paper NSD16.

constantine
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