SIVP ⇒ LWE

SIVP implies LWE.

Statement

Migrated verbatim from learning-with-errors § Reduction to lattice problems:

The hardness of LWE rests on worst-case lattice problems via a quantum reduction — Reg05:

  • Solving decision (or search) LWE on a noticeable fraction of inputs is at least as hard as quantum-approximating the Shortest Vector Problem (GapSVP) and the Shortest Independent Vectors Problem (SIVP) to within polynomial factors in the worst case

Notes

class: unstated: no citing page says which notion of reduction is meant. Recording a class the wiki does not state would add a claim.

Recorded during migration and not fixed — these are claims about the source text, not changes to it:

  • Second of the two reductions packed into one bullet (see the GapSVP record at the same line).
  • SIVP has no wiki page; identifier is ad hoc.