An empirical sweep shows LLL and BKZ solve small LWE-derived shortest vector problems with probability that falls with key length and rises with modulus, and the feasible key length grows logarithmically with the modulus.
Revisiting the Expected Cost of Solving uSVP and Applications to LWE,
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A parameter study for LLL and BKZ with application to shortest vector problems
An empirical sweep shows LLL and BKZ solve small LWE-derived shortest vector problems with probability that falls with key length and rises with modulus, and the feasible key length grows logarithmically with the modulus.