LaaMosPol14.short_vectors(beta, d, N=None, B=None, preprocess=True, sieve_dim=None)#

Cost of outputting many somewhat short vectors.

The output of this function is a tuple of four values:

  • ρ is a scaling factor. The output vectors are expected to be longer than the shortest vector expected from an SVP oracle by this factor.

  • c is the cost of outputting N vectors

  • N the number of vectors output, which may be larger than the value put in for N.

  • β’ the cost parameter associated with sampling, here: β or sieve_dim

This implementation uses that a sieve outputs many somehwat short vectors [Kyber17].

  • beta – Cost parameter (≈ SVP dimension).

  • d – Lattice dimension.

  • N – Number of vectors requested.

  • B – Bit-size of entries.

  • preprocess – Include the cost of preprocessing the basis with BKZ-β. If False we assume the basis is already BKZ-β reduced.

  • sieve_dim – Explicit sieving dimension.


(ρ, c, N, β')


>>> from estimator.reduction import RC
>>> RC.ADPS16.short_vectors(100, 500, 1)
(1.0, 6.16702733460158e8, 1, 100)
>>> RC.ADPS16.short_vectors(100, 500)
(1.1547..., 6.16702733460158e8, 1763487, 100)
>>> RC.ADPS16.short_vectors(100, 500, 1000)
(1.1547..., 6.16702733460158e8, 1763487, 100)