estimator.reduction.Kyber.short_vectors#

Kyber.short_vectors(beta, d, N=None, B=None, preprocess=True)[source]#

Cost of outputting many somewhat short vectors using BKZ-β.

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

This is using an observation insprired by [AC:GuoJoh21] that we can run a sieve on the first block of the basis with negligible overhead.

Parameters:

  • beta – Cost parameter (≈ SVP dimension).

  • d – Lattice dimension.

  • N – Number of vectors requested.

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

Returns:

(ρ, c, N, β')

EXAMPLES:

>>> from estimator.reduction import RC
>>> RC.Kyber.short_vectors(100, 500, 1)
(1.0, 2.7367476128136...19, 100, 1)
>>> RC.Kyber.short_vectors(100, 500)
(1.1547, 2.7367476128136...19, 176584, 84)
>>> RC.Kyber.short_vectors(100, 500, 1000)
(1.1547, 2.7367476128136...19, 176584, 84)