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Fixes in fpylll.algorithms.babai #274

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merged 4 commits into from
Jun 6, 2024
Merged

Fixes in fpylll.algorithms.babai #274

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cb77b7c
Fix norm calculation
TheBlupper Jun 6, 2024
0cf1973
Pass on arguments to LLL.reduction
TheBlupper Jun 6, 2024
e1b32b8
Pass on arguments again
TheBlupper Jun 6, 2024
ffe760d
Document +1
TheBlupper Jun 6, 2024
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13 changes: 8 additions & 5 deletions src/fpylll/algorithms/babai.py
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Original file line number Diff line number Diff line change
Expand Up @@ -8,15 +8,17 @@
"""

from fpylll import IntegerMatrix, LLL
from math import ceil
from math import isqrt


def babai(B, t):
def babai(B, t, *args, **kwargs):
"""
Run Babai's Nearest Plane algorithm by running LLL.

:param B: Input lattice basis.
:param target: Target point (∈ ZZ^n)
:param args: Passed onto LLL.reduction
:param kwargs: Passed onto LLL.reduction
:returns coordinates of the solution vector:

This implementation is more numerically stable compared to the one offered by `MatGSO.babai()`.
Expand Down Expand Up @@ -46,15 +48,16 @@ def babai(B, t):
A[i, j] = B[i, j]

# make sure the input is LLL reduced before reading the norm of the last vector
LLL.reduction(A)
LLL.reduction(A, *args, **kwargs)
# zero vector at the end
A.swap_rows(0, B.nrows)

for j in range(B.ncols):
A[-1, j] = t[j]
A[-1, -1] = ceil(A[-2].norm())
# precise norm
A[-1, -1] = isqrt(sum(x**2 for x in A[-2])) + 1
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This would be wrong if the sqrt is an integer, no?

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Technically yes, but it doesn't matter if it's too big only too small

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It should at least be documented lest future readers stumble over this

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True, does this look better?


LLL.reduction(A) # now call LLL to run Babai
LLL.reduction(A, *args, **kwargs) # now call LLL to run Babai

v = [0] * len(t)
if A[-1, -1] > 0:
Expand Down
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