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# -*- coding: utf-8 -*-
A minimal implementation of the Block Korkine Zolotarev algorithm in Python.
.. moduleauthor:: Martin R. Albrecht <>
from __future__ import absolute_import
from fpylll import IntegerMatrix, GSO, LLL, BKZ
from fpylll import Enumeration
class BKZReduction:
def __init__(self, A):
"""Construct a new BKZ reduction instance.
:param A: Integer matrix to reduce.
if not isinstance(A, IntegerMatrix):
raise TypeError("Matrix must be IntegerMatrix but got type '%s'"%type(A))
# run LLL first
wrapper = LLL.Wrapper(A)
self.A = A
self.m = GSO.Mat(A, flags=GSO.ROW_EXPO)
self.lll_obj = LLL.Reduction(self.m)
def __call__(self, block_size):
"""Perform BKZ reduction with given``block_size``.
Nothing is returned, the matrix ``A`` given during construction is modified in-place.
:param block_size: an integer > 2
auto_abort = BKZ.AutoAbort(self.m, self.A.nrows)
while True:
clean = self.bkz_loop(block_size, 0, self.A.nrows)
if clean:
if auto_abort.test_abort():
def bkz_loop(self, block_size, min_row, max_row):
"""Perform one BKZ loop, often also called a "BKZ tour".
:param block_size: an integer > 2
:param min_row: algorithm starts in this row (inclusive)
:param max_row: algorithm stops at this row (exclusive)
clean = True
for kappa in range(min_row, max_row-1):
bs = min(block_size, max_row - kappa)
clean &= self.svp_reduction(kappa, bs)
return clean
def svp_reduction(self, kappa, block_size):
"""Call the SVP oracle and insert found vector into basis.
:param kappa: row index
:param block_size: an integer > 2
clean = True
self.lll_obj(0, kappa, kappa + block_size)
if self.lll_obj.nswaps > 0:
clean = False
max_dist, expo = self.m.get_r_exp(kappa, kappa)
delta_max_dist = * max_dist
max_dist, solution = Enumeration(self.m).enumerate(kappa, kappa + block_size, max_dist, expo, pruning=None)[0]
if max_dist >= delta_max_dist * (1<<expo):
return clean
nonzero_vectors = len([x for x in solution if x])
if nonzero_vectors == 1:
first_nonzero_vector = None
for i in range(block_size):
if abs(solution[i]) == 1:
first_nonzero_vector = i
self.m.move_row(kappa + first_nonzero_vector, kappa)
self.lll_obj.size_reduction(kappa, kappa + first_nonzero_vector + 1)
d = self.m.d
with self.m.row_ops(d, d+1):
for i in range(block_size):
self.m.row_addmul(d, kappa + i, solution[i])
self.m.move_row(d, kappa)
self.lll_obj(kappa, kappa, kappa + block_size + 1)
self.m.move_row(kappa + block_size, d)
return False