When I utilise the BKZ algorithm on a basis as shown in the code below, I
will receive a runtime error "terminate called recursively". After running
the code again, I got another error that states "infinite loop in babai".
This made me confused as to what the issue is. I do not know if this is the
right place to ask, but does anyone have any advice on how to fix this
issue?
Platform: intel i7
OS: windows 11
Sage version: 10.4
*Code*
from fpylll import BKZ, IntegerMatrix
import numpy as np
def small_poly_vector(size, high=2, low=-1):
v = [R(list(np.random.randint(low, high, N)))
for _ in range(size)] if size==1:
return v[0]
return vector(v)
Q = 3329
N = 64
k = 2
eta1 = 2
eta2 = 2
HALF_Q = int((Q + 1) / 2)
PR.<x> = PolynomialRing(GF(Q))
R.<z> = PR.quotient_ring(x^N + 1)
A = random_matrix(R, k, k)
s = small_poly_vector(k, eta1)
e = small_poly_vector(k, eta2)
t = A*s+e
A_t = matrix(QQ, 2*N+1, 2*N)
A_t[:N,:N] = A[0][0].matrix()
A_t[N:2*N,:N] = A[0][1].matrix()
A_t[:N,N:] = A[1][0].matrix()
A_t[N:2*N,N:] = A[1][1].matrix()
A_t[2*N] = [int(i) for i in t[0]]+[int(i) for i in t[1]]
lattice_size = 4*N+1
B = matrix(QQ, lattice_size, lattice_size)
B[:2*N,:2*N] = Q * identity_matrix(QQ, 2*N, 2*N)
B[2*N:,:2*N] = A_t
B[2*N:,2*N:] = identity_matrix(QQ, 2*N+1, 2*N+1)
B = IntegerMatrix.from_matrix([[int(entry) for entry in row] for row in B])
BKZ.reduction(B, o=BKZ.Param(block_size=20))
reduced_matrix = [[B[i, j] for j in range(B.ncols)] for i in range(B.nrows)]
shortest_vector = reduced_matrix[0]
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