def ntru_plain_hybrid_basis(A, g, q, nsamples):
"""
Construct ntru basis for the MitM hybrid
"""
n = A.ncols
ell = n - g
B = IntegerMatrix(nsamples + ell, nsamples + ell)
for i in range(ell):
B[i, i] = 1
for j in range(nsamples):
B[i, j + ell] = A[i, j]
for i in range(nsamples):
B[i + ell, i + ell] = q
# print('B:')
# print(B)
Al = B.submatrix(0, ell, ell, ell + nsamples)
Ag = A.submatrix(ell, 0, nsamples, nsamples)
B = LLL.reduction(B)
return B, Al, Ag
