  The polarized thermal emission from Galactic dust is the main foreground
present in measurements of the polarization of the cosmic microwave background
(CMB) at frequencies above 100GHz. We exploit the Planck HFI polarization data
from 100 to 353GHz to measure the dust angular power spectra $C_\ell^{EE,BB}$
over the range $40<\ell<600$ well away from the Galactic plane. These will
bring new insights into interstellar dust physics and a precise determination
of the level of contamination for CMB polarization experiments. We show that
statistical properties of the emission can be characterized over large
fractions of the sky using $C_\ell$. For the dust, they are well described by
power laws in $\ell$ with exponents $\alpha^{EE,BB}=-2.42\pm0.02$. The
amplitudes of the polarization $C_\ell$ vary with the average brightness in a
way similar to the intensity ones. The dust polarization frequency dependence
is consistent with modified blackbody emission with $\beta_d=1.59$ and
$T_d=19.6$K. We find a systematic ratio between the amplitudes of the Galactic
$B$- and $E$-modes of 0.5. We show that even in the faintest dust-emitting
regions there are no "clean" windows where primordial CMB $B$-mode polarization
could be measured without subtraction of dust emission. Finally, we investigate
the level of dust polarization in the BICEP2 experiment field. Extrapolation of
the Planck 353GHz data to 150GHz gives a dust power
$\ell(\ell+1)C_\ell^{BB}/(2\pi)$ of $1.32\times10^{-2}\mu$K$_{CMB}^2$ over the
$40<\ell<120$ range; the statistical uncertainty is $\pm0.29$ and there is an
additional uncertainty (+0.28,-0.24) from the extrapolation, both in the same
units. This is the same magnitude as reported by BICEP2 over this $\ell$ range,
which highlights the need for assessment of the polarized dust signal even in
the cleanest windows of the sky.
