  We present the first measurement of temperature and polarization angular
power spectra of the diffuse emission of Galactic dust at 353 GHz as seen by
Archeops on 20% of the sky. The temperature angular power spectrum is
compatible with that provided by the extrapolation to 353 GHz of IRAS and DIRBE
maps using \cite{fds} model number 8. For Galactic latitudes $|b| \geq 5$ deg
we report a 4 sigma detection of large scale ($3\leq \ell \leq 8$)
temperature-polarization cross-correlation $(\ell+1)C_\ell^{TE}/2\pi = 76\pm 21
\mu\rm{K_{RJ}}^2$ and set upper limits to the $E$ and $B$ modes at $11
\mu\rm{K_{RJ}}^2$. For Galactic latitudes $|b| \geq 10$ deg, on the same
angular scales, we report a 2 sigma detection of temperature-polarization
cross-correlation $(\ell+1)C_\ell^{TE}/2\pi = 24\pm 13 \mu\rm{K_{RJ}}^2$. These
results are then extrapolated to 100 GHz to estimate the contamination in CMB
measurements by polarized diffuse Galactic dust emission. The $TE$ signal is
then $1.7\pm0.5$ and $0.5\pm0.3 \mu\rm{K^2_{CMB}}$ for $|b| \geq 5$ and 10 deg.
respectively. The upper limit on $E$ and $B$ becomes $0.2 \mu\rm{K^2_{CMB}}
(2\sigma)$. If polarized dust emission at higher Galactic latitude cuts is
similar to the one we report here, then dust polarized radiation will be a
major foreground for determining the polarization power spectra of the CMB at
high frequencies above 100 GHz.
