  We present new measurements of CIB anisotropies using Planck. Combining HFI
data with IRAS, the angular auto- and cross frequency power spectrum is
measured from 143 to 3000 GHz, and the auto-bispectrum from 217 to 545 GHz. The
total areas used to compute the CIB power spectrum and bispectrum are about
2240 and 4400 deg^2, respectively. After careful removal of the contaminants,
and a complete study of systematics, the CIB power spectrum and bispectrum are
measured with unprecedented signal to noise ratio from angular multipoles
ell~150 to 2500, and ell~130 to 1100, respectively. Two approaches are
developed for modelling CIB power spectrum anisotropies. The first approach
takes advantage of the unique measurements by Planck at large angular scales,
and models only the linear part of the power spectrum, with a mean bias of dark
matter halos hosting dusty galaxies at a given redshift weighted by their
contribution to the emissivities. The second approach is based on a model that
associates star-forming galaxies with dark matter halos and their subhalos,
using a parametrized relation between the dust-processed infrared luminosity
and (sub-)halo mass. The two approaches simultaneously fit all auto- and cross-
power spectra very well. We find that the star formation history is well
constrained up to z~2. However, at higher redshift, the accuracy of the star
formation history measurement is strongly degraded by the uncertainty in the
spectral energy distribution of CIB galaxies. We also find that CIB galaxies
have warmer temperatures as redshift increases. The CIB bispectrum is steeper
than that expected from the power spectrum, although well fitted by a power
law; this gives some information about the contribution of massive halos to the
CIB bispectrum.
