  We report the first robust detection of the hard X-ray emission in the
15--30\,keV band from Kepler's supernova remnant with the silicon PIN-type
semiconductor detector of the hard X-ray detector (HXD-PIN) onboard Suzaku. The
detection significance is 7.17 $\sigma$ for the emission from Kepler's entire
X-ray emitting region. The energy spectrum is found to be well reproduced by a
single power-law function with a photon index of
$3.13^{+1.85+0.69}_{-1.52-0.36}$, where the first and second errors represent
90\%-statistical and systematic errors, respectively. The X-ray flux is
determined to be
2.75$_{-0.77-0.82}^{+0.78+0.81}\times10^{-12}$\,erg\,s$^{-1}$\,cm$^{-2}$ in the
15--30\,keV band. The wider-band X-ray spectrum in the 3--30\,keV band, where
the soft X-ray Suzaku/XIS spectrum is combined, shows that the non-thermal
component does not have a significant X-ray roll-off structure. We find that
the broad-band energy spectrum from the radio band, X-ray data of this work,
and TeV upper limits can be reproduced with the one-zone leptonic model with a
roll-off energy of $\nu_{\mathrm{roll}}=1.0\times10^{17}$\,Hz and magnetic
field strength of $B>40\,\mathrm{\mu G}$. Application of the diagnostic method
using indices in the soft and hard X-ray band to the data indicates that the
maximum energy of the accelerated electrons in Kepler's SNR is limited by the
age of the remnant. The indication is consistent with the results of the
one-zone leptonic modeling.
