  We study particle acceleration at the termination shock of a striped pulsar
wind by integrating trajectories in a prescribed model of the magnetic field
and flow pattern. Drift motion on the shock surface maintains either electrons
or positrons on "Speiser" orbits in a ring-shaped region close to the
equatorial plane of the pulsar, enabling them to be accelerated to very high
energy by the first-order Fermi mechanism. A power-law spectrum results:
$dN_{\rm e}/d\gamma\propto\gamma^{\alpha_{\rm e}}$, where $\alpha_{\rm e}$ lies
in the range $-1.8$ to $-2.4$ and depends on the downstream turbulence level.
For sufficiently strong turbulence, we find $\alpha_{\rm e} \simeq -2.2$, and
both the photon index and the flux of $1-100$ keV X-rays from the Crab Nebula,
as measured by NuSTAR, can be reproduced. The particle spectrum hardens to
$\alpha_{\rm e} \simeq -1.8$ at lower turbulence levels, which may explain the
hard photon index observed by the Chandra X-ray Observatory in the central
regions of the Nebula.
