  For several decades now, wide-field coded mask cameras have been used with
success to localise Gamma-ray bursts (GRBs). In these instruments, the event
count rate is dominated by the photon background due to their large field of
view and large effective area. It is therefore essential to estimate the
instrument background expected in orbit during the early phases of the
instrument design in order to optimise the scientific performances of the
mission. We present here a detailed study of the instrument background and
sensitivity of the coded-mask camera for X- and Gamma-rays (CXG) to be used in
the detection and localisation of high-redshift GRBs on-board the international
GRB mission SVOM. To compute the background spectrum, a Monte-Carlo approach
was used to simulate the primary and secondary interactions between particles
from the main components of the space environment that SVOM will encounter
along its Low Earth Orbit (LEO) (with an altitude of 600 km and an inclination
of ~ 30 deg) and the body of the CXG. We consider the detailed mass model of
the CXG in its latest design. According to our results, i) the design of the
passive shield of the camera ensures that in the 4-50 keV imaging band the
cosmic X-Gamma-ray background is dominant whilst the internal background should
start to become dominant above 70-90 keV; ii) the current camera design ensures
that the CXG camera will be more sensitive to high-redshift GRBs than the Swift
Burst Alert Telescope thanks to a low-energy threshold of 4 keV.
