  This paper studies secrecy-capacity of an $n$-dimensional Gaussian wiretap
channel under the peak-power constraint. This work determines the largest
peak-power constraint $\bar{\mathsf{R}}_n$ such that an input distribution
uniformly distributed on a single sphere is optimal; this regime is termed the
small-amplitude regime. The asymptotic of $\bar{\mathsf{R}}_n$ as $n$ goes to
infinity is completely characterized as a function of noise variance at both
receivers. Moreover, the secrecy-capacity is also characterized in a form
amenable for computation. Furthermore, several numerical examples are provided,
such as the example of the secrecy-capacity achieving distribution outside of
the small amplitude regime.
