  This paper studies secrecy-capacity of an $n$-dimensional Gaussian wiretap
channel under a 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
low 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. Several numerical examples are provided, such as the
example of the secrecy-capacity-achieving distribution beyond the low amplitude
regime. Furthermore, for the scalar case $(n=1)$ we show that the
secrecy-capacity-achieving input distribution is discrete with finitely many
points at most of the order of $\frac{\mathsf{R}^2}{\sigma_1^2}$, where
$\sigma_1^2$ is the variance of the Gaussian noise over the legitimate channel.
