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The authors consider the Gaussian wiretap channel with an amplitude constraint, i.e., a peak power constraint, on the channel input. They show that the entire rate-equivocation region of the Gaussian wiretap channel with an amplitude constraint is obtained by discrete input distributions with finite support. They prove this result by considering the existing single-letter description of the rate-equivocation region, and showing that discrete distributions with finite support exhaust this region. Their result highlights an important difference between the peak power constraint and the average power constraint cases: although, in the average power constraint case, both the secrecy capacity and the capacity can be achieved simultaneously.
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