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This work studies the secrecy-capacity of a scalar-Gaussian wiretap channelwith an amplitude constraint on the input. It is known that for this channel,the secrecy-capacity-achieving distribution is discrete with finitely manypoints. This work improves such result by showing an upper bound of the order$\frac{\mathsf{A}}{\sigma_1^2}$ where $\mathsf{A}$ is the amplitude constraintand $\sigma_1^2$ is the variance of the Gaussian noise over the legitimatechannel.

Scalar Gaussian Wiretap Channel: Properties of the Support Size of the Secrecy-Capacity-Achieving Distribution