This paper considers a two-user multiple-input single-output Gaussian broadcast channel model with two sorts of information transfer, i.e., multicasting and confidential broadcasting. Specifically, three service messages are combined at the transmitter. The transmitter sends a
multicast message to both users, and a confidential message to each user which is kept perfectly secret from the other user. Our goal
is to jointly design the optimal input covariances for the multicast message and the two confidential messages, such that the secrecy capacity region is maximized. This problem can be formulated as a secrecy rate maximization (SRM) problem with the quality of multicast service constraint and the quality of confidential service constraint. This SRM problem is nonconvex by nature. To solve it, we reveal its hidden convexity and transform the original SRM problem into a semidefinite programming problem. Furthermore, we prove that the optimal input covariance matrices of the multicast message and the two confidential messages are always with rank one, which implies the optimality of beamforming. Besides, we show that the arithmetic complexity of our proposed method is polynomial with regard to the dimension of the optimization variables. Numerical results are finally presented to show the efficacy of our proposed method.