We have applied the open-plus-closed-loop control method, recently devised by Grosu et al., to chaos-based communications. In our method, a message is handled as if it were part of a parameter mismatch between the chaotic oscillators installed on a drive and a response system. In the drive system, the message is encrypted by adding it to a state variable of the oscillator as dynamical noise. In the response system, the message is decrypted by subtracting the chaotic signal reproduced by chaotic synchronization using the open-plus-closed-loop control method from the received signal, followed by differentiation with respect to time. When the oscillators have multiple parameter mismatches, multiple messages can be simultaneously encrypted and decrypted to achieve multiplex secure communications.