The use of signal processing techniques in cryptographic field has been an attractive approach in recent years. As an example, the intractability of the under-determined blind source separation (BSS) problem has been used for the proposal of BSS-based speech encryption. However, some weaknesses of this proposal from a cryptographic point of view have been recently published. In this paper, we propose a new encryption method that bypass these weaknesses. The proposed approach is based on the subspace concept together with the use of nonlinear functions and key signals. An interesting feature of the proposed technique is that only a part of the secret key parameters used during encryption is necessary for decryption. Furthermore, if no plain-text is fed to the encryption algorithm, the latter will provide no contents. Analysis results show that the proposed method enhances the security level of existing BSS-based speech encryption methods.