A novel cryptosystem based on subband decomposition independent component analysis (SDICA) is proposed in this work, where no assumption of independence for the ciphers and the plaintexts is required. In the proposed cryptosystem, the encryption is asynchronous, i.e. the plaintexts are mixed mutually firstly and then mixed with the ciphers. In addition, the decryption is asynchronous, such that the decryption accuracy of the plaintexts can be enhanced. Some special information about the original mixing matrix is used for solving the indeterminacy of the permutation and scale of columns of the recovered mixing matrix in SDICA, instead of the characteristics of the plaintexts. Simulations are given to illustrate security and availability of our cryptosystem.