Abstract: Fast correlation attack is the best method for analysing the stream cipher combination generators, its idea is transforming the decryption of the combination stream cipher to a decoding problem, and realizing its attack using decoding techniques in error-correcting codes. In past few years, there are important developments and applications in stream cipher fast correlation attack based on error correcting codes, so it has important scientific and applied values to summarizing the development of the fast correlation attack and propose and analyze the new problems. In this paper, we apply the stream cipher fast correlation attack model to error-correcting codes and propose firstly the new direction for joint design of stream cipher and error-correcting codes. The research results may resolve the reliable communication under the lower SNR. According to the principles of the fast correlation attack, four kind primary fast correlation attack algorithms and their performances are analysed. In the end, the general applicable rules has been drawed, and open problems and future works of fast correlation attack are proposed.