Based On Fast Correlation Attack Of The Truncated Linear Sequence Of Ldpc Codes And Their Communication At Very Low Signal To Noise Ratio

The reliable communication is a difficult problem under the low SNR in communication field. Low-Density-Parity-Check code is currently one of the pop research theses in communication field for the excellent performance approaching Shannon limit. Fast Correlation attack is the best method for analyzing stream cipher combination generators. Its main idea is to use the correlation of combination generators and the output sequence, and its idea is transforming the decryption of combination stream cipher to a decoding problem. In this paper, its main research is fast correlation attack decoding algorithm based on via equal error correcting LDPC codes, and analyzing four kind primary fast correlation attack algorithms in modern times.1,According to the fast correlation attack based on via equal error correcting LDPC codes presented by A. Canteaut. We could obtain many parity check equations based on the characteristic function of LFSR. we make use of Gauss elimination algorithm to construct low density parity matrix based on check equations, thereby we could transform the LFSR sequences into LDPC codes in different bit rate, then using sum-product algorithm to recovery the initial states of LFSR.2,When the progression and weight of characteristic polynomial are respectively 21 , 40 and 3,4,5, whose error probabilities of channel are between 0.26 and 0.4, we need the bit number of truncated sequences are 6958 to 16993, 687 to 2217 and 274 to 1021 to recovery the initial states of LFSR successfully. We use sum-product algorithm to recovery the initial states of LFSR to simulation in BSC and AWGN channel. In the same error probabilities, when the progression of characteristic polynomial is 17 and 21, and the length of truncated sequences are 1000, 2000, 3000, and 1000, 3000, 5000. We compare the performance in BSC and AWGN channel.3,Four kinds of fast correlation attack methods have been summarized in modern times. They are respectively the Meier-Staffelbach algorithm, fast correlation attack based on convolutional codes and Turbo codes, the CJS algorithm and fast correlation attack based on LDPC codes. Fundamental theory, the process of attack have been particularly analyzed, then we analyz the computational complexity and whether restricting the tap number of LFSR, then analyzing the number of check equations to attack successfully. In the last, the general applicable rules have been drawed.Finally, we present the problem yet to be resolved and urther prospect in this thesis.