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This paper presents improvement in the ciphertext only reconstruction technique of LFSR based stream ciphers. The original algorithm involves huge computations and requires a large number of ciphertext bits to be processed (for original article by A. Canteaut and E. Filiol, see FSE 2000, LCNS 1978, Spriger Verlag, 2001) . We present techniques to increase the efficiency of the reconstruction algorithm and reduce the computation time. In this regards, the first improvement is achieved by modifying the decision threshold value according to the available ciphertext bits. With this, we achieved a reduction by one fourth in the computation time as well as the minimum ciphertext requirement. Further improvement is achieved by the parallelization of the algorithm. Experimental results of the improvement in computation time and efficiency have been detailed. A generalization of the reconstruction technique to a wide range of stream ciphers is also presented.