An algorithm for cryptanalysis of certain keystream generators is proposed. The developed algorithm has the following two advantages over other reported ones: (i) it is more powerful and (ii) it provides a high-speed software implementation, as well as a simple hardware one, suitable for high parallel architectures. The novel algorithm is a method for the fast correlation attack with significantly better performance than other reported methods, assuming a lower complexity and the same inputs. The algorithm is based on decoding procedures of the corresponding binary block code with novel constructions of the paritychecks, and the following two decoding approaches are employed: the a posterior probability based threshold decoding and the belief propagation based bit-flipping iterative decoding. These decoding procedures offer good trade-offs between the required sample length, overall complexity and performance. The novel algorithm is compared with recently proposed improved fast correlation attacks based on convolutional codes and turbo decoding. The underlying principles, performance and complexity are compared, and the gain obtained with the novel approach is pointed out.