Improved message passing techniques in fast correlation attacks on stream ciphers

The fast correlation attack is a general cryptanalytic attack directed at stream ciphers and is related to the decoding of low-density parity-check (LDPC) codes. In this paper, we improve the message passing algorithm by exploiting the fact that the sum of an arbitrary number of initial state variables, called a fixed point, can be written as the sum of only a few other variables. This will result in better use of information in the message passing algorithm. Simulations show that this added information results in better success probabilities for the attack. Our technique may also find applications to LDPC codes with girth 4, although such codes are normally avoided.