Analysis of a measure of correlation between two binary strings of different lengths

The joint probability between two binary strings of different lengths has been demonstrated as a suitable basis for a correlation attack on the shrinking generator when the decimation probability is 0.5. As an extension of this, further computer simulations have been conducted to determine whether the joint probability can be used as a basis of similar correlation attacks on irregularly clocked shift registers, where the deletions occur independently with a fixed probability different from 0.5. These results show that as the decimation probability increases, the length of the known keystream required for the joint probability to be a useful measure of correlation must also be increased. Thus, the joint probability is shown to be a suitable basis for such correlation attacks, provided a sufficient length of the keystream is known. Australasian Journal of Combinatorics 25(2002), pp.185–199