Three ways to mount distinguishing attacks on irregularly clocked stream ciphers

Many stream ciphers use irregular clocking to introduce nonlinearity to the keystream. We present three distinguishers on irregularly clocked linear feedback shift registers. The general idea used is to find suitable linear combinations of keystream bits, here called samples, that are drawn from a biased distribution. We describe how to place windows around the estimated positions around members of the linear combinations, and very efficiently create many samples with low computational complexity. We also describe ideas based on constructing samples consisting of vectors of bits (words) instead of single binary samples. These vectors based methods can distinguish the cipher using fewer keystream bits but sometimes require a higher computational complexity.