Correlation attacks on up/down and stop/go cascades

A probabilistic analysis is conducted to determine conditional and unconditional correlation weaknesses of cascades of up/down clocked shift registers. Similar results are also obtained for cascades of stop/go clocked shift registers. It is theoretically explained how to use the derived properties for fast correlation attacks, whose objective is to recover the linear feedback shift-register initial states, and the conditions for their success are obtained. The analysis and computations conducted indicate that the attacks are feasible in the practical case of relatively short cascades composed of long shift registers.