Cryptanalysis of three mutually clock-controlled stop/go shift registers

A binary stream cipher consisting of three short linear-feedback shift registers (LFSRs) of total length 64 that are mutually clocked in the stop/go manner is cryptanalyzed in the known keystream sequence scenario. To reconstruct the internal state candidates at a known time from about 64 known keystream bits, two algorithms are developed. One is based on guessing a number of elements of the clock-control sequence and has a computational complexity of about 2/sup 40/ steps, where the average step complexity is comparable to the step complexity of the exhaustive search method. The other exploits a time-memory tradeoff based on the well-known birthday paradox and is successful if approximately T/spl middot/M/spl ges/2/sup 64/, where T is the required computational time in table lookups and M is the memory in 64-bit words. As the state-transition function is not one-to-one, to recover the initial state from the internal state candidates, two algorithms are introduced. One consists in guessing the number of clocks for each of the LFSRs. The other consists in the reversion of the internal states and is based on the theory of critical and subcritical branching processes.