An Efficient State Recovery Attack on the X-FCSR Family of Stream Ciphers

We describe a state recovery attack on the X-FCSR family of stream ciphers. In this attack we analyse each block of output keystream and try to solve for the state. The solver will succeed when a number of state conditions are satisfied. For X-FCSR-256, our best attack has a computational complexity of only 2(4.7) table lookups per block of keystream, with an expected 2(44.3) such blocks before the attack is successful. The precomputational storage requirement is 2(33). For X-FCSR-128, the computational complexity of our best attack is 2(16.3) table lookups per block of keystream, where we expect 2(55.2) output blocks before the attack comes through. The precomputational storage requirement for X-FCSR-128 is 2(67).