Can anyone tell me how I can calculate the period of the outputs of stream ciphers? For example RC4, HC-128,256, SALSA20,and others?In some papers it is given the RC4 period but did not specify how to reach that result. That is my question regarding the RC4 and the winners of the eSTREAM project.
A streamcipher, once initialized with the key and the IV, is just a state machine that produces arbitrarily many bits (the keystream) while updating its internal state with some transformation state = F(state). So the period is the number N of iterations of F required to get the initial state again. What you need to do is look at F and figure out N such that F^N = Identity.
In some ciphers, F is a mono-orbit permutation and F^k(initial state) cycles over all possible states so that N is the number of possible states. If F is some ad hoc function (not permutation) then you expect to get a collision after roughly the square root of that.
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