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I'm trying to understand how MICKEY 2.0 works in detail.

In [1], page 6, it says:

... the state of the generator does not repeat within the generation of a single keystream sequence ...

What consequences does this have? As the internal state generates the output, I think that two identical inputs within the same keystream sequence therefore have different outputs. Or are there any other reasons for this?

Further, on page 6 it says:

The influence of R on the clocking of S also prevents S from becoming stuck in a short cycle

As I read, a short cycle in this context is a sequence of continuously recurring states. Because the state of S depends on the output of R (whose states do not repeat), also the state of S does not repeat within the generation of a single keystream sequence. Is that right?

What exactly is meant by the mutual irregular clocking? I think that this refers to the dependence between register R and register S (see Fig. 3, page 6). The output of each of them depends on the state of the other one. As they are not clocking in regular time intervals, the term irregular clocking is used.

[1] http://www.ecrypt.eu.org/stream/p3ciphers/mickey/mickey_p3.pdf

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In any keystream generator, if the state repeats, so does the keystream; which, under some standards assumptions, can be detected, and leads to a serious break (e.g. if the beginning of the plaintext is known for length a little above $k+\log_2k$ bits, where $k$ is the period of the keystream, then the period $k$ and the rest of the plaintext can be found). A necessary condition for security is thus that odds of the state repeating are negligibly low. This is insured (odds are zero) if the quoted property holds:

... the state of the generator does not repeat within the generation of a single keystream sequence ...

and that's why that property is desirable: it insures there is no class of weak keys leading to attack.

I'm not seeing assertion in the article, or simple proof, that “the state of S does not repeat within the generation of a single keystream sequence”. Rather, I see the reasonable assertion, without formal proof, that starting from a generator S based on iterating a lossless function, and using another unrelated generator R as an excitation to S by a combination with XOR keeping the iterated function lossless, it seems unlikely that the resulting generator S' ends up having a period shorter than R (that could occur only for a limited number of R having some sort of tight relation to S; perhaps that's even demonstrable). Rather, it is expected (in the absence of feedback of S to R, and if the function used in S is random enough) that S' has period a large multiple of the period of R, with the large factor commensurate to the square root of the number of possible states for S.

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