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could someone tell me how long the cycle length must be in stream ciphers, so a security exists. how to compare the cycle length to the state space?

I investigate the algorithm spritz and I have the attainability of the states under investigation with key lengths of 1 - 10 and n = 6. now I have the values ​​but I still do not know how to interpret them. the maximum cycle length for N = 6 is 660.390 and the smallest 12. But how should I evaluate this with regard to the safety? I hope I have described it somewhat better.

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marked as duplicate by Maarten Bodewes, SEJPM, e-sushi Oct 29 '17 at 15:07

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  • $\begingroup$ many thanks for the link but I still have a question. For example- if I have a statespace with initial states of 4500 and the largest cycle length has the value 1500 what says that. (I only look at the input of keys until they run into a cycle) $\endgroup$ – kemasio Oct 28 '17 at 11:49
  • $\begingroup$ If you only have 4500 different states then you are in trouble. If you have a cycle length of anything that is 1500 then you are in trouble. If you try and input keys instead of producing output then you are in trouble. But without further specifications there is little more to say. If this is an exercise, which I suppose it is, then you should ask clarification about the exercise from the person/institution that created it. $\endgroup$ – Maarten Bodewes Oct 28 '17 at 11:53
  • $\begingroup$ Yes it's an exercise. Is there not a guideline for the perfect cycle length? $\endgroup$ – kemasio Oct 28 '17 at 12:01
  • $\begingroup$ Well, yes, it's mentioned in the post above, about half of the size of the state in bits, but that's considering that the state itself should be considered random. WRT the question above, I think we would need more context to give the correct answer, context that is undoubtedly present in your study materials. $\endgroup$ – Maarten Bodewes Oct 28 '17 at 12:45
  • $\begingroup$ I investigate the algorithm spritz and I have the attainability of the states under investigation with key lengths of 1 - 10 and n = 6. now I have the values ​​but I still do not know how to interpret them. the maximum cycle length for N = 6 is 660.390 and the smallest 12. But how should I evaluate this with regard to the safety? I hope I have described it somewhat better. $\endgroup$ – kemasio Oct 28 '17 at 12:52
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There's a bioinfomatics paper that might be of interest. Good Practice in (Pseudo) Random Number Generation for Bioinformatics Applications suggests some values to the maximum run length of a PRNG. Not strictly crypto, but I've not seen anything else.

In summary, it says that Knuth recommends a max. output of states /1000. However there is also a much more conservative limit of (states)^(1/3).

I'm not sure of how you exactly determined your baby Spritz cycles, but for comparison consider the grown up version with the full 256 byte permutation and assume that all states are achieved. (This may not be possible due to the creation of weak states.) The conservative estimate would suggest that you could output ~10^167 bits of key material.

For N = 6, I estimate that you couldn't get a single safe bit from it if you follow the guidance above.

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