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I want to ask that does the common reference string in NIZK have to be random?

Or can it be anything?

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The common reference string in NIZK does not have to be uniformly distributed.
It is to be sampled from whatever distribution the NIZK protocol specifies.

However, the common random string in NIZK does have to be uniformly distributed,
and the setup strings in NIZK also have to be uniformly distributed.

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