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Traditionally, I think that implementing the CRS (common reference string) model in the real world is usually through a trusted third party or running a distributed protocol. Are there specific papers on this that I can refer to? Thanks a lot!

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  • $\begingroup$ Does the R in your question stand for "random" or "reference"? $\endgroup$
    – Maeher
    Dec 7, 2022 at 8:02
  • $\begingroup$ "reference", I'm so sorry for this confusion! $\endgroup$
    – Emison Lu
    Dec 7, 2022 at 8:12
  • $\begingroup$ I think Diffie Hellman is a trivial example it can be extended to Multi Party Diffie Hellman but it doesn't have good efficiency. $\endgroup$
    – tur11ng
    Dec 7, 2022 at 12:11
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    $\begingroup$ Depending on the type of setup needed, Multiparty computation (MPC) can help. For example, see how ZCash ([z.cash/technology/paramgen) went at it (including further "defense in-depth" mechanisms). $\endgroup$ Dec 7, 2022 at 14:59
  • $\begingroup$ @JAAAY this only works for the common random string model AFAIK. $\endgroup$
    – Grifball
    Dec 12, 2022 at 18:27

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You are correct: CRS can be realized by a set of trusted parties.

To my knowledge, the closest reference to a practical solution to a CRS is the one that Zerocash uses, and that we can read from: Updatable and Universal Common Reference Strings with Applications to zk-SNARKs.

A similar construction is the correlated randomness setting, an excellent reading about the last one is this On the Power of Correlated Randomness in Secure Computation.

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