= Cryptographic setup
\b[Cryptographic setup] is the generation and distribution of initial parameters or other resources required by a <cryptographic protocol>. Its specification includes the input <cryptographic security parameter>, the sampling procedure, the public output and any information that must remain secret. Setup is part of the protocol's security model, rather than an arbitrary source of well-formatted constants.
A <common reference string> gives one example. Parties to a <non-interactive zero-knowledge proof> may share a public string $\sigma$ sampled by the prescribed setup. The definition describes both its distribution and how that setup participates in real and simulated proof experiments.<Zero-Knowledge: a tutorial by Oded Goldreich>[Section8, shared reference-string model and joint simulation]{ref}
An original distribution example makes the generation rule explicit. Let a toy setup sample two independent uniform bits $a,b$ and publish
$$
\sigma=(a,b,a\mathbin{\oplus}b).
$$
Its support is $\{000,011,101,110\}$, each with probability $1/4$. A uniformly sampled three-bit string instead has eight possible values, each with probability $1/8$. The two generators publish strings of the same length, but the second satisfies the parity equation only half the time.
This toy setup is not a secure proof-system construction. It demonstrates why replacing a specified generator by a different random-looking source changes the experiment. Public availability of setup data and correctness of its generation are separate properties.
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