Some proof systems need a one-time setup using a secret that must then be destroyed. Ceremonies with many participants make sure at least one destroyed their part.
The idea: These proof systems need public numbers built from a secret τ, so that provers can do math "at τ" without knowing it. Whoever knew τ could fake proofs, so it must be destroyed. A ceremony makes that easy to trust: each participant mixes in their own secret randomness, so the final τ is effectively the combination of all of them, and it stays unknown as long as a single participant threw their piece away.
Why it matters: If the secret leaked, fake proofs would become possible.
On the map: ≥ 1 ceremony participant destroyed the secret τ
Some proof systems need public parameters derived from a secret τ that nobody may know. Whoever knows τ (the "toxic waste") can forge proofs.
Ceremonies spread the secret over many contributors[1]: the result is safe if at least one of them generated their part honestly and destroyed it. Zcash's first ceremony (2016) had six participants[2]. Ethereum's KZG ceremony (2023) gathered about 141,000 contributions[3].
If any of these breaks, this breaks too.
If this breaks, these break with it.