Nullifier

Zcash's shielded pool can't just check "has this address run out of balance" the way a transparent one does — the whole point is that balances stay private. Instead, spending a shielded note publishes a nullifier: a value derived from that specific note using its owner's own spending key, unique to that note, that could only be produced by whoever was actually entitled to spend it.

Full nodes reject any transaction that reuses a nullifier already seen on-chain, which is what prevents double-spending shielded funds. A nullifier proves *that* some shielded note was spent — it does not reveal which note, who spent it, who received the result, or the amount involved.