What is a nullifier?

A nullifier is a unique value published when a private note is spent. It lets the chain reject a second spend of the same note without revealing which note was spent.

The double-spend problem

On a public ledger, stopping a double spend is easy because every coin is visible. In a shielded pool the chain cannot see which note is being spent. So every note has a nullifier, derived from the note and its owner’s secret key. Spending publishes the nullifier, the contract records it, and any later spend with the same nullifier fails.

Why it does not give the note away

Without the owner’s key, nobody can compute which commitment a nullifier belongs to. Observers see that some note was spent, never which one.

In Redacted

In Redacted a nullifier retires each spent note forever, so a note can be spent only once, and the mark it leaves points to no note in particular.

Architecture →

Related terms

CommitmentA commitment locks in a piece of data without revealing it. Later it can be opened and anyone can check that it matches, but until then it gives nothing away and cannot be changed.NoteA note is a sealed entry on-chain that records coins in Redacted’s Reserve and that only your keys can open. From the outside all notes look alike, whoever owns them and whatever they hold.Zero-knowledge proofA zero-knowledge proof lets someone prove that a statement is true without revealing anything else, for example that they own funds and may spend them, without showing which funds or who they are.Shielded poolA shielded pool holds funds as private notes inside a smart contract. Deposits and withdrawals are public, but what happens inside is proved with zero-knowledge proofs and does not reveal who owns what.

Sources: Zcash protocol specification

Updated October 7, 2026. All terms