Nullifier

Nullifier is a term used in several domains to denote a value or mechanism that invalidates or marks as spent, revoked, or otherwise unusable a previously valid state or credential. In digital privacy and blockchain contexts, a nullifier is a cryptographic construct that allows systems to prove that a resource has been consumed or used without disclosing its origin or owner. Typically, a nullifier is derived from a user's secret material and a specific resource identifier, producing a unique token that, once published, renders the corresponding resource unusable again.

In privacy-preserving blockchain schemes, nullifiers are used to prevent double-spending of anonymous notes while preserving user anonymity. For example, in shielded-note-based systems, each note has an associated nullifier that is revealed when the note is spent. The network maintains a record of spent nullifiers; if a nullifier is observed twice, it signals an attempt to spend the same note more than once. Because the nullifier is tied to the specific note but not to the owner's identity, spending remains private while double-spending is detectable.

Outside of blockchain, the term may appear in other cryptographic protocols and access-control systems where a token, credential, or resource must be invalidated after use without necessarily destroying other privacy properties. The exact construction and interpretation of a nullifier depend on the protocol in question. See also: double spending, zero-knowledge proofs, shielded transactions.