Nullifier
A unique cryptographic value published when spending shielded funds, allowing the network to prevent double-spending without revealing which specific funds were spent.
A nullifier is a unique cryptographic value derived from a piece of shielded, hidden funds (see Kaavon's "Shielded Transaction" glossary definition) and published publicly whenever those funds are spent. Because the nullifier is mathematically tied to one specific set of hidden funds but reveals nothing about what those funds actually were or who owned them, the network can check whether a given nullifier has already been published — preventing the same funds from being spent twice — without ever learning which specific funds the nullifier corresponds to.
This solves a fundamental problem shielded, privacy-preserving transaction systems face: a conventional UTXO model (see Kaavon's "UTXO" glossary definition) prevents double-spending by tracking which specific outputs have already been consumed, but doing so directly for shielded funds would require revealing the exact funds being spent, defeating the entire purpose of shielding them. A growing public list of spent nullifiers lets the network enforce the no-double-spend rule while funds themselves stay cryptographically hidden throughout.
Examples
- When shielded funds are spent, their corresponding nullifier is published on-chain, letting the network reject any future attempt to spend the same funds again without revealing what those funds were.
- A nullifier solves the double-spend problem for shielded transactions in a way that doesn't require exposing the hidden transaction details a conventional UTXO check would otherwise need.