# Nullifiers

The nullifier is a unique value calculated on the transaction *input* account. It is included in the public transaction portion. The nullifier depends on the input account, the intermediate key $$\eta$$ and the account position in the Merke tree ($$path$$):

$$Nullifier(Acc^\text{in}) = Hash\_{nullifier}(Hash\_{account}(Acc^\text{in}), I)$$

where $$I$$is intermediate nullifier hash calculated as:

$$I = Hash\_{inh}(Hash\_{account}(Acc^{in}), \eta, path)$$

$$Hash\_{nullifier}$$, $$Hash\_{inh}$$ and $$Hash\_{account}$$ is a[ $$Poseidon$$ hash functions](https://docs.zkbob.com/implementation/untitled/the-poseidon-hash)

There is an archive on the contract side which holds nullifiers. In the case of account double-spending the nullifiers for the same accounts will equal one another. In this case the contract will reject a second transaction with the repeated nullifier value.

A nullifier pre-image could be safely disclosed without opening any sensitive data, like an intermediate key $$\eta$$ used for encryption and decryption. For example the nullifier disclosure could be useful in compliance reports to prove account-chain linkage.