> ## Documentation Index
> Fetch the complete documentation index at: https://sdk.umbraprivacy.com/llms.txt
> Use this file to discover all available pages before exploring further.

# Poseidon Hash

> ZK-friendly hash function over BN254 used for Stealth Pool Note commitments, nullifiers, and user identity.

[Poseidon](https://eprint.iacr.org/2019/458.pdf) is a ZK-friendly hash function designed to be efficient inside R1CS and Plonk circuits. Unlike general-purpose hashes, Poseidon is defined natively over prime fields, making it orders of magnitude cheaper to evaluate inside a zero-knowledge proof circuit than SHA-256 or Keccak.

Umbra uses the BN254 (alt-bn128) variant - the same curve as Ethereum's `ecPairing` precompile and the Groth16 verifier on Solana. Poseidon operates over the BN254 scalar field, whose prime order is approximately 2^254.

See the [Poseidon Cipher](https://docs.umbraprivacy.com/docs/security-cryptography/poseidon-cipher) and [Poseidon as a PRF: Security Proofs](https://docs.umbraprivacy.com/docs/security-cryptography/poseidon-prf-security) pages for the full cryptographic treatment.

## Uses in Umbra

**Stealth Pool Note commitments**: each note inserts a Poseidon commitment into the Indexed Merkle Tree. The commitment hides the note inputs on-chain while binding the writer to them for the ZK proof.

**Nullifiers**: each note has a corresponding Poseidon nullifier derived from the holder's private key. Burning the nullifier on-chain prevents double-spending, and only the key holder can produce the correct nullifier for a given commitment.

**User commitment**: Each registered user has a Poseidon commitment stored on-chain that links their ZK identity to their encryption key without revealing either in plaintext.

## References

* [Poseidon: A New Hash Function for Zero-Knowledge Proof Systems](https://eprint.iacr.org/2019/458.pdf) - Grassi et al., 2019
* [Poseidon Cipher - Umbra Architecture](https://docs.umbraprivacy.com/docs/security-cryptography/poseidon-cipher)
* [Poseidon as a PRF: Security Proofs](https://docs.umbraprivacy.com/docs/security-cryptography/poseidon-prf-security)