orchard/src/note/nullifier.rs

use ff::Field;
use halo2::arithmetic::CurveExt;
use pasta_curves::pallas;
use rand::RngCore;

use super::NoteCommitment;
use crate::{
    keys::NullifierDerivingKey,
    spec::{extract_p, mod_r_p},
};

/// A unique nullifier for a note.
#[derive(Debug)]
pub struct Nullifier(pub(super) pallas::Base);

impl Nullifier {
    /// Generates a dummy nullifier for use as $\rho$ in dummy spent notes.
    ///
    /// Nullifiers are required by consensus to be unique. For dummy output notes, we get
    /// this restriction as intended: the note's $\rho$ value is set to the nullifier of
    /// the accompanying spent note within the action, which is constrained by consensus
    /// to be unique. In the case of dummy spent notes, we get this restriction by
    /// following the chain backwards: the nullifier of the dummy spent note will be
    /// constrained by consensus to be unique, and the nullifier's uniqueness is derived
    /// from the uniqueness of $\rho$.
    ///
    /// Instead of explicitly sampling for a unique nullifier, we rely here on the size of
    /// the base field to make the chance of sapling a colliding nullifier negligible.
    pub(crate) fn dummy(rng: &mut impl RngCore) -> Self {
        Nullifier(pallas::Base::random(rng))
    }

    /// $DeriveNullifier$.
    ///
    /// Defined in [Zcash Protocol Spec § 4.16: Note Commitments and Nullifiers][commitmentsandnullifiers].
    ///
    /// [commitmentsandnullifiers]: https://zips.z.cash/protocol/nu5.pdf#commitmentsandnullifiers
    pub(super) fn derive(
        nk: &NullifierDerivingKey,
        rho: pallas::Base,
        psi: pallas::Base,
        cm: NoteCommitment,
    ) -> Self {
        let k = pallas::Point::hash_to_curve("z.cash:Orchard")(b"K");

        Nullifier(extract_p(&(k * mod_r_p(nk.prf_nf(rho) + psi) + cm.0)))
    }
}