Use FCMP implementation of BP+ in monero-serai (#344)

* Add in an implementation of BP+ based off the paper, intended for clarity and review

This was done as part of my work on FCMPs from Monero, and is copied from https://github.com/kayabaNerve/full-chain-membership-proofs

* Remove crate structure of BP+

* Remove arithmetic circuit code

* Remove AC/VC generators code

* Remove generator transcript

Monero uses non-transcripted static generators.

* Further trimming of generators

* Remove the single range proof

It's unused by Monero and accordingly unhelpful.

* Work on getting BP+ to compile in its new env

* Correct BP+ folder name

* Further tweaks to get closer to compiling

* Remove the ScalarMatrix file

It's only used for AC proofs

* Compiles, with tests passing

* Lock BP+ to Ed25519 instead of the generic Ciphersuite

* Resolve most warnings in BP+

* Make existing bulletproofs test easier to read

* Further strip generators

* Swap G/H as Monero did

* Replace RangeCommitment with Commitment

* Hard-code BP+ h to Ed25519's generator

* Use pub(crate) for BP+, not pub

* Replace initial_transcript with hash_plus

* Rename hash_plus to initial_transcript

* Finish integrating the FCMP BP+ impl

* Move BP+ folder

* Correct no-std support

* Rename "long_n" to eta

* Add note on non-prime order dfg points

coins/monero/src/ringct/bulletproofs/plus/aggregate_range_proof.rs

@@ -0,0 +1,249 @@
+use std_shims::vec::Vec;
+
+use rand_core::{RngCore, CryptoRng};
+
+use zeroize::{Zeroize, ZeroizeOnDrop};
+
+use multiexp::{multiexp, multiexp_vartime, BatchVerifier};
+use group::{
+  ff::{Field, PrimeField},
+  Group, GroupEncoding,
+};
+use dalek_ff_group::{Scalar, EdwardsPoint};
+
+use crate::{
+  Commitment,
+  ringct::{
+    bulletproofs::core::{MAX_M, N},
+    bulletproofs::plus::{
+      ScalarVector, PointVector, GeneratorsList, Generators,
+      transcript::*,
+      weighted_inner_product::{WipStatement, WipWitness, WipProof},
+      padded_pow_of_2, u64_decompose,
+    },
+  },
+};
+
+// Figure 3
+#[derive(Clone, Debug)]
+pub(crate) struct AggregateRangeStatement {
+  generators: Generators,
+  V: Vec<EdwardsPoint>,
+}
+
+impl Zeroize for AggregateRangeStatement {
+  fn zeroize(&mut self) {
+    self.V.zeroize();
+  }
+}
+
+#[derive(Clone, Debug, Zeroize, ZeroizeOnDrop)]
+pub(crate) struct AggregateRangeWitness {
+  values: Vec<u64>,
+  gammas: Vec<Scalar>,
+}
+
+impl AggregateRangeWitness {
+  pub(crate) fn new(commitments: &[Commitment]) -> Option<Self> {
+    if commitments.is_empty() || (commitments.len() > MAX_M) {
+      return None;
+    }
+
+    let mut values = Vec::with_capacity(commitments.len());
+    let mut gammas = Vec::with_capacity(commitments.len());
+    for commitment in commitments {
+      values.push(commitment.amount);
+      gammas.push(Scalar(commitment.mask));
+    }
+    Some(AggregateRangeWitness { values, gammas })
+  }
+}
+
+#[derive(Clone, PartialEq, Eq, Debug, Zeroize)]
+pub struct AggregateRangeProof {
+  pub(crate) A: EdwardsPoint,
+  pub(crate) wip: WipProof,
+}
+
+impl AggregateRangeStatement {
+  pub(crate) fn new(V: Vec<EdwardsPoint>) -> Option<Self> {
+    if V.is_empty() || (V.len() > MAX_M) {
+      return None;
+    }
+
+    Some(Self { generators: Generators::new(), V })
+  }
+
+  fn transcript_A(transcript: &mut Scalar, A: EdwardsPoint) -> (Scalar, Scalar) {
+    let y = hash_to_scalar(&[transcript.to_repr().as_ref(), A.to_bytes().as_ref()].concat());
+    let z = hash_to_scalar(y.to_bytes().as_ref());
+    *transcript = z;
+    (y, z)
+  }
+
+  fn d_j(j: usize, m: usize) -> ScalarVector {
+    let mut d_j = Vec::with_capacity(m * N);
+    for _ in 0 .. (j - 1) * N {
+      d_j.push(Scalar::ZERO);
+    }
+    d_j.append(&mut ScalarVector::powers(Scalar::from(2u8), N).0);
+    for _ in 0 .. (m - j) * N {
+      d_j.push(Scalar::ZERO);
+    }
+    ScalarVector(d_j)
+  }
+
+  fn compute_A_hat(
+    mut V: PointVector,
+    generators: &Generators,
+    transcript: &mut Scalar,
+    mut A: EdwardsPoint,
+  ) -> (Scalar, ScalarVector, Scalar, Scalar, ScalarVector, EdwardsPoint) {
+    let (y, z) = Self::transcript_A(transcript, A);
+    A = A.mul_by_cofactor();
+
+    while V.len() < padded_pow_of_2(V.len()) {
+      V.0.push(EdwardsPoint::identity());
+    }
+    let mn = V.len() * N;
+
+    let mut z_pow = Vec::with_capacity(V.len());
+
+    let mut d = ScalarVector::new(mn);
+    for j in 1 ..= V.len() {
+      z_pow.push(z.pow(Scalar::from(2 * u64::try_from(j).unwrap()))); // TODO: Optimize this
+      d = d.add_vec(&Self::d_j(j, V.len()).mul(z_pow[j - 1]));
+    }
+
+    let mut ascending_y = ScalarVector(vec![y]);
+    for i in 1 .. d.len() {
+      ascending_y.0.push(ascending_y[i - 1] * y);
+    }
+    let y_pows = ascending_y.clone().sum();
+
+    let mut descending_y = ascending_y.clone();
+    descending_y.0.reverse();
+
+    let d_descending_y = d.mul_vec(&descending_y);
+
+    let y_mn_plus_one = descending_y[0] * y;
+
+    let mut commitment_accum = EdwardsPoint::identity();
+    for (j, commitment) in V.0.iter().enumerate() {
+      commitment_accum += *commitment * z_pow[j];
+    }
+
+    let neg_z = -z;
+    let mut A_terms = Vec::with_capacity((generators.len() * 2) + 2);
+    for (i, d_y_z) in d_descending_y.add(z).0.drain(..).enumerate() {
+      A_terms.push((neg_z, generators.generator(GeneratorsList::GBold1, i)));
+      A_terms.push((d_y_z, generators.generator(GeneratorsList::HBold1, i)));
+    }
+    A_terms.push((y_mn_plus_one, commitment_accum));
+    A_terms.push((
+      ((y_pows * z) - (d.sum() * y_mn_plus_one * z) - (y_pows * z.square())),
+      generators.g(),
+    ));
+
+    (y, d_descending_y, y_mn_plus_one, z, ScalarVector(z_pow), A + multiexp_vartime(&A_terms))
+  }
+
+  pub(crate) fn prove<R: RngCore + CryptoRng>(
+    self,
+    rng: &mut R,
+    witness: AggregateRangeWitness,
+  ) -> Option<AggregateRangeProof> {
+    // Check for consistency with the witness
+    if self.V.len() != witness.values.len() {
+      return None;
+    }
+    for (commitment, (value, gamma)) in
+      self.V.iter().zip(witness.values.iter().zip(witness.gammas.iter()))
+    {
+      if Commitment::new(**gamma, *value).calculate() != **commitment {
+        return None;
+      }
+    }
+
+    let Self { generators, V } = self;
+    // Monero expects all of these points to be torsion-free
+    // Generally, for Bulletproofs, it sends points * INV_EIGHT and then performs a torsion clear
+    // by multiplying by 8
+    // This also restores the original value due to the preprocessing
+    // Commitments aren't transmitted INV_EIGHT though, so this multiplies by INV_EIGHT to enable
+    // clearing its cofactor without mutating the value
+    // For some reason, these values are transcripted * INV_EIGHT, not as transmitted
+    let mut V = V.into_iter().map(|V| EdwardsPoint(V.0 * crate::INV_EIGHT())).collect::<Vec<_>>();
+    let mut transcript = initial_transcript(V.iter());
+    V.iter_mut().for_each(|V| *V = V.mul_by_cofactor());
+
+    // Pad V
+    while V.len() < padded_pow_of_2(V.len()) {
+      V.push(EdwardsPoint::identity());
+    }
+
+    let generators = generators.reduce(V.len() * N);
+
+    let mut d_js = Vec::with_capacity(V.len());
+    let mut a_l = ScalarVector(Vec::with_capacity(V.len() * N));
+    for j in 1 ..= V.len() {
+      d_js.push(Self::d_j(j, V.len()));
+      a_l.0.append(&mut u64_decompose(*witness.values.get(j - 1).unwrap_or(&0)).0);
+    }
+
+    let a_r = a_l.sub(Scalar::ONE);
+
+    let alpha = Scalar::random(&mut *rng);
+
+    let mut A_terms = Vec::with_capacity((generators.len() * 2) + 1);
+    for (i, a_l) in a_l.0.iter().enumerate() {
+      A_terms.push((*a_l, generators.generator(GeneratorsList::GBold1, i)));
+    }
+    for (i, a_r) in a_r.0.iter().enumerate() {
+      A_terms.push((*a_r, generators.generator(GeneratorsList::HBold1, i)));
+    }
+    A_terms.push((alpha, generators.h()));
+    let mut A = multiexp(&A_terms);
+    A_terms.zeroize();
+
+    // Multiply by INV_EIGHT per earlier commentary
+    A.0 *= crate::INV_EIGHT();
+
+    let (y, d_descending_y, y_mn_plus_one, z, z_pow, A_hat) =
+      Self::compute_A_hat(PointVector(V), &generators, &mut transcript, A);
+
+    let a_l = a_l.sub(z);
+    let a_r = a_r.add_vec(&d_descending_y).add(z);
+    let mut alpha = alpha;
+    for j in 1 ..= witness.gammas.len() {
+      alpha += z_pow[j - 1] * witness.gammas[j - 1] * y_mn_plus_one;
+    }
+
+    Some(AggregateRangeProof {
+      A,
+      wip: WipStatement::new(generators, A_hat, y)
+        .prove(rng, transcript, WipWitness::new(a_l, a_r, alpha).unwrap())
+        .unwrap(),
+    })
+  }
+
+  pub(crate) fn verify<Id: Copy + Zeroize, R: RngCore + CryptoRng>(
+    self,
+    rng: &mut R,
+    verifier: &mut BatchVerifier<Id, EdwardsPoint>,
+    id: Id,
+    proof: AggregateRangeProof,
+  ) -> bool {
+    let Self { generators, V } = self;
+
+    let mut V = V.into_iter().map(|V| EdwardsPoint(V.0 * crate::INV_EIGHT())).collect::<Vec<_>>();
+    let mut transcript = initial_transcript(V.iter());
+    V.iter_mut().for_each(|V| *V = V.mul_by_cofactor());
+
+    let generators = generators.reduce(V.len() * N);
+
+    let (y, _, _, _, _, A_hat) =
+      Self::compute_A_hat(PointVector(V), &generators, &mut transcript, proof.A);
+    WipStatement::new(generators, A_hat, y).verify(rng, verifier, id, transcript, proof.wip)
+  }
+}