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/tests/bulletproofs/mod.rs

@@ -0,0 +1,94 @@
+use hex_literal::hex;
+use rand_core::OsRng;
+
+use curve25519_dalek::{scalar::Scalar, edwards::CompressedEdwardsY};
+use multiexp::BatchVerifier;
+
+use crate::{
+  Commitment, random_scalar,
+  ringct::bulletproofs::{Bulletproofs, original::OriginalStruct},
+};
+
+mod plus;
+
+#[test]
+fn bulletproofs_vector() {
+  let scalar = |scalar| Scalar::from_canonical_bytes(scalar).unwrap();
+  let point = |point| CompressedEdwardsY(point).decompress().unwrap();
+
+  // Generated from Monero
+  assert!(Bulletproofs::Original(OriginalStruct {
+    A: point(hex!("ef32c0b9551b804decdcb107eb22aa715b7ce259bf3c5cac20e24dfa6b28ac71")),
+    S: point(hex!("e1285960861783574ee2b689ae53622834eb0b035d6943103f960cd23e063fa0")),
+    T1: point(hex!("4ea07735f184ba159d0e0eb662bac8cde3eb7d39f31e567b0fbda3aa23fe5620")),
+    T2: point(hex!("b8390aa4b60b255630d40e592f55ec6b7ab5e3a96bfcdcd6f1cd1d2fc95f441e")),
+    taux: scalar(hex!("5957dba8ea9afb23d6e81cc048a92f2d502c10c749dc1b2bd148ae8d41ec7107")),
+    mu: scalar(hex!("923023b234c2e64774b820b4961f7181f6c1dc152c438643e5a25b0bf271bc02")),
+    L: vec![
+      point(hex!("c45f656316b9ebf9d357fb6a9f85b5f09e0b991dd50a6e0ae9b02de3946c9d99")),
+      point(hex!("9304d2bf0f27183a2acc58cc755a0348da11bd345485fda41b872fee89e72aac")),
+      point(hex!("1bb8b71925d155dd9569f64129ea049d6149fdc4e7a42a86d9478801d922129b")),
+      point(hex!("5756a7bf887aa72b9a952f92f47182122e7b19d89e5dd434c747492b00e1c6b7")),
+      point(hex!("6e497c910d102592830555356af5ff8340e8d141e3fb60ea24cfa587e964f07d")),
+      point(hex!("f4fa3898e7b08e039183d444f3d55040f3c790ed806cb314de49f3068bdbb218")),
+      point(hex!("0bbc37597c3ead517a3841e159c8b7b79a5ceaee24b2a9a20350127aab428713")),
+    ],
+    R: vec![
+      point(hex!("609420ba1702781692e84accfd225adb3d077aedc3cf8125563400466b52dbd9")),
+      point(hex!("fb4e1d079e7a2b0ec14f7e2a3943bf50b6d60bc346a54fcf562fb234b342abf8")),
+      point(hex!("6ae3ac97289c48ce95b9c557289e82a34932055f7f5e32720139824fe81b12e5")),
+      point(hex!("d071cc2ffbdab2d840326ad15f68c01da6482271cae3cf644670d1632f29a15c")),
+      point(hex!("e52a1754b95e1060589ba7ce0c43d0060820ebfc0d49dc52884bc3c65ad18af5")),
+      point(hex!("41573b06140108539957df71aceb4b1816d2409ce896659aa5c86f037ca5e851")),
+      point(hex!("a65970b2cc3c7b08b2b5b739dbc8e71e646783c41c625e2a5b1535e3d2e0f742")),
+    ],
+    a: scalar(hex!("0077c5383dea44d3cd1bc74849376bd60679612dc4b945255822457fa0c0a209")),
+    b: scalar(hex!("fe80cf5756473482581e1d38644007793ddc66fdeb9404ec1689a907e4863302")),
+    t: scalar(hex!("40dfb08e09249040df997851db311bd6827c26e87d6f0f332c55be8eef10e603"))
+  })
+  .verify(
+    &mut OsRng,
+    &[
+      // For some reason, these vectors are * INV_EIGHT
+      point(hex!("8e8f23f315edae4f6c2f948d9a861e0ae32d356b933cd11d2f0e031ac744c41f"))
+        .mul_by_cofactor(),
+      point(hex!("2829cbd025aa54cd6e1b59a032564f22f0b2e5627f7f2c4297f90da438b5510f"))
+        .mul_by_cofactor(),
+    ]
+  ));
+}
+
+macro_rules! bulletproofs_tests {
+  ($name: ident, $max: ident, $plus: literal) => {
+    #[test]
+    fn $name() {
+      // Create Bulletproofs for all possible output quantities
+      let mut verifier = BatchVerifier::new(16);
+      for i in 1 ..= 16 {
+        let commitments = (1 ..= i)
+          .map(|i| Commitment::new(random_scalar(&mut OsRng), u64::try_from(i).unwrap()))
+          .collect::<Vec<_>>();
+
+        let bp = Bulletproofs::prove(&mut OsRng, &commitments, $plus).unwrap();
+
+        let commitments = commitments.iter().map(Commitment::calculate).collect::<Vec<_>>();
+        assert!(bp.verify(&mut OsRng, &commitments));
+        assert!(bp.batch_verify(&mut OsRng, &mut verifier, i, &commitments));
+      }
+      assert!(verifier.verify_vartime());
+    }
+
+    #[test]
+    fn $max() {
+      // Check Bulletproofs errors if we try to prove for too many outputs
+      let mut commitments = vec![];
+      for _ in 0 .. 17 {
+        commitments.push(Commitment::new(Scalar::ZERO, 0));
+      }
+      assert!(Bulletproofs::prove(&mut OsRng, &commitments, $plus).is_err());
+    }
+  };
+}
+
+bulletproofs_tests!(bulletproofs, bulletproofs_max, false);
+bulletproofs_tests!(bulletproofs_plus, bulletproofs_plus_max, true);

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

@@ -0,0 +1,30 @@
+use rand_core::{RngCore, OsRng};
+
+use multiexp::BatchVerifier;
+use group::ff::Field;
+use dalek_ff_group::{Scalar, EdwardsPoint};
+
+use crate::{
+  Commitment,
+  ringct::bulletproofs::plus::aggregate_range_proof::{
+    AggregateRangeStatement, AggregateRangeWitness,
+  },
+};
+
+#[test]
+fn test_aggregate_range_proof() {
+  let mut verifier = BatchVerifier::new(16);
+  for m in 1 ..= 16 {
+    let mut commitments = vec![];
+    for _ in 0 .. m {
+      commitments.push(Commitment::new(*Scalar::random(&mut OsRng), OsRng.next_u64()));
+    }
+    let commitment_points = commitments.iter().map(|com| EdwardsPoint(com.calculate())).collect();
+    let statement = AggregateRangeStatement::new(commitment_points).unwrap();
+    let witness = AggregateRangeWitness::new(&commitments).unwrap();
+
+    let proof = statement.clone().prove(&mut OsRng, witness).unwrap();
+    statement.verify(&mut OsRng, &mut verifier, (), proof);
+  }
+  assert!(verifier.verify_vartime());
+}

coins/monero/src/tests/bulletproofs/plus/mod.rs

@@ -0,0 +1,4 @@
+#[cfg(test)]
+mod weighted_inner_product;
+#[cfg(test)]
+mod aggregate_range_proof;

coins/monero/src/tests/bulletproofs/plus/weighted_inner_product.rs

@@ -0,0 +1,82 @@
+// The inner product relation is P = sum(g_bold * a, h_bold * b, g * (a * y * b), h * alpha)
+
+use rand_core::OsRng;
+
+use multiexp::BatchVerifier;
+use group::{ff::Field, Group};
+use dalek_ff_group::{Scalar, EdwardsPoint};
+
+use crate::ringct::bulletproofs::plus::{
+  ScalarVector, PointVector, GeneratorsList, Generators,
+  weighted_inner_product::{WipStatement, WipWitness},
+  weighted_inner_product,
+};
+
+#[test]
+fn test_zero_weighted_inner_product() {
+  #[allow(non_snake_case)]
+  let P = EdwardsPoint::identity();
+  let y = Scalar::random(&mut OsRng);
+
+  let generators = Generators::new().reduce(1);
+  let statement = WipStatement::new(generators, P, y);
+  let witness = WipWitness::new(ScalarVector::new(1), ScalarVector::new(1), Scalar::ZERO).unwrap();
+
+  let transcript = Scalar::random(&mut OsRng);
+  let proof = statement.clone().prove(&mut OsRng, transcript, witness).unwrap();
+
+  let mut verifier = BatchVerifier::new(1);
+  statement.verify(&mut OsRng, &mut verifier, (), transcript, proof);
+  assert!(verifier.verify_vartime());
+}
+
+#[test]
+fn test_weighted_inner_product() {
+  // P = sum(g_bold * a, h_bold * b, g * (a * y * b), h * alpha)
+  let mut verifier = BatchVerifier::new(6);
+  let generators = Generators::new();
+  for i in [1, 2, 4, 8, 16, 32] {
+    let generators = generators.reduce(i);
+    let g = generators.g();
+    let h = generators.h();
+    assert_eq!(generators.len(), i);
+    let mut g_bold = vec![];
+    let mut h_bold = vec![];
+    for i in 0 .. i {
+      g_bold.push(generators.generator(GeneratorsList::GBold1, i));
+      h_bold.push(generators.generator(GeneratorsList::HBold1, i));
+    }
+    let g_bold = PointVector(g_bold);
+    let h_bold = PointVector(h_bold);
+
+    let mut a = ScalarVector::new(i);
+    let mut b = ScalarVector::new(i);
+    let alpha = Scalar::random(&mut OsRng);
+
+    let y = Scalar::random(&mut OsRng);
+    let mut y_vec = ScalarVector::new(g_bold.len());
+    y_vec[0] = y;
+    for i in 1 .. y_vec.len() {
+      y_vec[i] = y_vec[i - 1] * y;
+    }
+
+    for i in 0 .. i {
+      a[i] = Scalar::random(&mut OsRng);
+      b[i] = Scalar::random(&mut OsRng);
+    }
+
+    #[allow(non_snake_case)]
+    let P = g_bold.multiexp(&a) +
+      h_bold.multiexp(&b) +
+      (g * weighted_inner_product(&a, &b, &y_vec)) +
+      (h * alpha);
+
+    let statement = WipStatement::new(generators, P, y);
+    let witness = WipWitness::new(a, b, alpha).unwrap();
+
+    let transcript = Scalar::random(&mut OsRng);
+    let proof = statement.clone().prove(&mut OsRng, transcript, witness).unwrap();
+    statement.verify(&mut OsRng, &mut verifier, (), transcript, proof);
+  }
+  assert!(verifier.verify_vartime());
+}