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Merge pull request #27 from mir-protocol/fri-reduction-arity-contd

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More work on FRI reduction arity
This commit is contained in:
wborgeaud 2021-04-29 08:23:40 +02:00 committed by GitHub
commit c464c038af
4 changed files with 79 additions and 172 deletions
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4
src/field/crandall_field.rs
View File

@ -38,13 +38,13 @@ impl Hash for CrandallField {
impl Display for CrandallField {
fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
Display::fmt(&self.0, f)
Display::fmt(&self.to_canonical_u64(), f)
}
}
impl Debug for CrandallField {
fn fmt(&self, f: &mut Formatter<'_>) -> fmt::Result {
Debug::fmt(&self.0, f)
Debug::fmt(&self.to_canonical_u64(), f)
}
}

147
src/fri.rs
View File

@ -2,13 +2,13 @@ use crate::field::fft::fft;
use crate::field::field::Field;
use crate::field::lagrange::{barycentric_weights, interpolate};
use crate::hash::hash_n_to_1;
use crate::merkle_proofs::verify_merkle_proof_subtree;
use crate::merkle_proofs::verify_merkle_proof;
use crate::merkle_tree::MerkleTree;
use crate::plonk_challenger::Challenger;
use crate::plonk_common::reduce_with_powers;
use crate::polynomial::polynomial::{PolynomialCoeffs, PolynomialValues};
use crate::proof::{FriProof, FriQueryRound, FriQueryStep, Hash};
use crate::util::{log2_strict, reverse_bits};
use crate::util::{log2_strict, reverse_bits, reverse_index_bits_in_place};
use anyhow::{ensure, Result};
/// Somewhat arbitrary. Smaller values will increase delta, but with diminishing returns,
@ -93,18 +93,28 @@ fn fri_committed_trees<F: Field>(
challenger: &mut Challenger<F>,
config: &FriConfig,
) -> (Vec<MerkleTree<F>>, PolynomialCoeffs<F>) {
let mut trees = vec![MerkleTree::new(
polynomial_values.values.iter().map(|&v| vec![v]).collect(),
true,
)];
let mut values = polynomial_values.clone();
let mut coeffs = polynomial_coeffs.clone();
let mut values;
challenger.observe_hash(&trees[0].root);
let mut trees = Vec::new();
let num_reductions = config.reduction_arity_bits.len();
for i in 0..num_reductions {
let arity = 1 << config.reduction_arity_bits[i];
reverse_index_bits_in_place(&mut values.values);
let tree = MerkleTree::new(
values
.values
.chunks(arity)
.map(|chunk| chunk.to_vec())
.collect(),
false,
);
challenger.observe_hash(&tree.root);
trees.push(tree);
let beta = challenger.get_challenge();
// P(x) = sum_{i<r} x^i * P_i(x^r) becomes sum_{i<r} beta^i * P_i(x).
coeffs = PolynomialCoeffs::new(
@ -114,17 +124,10 @@ fn fri_committed_trees<F: Field>(
.map(|chunk| reduce_with_powers(chunk, beta))
.collect::<Vec<_>>(),
);
if i == num_reductions - 1 {
// We don't need a Merkle root for the final polynomial, since we send its
// coefficients directly to the verifier.
break;
}
// TODO: Is it faster to interpolate?
values = fft(coeffs.clone());
let tree = MerkleTree::new(values.values.iter().map(|&v| vec![v]).collect(), true);
challenger.observe_hash(&tree.root);
trees.push(tree);
}
challenger.observe_elements(&coeffs.coeffs);
(trees, coeffs)
}
@ -180,11 +183,11 @@ fn fri_prover_query_rounds<F: Field>(
config: &FriConfig,
) -> Vec<FriQueryRound<F>> {
(0..config.num_query_rounds)
.map(|_| fri_query_round(trees, challenger, n, config))
.map(|_| fri_prover_query_round(trees, challenger, n, config))
.collect()
}
fn fri_query_round<F: Field>(
fn fri_prover_query_round<F: Field>(
trees: &[MerkleTree<F>],
challenger: &mut Challenger<F>,
n: usize,
@ -194,28 +197,22 @@ fn fri_query_round<F: Field>(
// TODO: Challenger doesn't change between query rounds, so x is always the same.
let x = challenger.get_challenge();
let mut domain_size = n;
let mut x_index = x.to_canonical_u64() as usize;
let mut x_index = x.to_canonical_u64() as usize % n;
for (i, tree) in trees.iter().enumerate() {
let arity_bits = config.reduction_arity_bits[i];
let arity = 1 << arity_bits;
let next_domain_size = domain_size >> arity_bits;
x_index %= domain_size;
let roots_coset_indices = coset_indices(x_index, next_domain_size, domain_size, arity);
let evals = if i == 0 {
// For the first layer, we need to send the evaluation at `x` too.
roots_coset_indices
.iter()
.map(|&index| tree.get(index)[0])
.collect()
tree.get(x_index >> arity_bits).to_vec()
} else {
// For the other layers, we don't need to send the evaluation at `x`, since it can
// be inferred by the verifier. See the `compute_evaluation` function.
roots_coset_indices[1..]
.iter()
.map(|&index| tree.get(index)[0])
.collect()
let mut evals = tree.get(x_index >> arity_bits).to_vec();
evals.remove(x_index & (arity - 1));
evals
};
let merkle_proof = tree.prove_subtree(x_index & (next_domain_size - 1), arity_bits);
let merkle_proof = tree.prove(x_index >> arity_bits);
query_steps.push(FriQueryStep {
evals,
@ -223,32 +220,34 @@ fn fri_query_round<F: Field>(
});
domain_size = next_domain_size;
x_index >>= arity_bits;
}
FriQueryRound { steps: query_steps }
}
/// Returns the indices in the domain of all `y` in `F` with `y^arity=x^arity`, starting with `x` itself.
fn coset_indices(
x_index: usize,
next_domain_size: usize,
domain_size: usize,
arity: usize,
) -> Vec<usize> {
(0..arity)
.map(|i| (i * next_domain_size + x_index) % domain_size)
.collect()
}
/// Computes P'(x^arity) from {P(x*g^i)}_(i=0..arity), where g is a `arity`-th root of unity
/// and P' is the FRI reduced polynomial.
fn compute_evaluation<F: Field>(x: F, arity_bits: usize, last_evals: &[F], beta: F) -> F {
fn compute_evaluation<F: Field>(
x: F,
old_x_index: usize,
arity_bits: usize,
last_evals: &[F],
beta: F,
) -> F {
debug_assert_eq!(last_evals.len(), 1 << arity_bits);
// The answer is gotten by interpolating {(x*g^i, P(x*g^i))} and evaluating at beta.
let g = F::primitive_root_of_unity(arity_bits);
// The evaluation vector needs to be reordered first.
let mut evals = last_evals.to_vec();
reverse_index_bits_in_place(&mut evals);
evals.rotate_left(reverse_bits(old_x_index, arity_bits));
// The answer is gotten by interpolating {(x*g^i, P(x*g^i))} and evaluating at beta.
let points = g
.powers()
.zip(last_evals)
.map(|(y, &e)| (x * y, e))
.zip(evals)
.map(|(y, e)| (x * y, e))
.collect::<Vec<_>>();
let barycentric_weights = barycentric_weights(&points);
interpolate(&points, beta, &barycentric_weights)
@ -312,12 +311,13 @@ fn fri_verifier_query_round<F: Field>(
let mut evaluations = Vec::new();
let x = challenger.get_challenge();
let mut domain_size = n;
let mut x_index = x.to_canonical_u64() as usize;
let mut x_index = x.to_canonical_u64() as usize % n;
let mut old_x_index = 0;
// `subgroup_x` is `subgroup[x_index]`, i.e., the actual field element in the domain.
let mut subgroup_x = F::primitive_root_of_unity(log2_strict(n)).exp_usize(x_index % n);
let log_n = log2_strict(n);
let mut subgroup_x = F::primitive_root_of_unity(log_n).exp_usize(reverse_bits(x_index, log_n));
for (i, &arity_bits) in config.reduction_arity_bits.iter().enumerate() {
let arity = 1 << arity_bits;
x_index %= domain_size;
let next_domain_size = domain_size >> arity_bits;
if i == 0 {
let evals = round_proof.steps[0].evals.clone();
@ -327,33 +327,22 @@ fn fri_verifier_query_round<F: Field>(
// Infer P(y) from {P(x)}_{x^arity=y}.
let e_x = compute_evaluation(
subgroup_x,
old_x_index,
config.reduction_arity_bits[i - 1],
last_evals,
betas[i - 1],
);
let mut evals = round_proof.steps[i].evals.clone();
// Insert P(y) into the evaluation vector, since it wasn't included by the prover.
evals.insert(0, e_x);
evals.insert(x_index & (arity - 1), e_x);
evaluations.push(evals);
};
let sorted_evals = {
let roots_coset_indices = coset_indices(x_index, next_domain_size, domain_size, arity);
let mut sorted_evals_enumerate = evaluations[i].iter().enumerate().collect::<Vec<_>>();
// We need to sort the evaluations so that they match their order in the Merkle tree.
sorted_evals_enumerate.sort_by_key(|&(j, _)| {
reverse_bits(roots_coset_indices[j], log2_strict(domain_size))
});
sorted_evals_enumerate
.into_iter()
.map(|(_, &e)| vec![e])
.collect()
};
verify_merkle_proof_subtree(
sorted_evals,
x_index & (next_domain_size - 1),
verify_merkle_proof(
evaluations[i].clone(),
x_index >> arity_bits,
proof.commit_phase_merkle_roots[i],
&round_proof.steps[i].merkle_proof,
true,
false,
)?;
if i > 0 {
@ -363,12 +352,15 @@ fn fri_verifier_query_round<F: Field>(
}
}
domain_size = next_domain_size;
old_x_index = x_index;
x_index >>= arity_bits;
}
let last_evals = evaluations.last().unwrap();
let final_arity_bits = *config.reduction_arity_bits.last().unwrap();
let purported_eval = compute_evaluation(
subgroup_x,
old_x_index,
final_arity_bits,
last_evals,
*betas.last().unwrap(),
@ -393,6 +385,7 @@ mod tests {
use crate::field::crandall_field::CrandallField;
use crate::field::fft::ifft;
use anyhow::Result;
use rand::rngs::ThreadRng;
use rand::Rng;
fn test_fri(
@ -421,8 +414,7 @@ mod tests {
Ok(())
}
fn gen_arities(degree_log: usize) -> Vec<usize> {
let mut rng = rand::thread_rng();
fn gen_arities(degree_log: usize, rng: &mut ThreadRng) -> Vec<usize> {
let mut arities = Vec::new();
let mut remaining = degree_log;
while remaining > 0 {
@ -435,15 +427,18 @@ mod tests {
#[test]
fn test_fri_multi_params() -> Result<()> {
let mut rng = rand::thread_rng();
for degree_log in 1..6 {
for rate_bits in 0..4 {
for rate_bits in 0..3 {
for num_query_round in 0..4 {
test_fri(
degree_log,
rate_bits,
gen_arities(degree_log),
num_query_round,
)?;
for _ in 0..3 {
test_fri(
degree_log,
rate_bits,
gen_arities(degree_log, &mut rng),
num_query_round,
)?;
}
}
}
}

33
src/merkle_proofs.rs
View File

@ -29,6 +29,11 @@ pub(crate) fn verify_merkle_proof<F: Field>(
proof: &MerkleProof<F>,
reverse_bits: bool,
) -> Result<()> {
ensure!(
leaf_index >> proof.siblings.len() == 0,
"Merkle leaf index is too large."
);
let index = if reverse_bits {
crate::util::reverse_bits(leaf_index, proof.siblings.len())
} else {
@ -48,34 +53,6 @@ pub(crate) fn verify_merkle_proof<F: Field>(
Ok(())
}
/// Verifies that the given subtree is present at the given index in the Merkle tree with the
/// given root.
pub(crate) fn verify_merkle_proof_subtree<F: Field>(
subtree_leaves_data: Vec<Vec<F>>,
subtree_index: usize,
merkle_root: Hash<F>,
proof: &MerkleProof<F>,
reverse_bits: bool,
) -> Result<()> {
let index = if reverse_bits {
crate::util::reverse_bits(subtree_index, proof.siblings.len())
} else {
subtree_index
};
let mut current_digest = MerkleTree::new(subtree_leaves_data, false).root;
for (i, &sibling_digest) in proof.siblings.iter().enumerate() {
let bit = (index >> i & 1) == 1;
current_digest = if bit {
compress(sibling_digest, current_digest)
} else {
compress(current_digest, sibling_digest)
}
}
ensure!(current_digest == merkle_root, "Invalid Merkle proof.");
Ok(())
}
impl<F: Field> CircuitBuilder<F> {
/// Verifies that the given leaf data is present at the given index in the Merkle tree with the
/// given root.

67
src/merkle_tree.rs
View File

@ -78,42 +78,6 @@ impl<F: Field> MerkleTree<F> {
.collect(),
}
}
/// Create a Merkle proof for an entire subtree.
/// Example:
/// ```tree
/// G
/// / \
/// / \
/// / \
/// E F
/// / \ / \
/// A B C D
/// ```
/// `self.prove_subtree(0, 1)` gives a Merkle proof for the subtree E->(A,B), i.e., the
/// path (F,).
pub fn prove_subtree(&self, subtree_index: usize, subtree_height: usize) -> MerkleProof<F> {
let index = if self.reverse_bits {
reverse_bits(
subtree_index,
log2_strict(self.leaves.len()) - subtree_height,
)
} else {
subtree_index
};
MerkleProof {
siblings: self
.layers
.iter()
.skip(subtree_height)
.scan(index, |acc, layer| {
let index = *acc ^ 1;
*acc >>= 1;
Some(layer[index])
})
.collect(),
}
}
}
#[cfg(test)]
@ -121,7 +85,7 @@ mod tests {
use anyhow::Result;
use crate::field::crandall_field::CrandallField;
use crate::merkle_proofs::{verify_merkle_proof, verify_merkle_proof_subtree};
use crate::merkle_proofs::verify_merkle_proof;
use super::*;
@ -143,32 +107,6 @@ mod tests {
}
Ok(())
}
fn verify_all_subtrees<F: Field>(
leaves: Vec<Vec<F>>,
n: usize,
log_n: usize,
reverse_bits: bool,
) -> Result<()> {
let tree = MerkleTree::new(leaves.clone(), reverse_bits);
for height in 0..=log_n {
for i in 0..(n >> height) {
let index = if reverse_bits {
crate::util::reverse_bits(i, log_n - height)
} else {
i
};
let subtree_proof = tree.prove_subtree(i, height);
verify_merkle_proof_subtree(
tree.leaves[index << height..(index + 1) << height].to_vec(),
i,
tree.root,
&subtree_proof,
reverse_bits,
)?;
}
}
Ok(())
}
#[test]
fn test_merkle_trees() -> Result<()> {
@ -179,10 +117,7 @@ mod tests {
let leaves = random_data::<F>(n, 7);
verify_all_leaves(leaves.clone(), n, false)?;
verify_all_subtrees(leaves.clone(), n, log_n, false)?;
verify_all_leaves(leaves.clone(), n, true)?;
verify_all_subtrees(leaves, n, log_n, true)?;
Ok(())
}