Fibonacci Stark Prover (#59)

* prover sub crate created

* working on fold function

* merge

* test working

* fold test completed

* next_fri_layer function

* Dependencies removed

* using iterator step_by

* fmt

* reordering fri functions

* fri_decommit init

* evaluate_vec in polynomial and reference in evaluate

* using evaluate_vec

* evaluate_vec changed to evaluate_slice

* evaluate_slice changed

* fri_commitment

* fri continuation

* comment moved

* fri_decommit_layers

* comments added

* polynomial.rs merge confilct

* adapting to the new code

* conflicts solved

* append in transcript

* insert last_evaluation in transcript

* beta from transcript.challenge()

* test: generating subgroups

* prover sub crate created

* Save work in progress

* Add first iteration of function to get composition polynomials from trace and air

* Add test for get_composition_poly

* Add get_coefficients function

* Tidy up code

* Add docs

* Fix tests

* Add u128_prime field and make get_composition_poly return a Polynomial data structure

* Fixes from rebasing

* Apply clippy suggestions

* Make functions pub crate

* Tidy up code

* Tidy up code

* Minor fixes

* Use U384 instead of U128

* Tidy up code and remove unnecessary u128 field element module

* generate_vec_roots

* generate_vec_roots in lib

* Return trace polynomial from get_composition_poly

* coset_factor

* Add coset evaluation and fri commitment steps

* Add result to get_cp_and_tp

* Change error description and module name

* Add decommitment step

* Start filling the stark proof struct

* Small comments

* Add first verifier step

* Switch to hardcoded fibonacci trace

* Start FRI verification step

* More progress

* Improve code, change field to 17 for testing purposes

* Fix FRI operation

* Go back to fibonacci example with test passing

* Refactor functions that use fiat shamir to take in a transcript

* Add TODO

* Add comments

* Moved field definition to lib, removed duplicated definitions

* Renamed types

* Simplified operations

* Refactor roots of unity generator

* Small refactor

* Refactor roots of unity generator

* Update comment

* Extracted FRI

* Refactor verify

* Refactor clippy

* Re ordered prover

* cargo fmt

* fix roots of unity

* Remove air

* Prover -> Stark

* Move folders

* Uncomment tests, remove unused code

* Fix fri_functions tests

* Remove fri_merkle_tree module, move to mod.rs

* Clippy

* Remove TODOs

---------

Co-authored-by: Pablo Deymonnaz <deymonnaz@gmail.com>
Co-authored-by: Mariano Nicolini <mariano.nicolini.91@gmail.com>
Co-authored-by: Javier Chatruc <jrchatruc@gmail.com>
Co-authored-by: MauroFab <maurotoscano2@gmail.com>

Cargo.toml

@@ -3,4 +3,5 @@
 members = [
     "math",
     "crypto",
+    "proving-system/stark",
 ]

crypto/src/fiat_shamir/mod.rs

@@ -1 +1 @@
-mod transcript;
+pub mod transcript;

crypto/src/fiat_shamir/transcript.rs

@@ -1,24 +1,24 @@
 use sha3::{Digest, Sha3_256};
 
-struct Transcript {
+pub struct Transcript {
     hasher: Sha3_256,
 }
 
 impl Transcript {
-    #[allow(unused)]
-    fn new() -> Self {
+    #[allow(clippy::new_without_default)]
+    pub fn new() -> Self {
         Self {
             hasher: Sha3_256::new(),
         }
     }
 
     #[allow(unused)]
-    fn append(&mut self, new_data: &[u8]) {
+    pub fn append(&mut self, new_data: &[u8]) {
         self.hasher.update(&mut new_data.to_owned());
     }
 
     #[allow(unused)]
-    fn challenge(&mut self) -> [u8; 32] {
+    pub fn challenge(&mut self) -> [u8; 32] {
         let mut result_hash = [0_u8; 32];
         result_hash.copy_from_slice(&self.hasher.finalize_reset());
         self.hasher.update(result_hash);

crypto/src/merkle_tree/mod.rs

@@ -8,7 +8,7 @@ use crate::hash::traits::IsCryptoHash;
 use self::{merkle::MerkleTree, proof::Proof};
 
 pub mod merkle;
-mod proof;
+pub mod proof;
 mod utils;
 
 pub type U64F = U64PrimeField<0xFFFF_FFFF_0000_0001_u64>;

crypto/src/merkle_tree/proof.rs

@@ -5,12 +5,29 @@ use lambdaworks_math::{
     traits::ByteConversion,
 };
 
+#[derive(Debug, Clone)]
 pub struct Proof<F: IsField, H: IsCryptoHash<F>> {
     pub value: FieldElement<F>,
     pub merkle_path: Vec<(FieldElement<F>, bool)>,
     pub hasher: H,
 }
 
+impl<F: IsField, H: IsCryptoHash<F>> Proof<F, H> {
+    pub fn verify(&self, root_hash: FieldElement<F>) -> bool {
+        let mut hashed_value = self.hasher.hash_one(self.value.clone());
+
+        for (sibling_node, is_left) in self.merkle_path.iter().rev() {
+            if *is_left {
+                hashed_value = self.hasher.hash_two(hashed_value, sibling_node.clone());
+            } else {
+                hashed_value = self.hasher.hash_two(sibling_node.clone(), hashed_value);
+            }
+        }
+
+        root_hash == hashed_value
+    }
+}
+
 impl<F, H> ByteConversion for Proof<F, H>
 where
     F: IsField,

math/src/field/element.rs

@@ -300,6 +300,11 @@ where
         &self.value
     }
 
+    // Returns the representative of the value stored
+    pub fn representative(&self) -> F::BaseType {
+        F::representative(self.value.clone())
+    }
+
     /// Returns the multiplicative inverse of `self`
     pub fn inv(&self) -> Self {
         Self {

math/src/field/extensions/cubic.rs

@@ -127,6 +127,10 @@ where
     fn from_base_type(x: [FieldElement<Q::BaseField>; 3]) -> [FieldElement<Q::BaseField>; 3] {
         x
     }
+
+    fn representative(_x: Self::BaseType) -> Self::BaseType {
+        todo!()
+    }
 }
 
 #[cfg(test)]

math/src/field/extensions/quadratic.rs

@@ -105,6 +105,10 @@ where
     fn from_base_type(x: [FieldElement<Q::BaseField>; 2]) -> [FieldElement<Q::BaseField>; 2] {
         x
     }
+
+    fn representative(_x: Self::BaseType) -> Self::BaseType {
+        todo!()
+    }
 }
 
 #[cfg(test)]

math/src/field/fields/u384_prime_field.rs

@@ -151,6 +151,11 @@ where
     fn from_base_type(x: Self::BaseType) -> Self::BaseType {
         MontgomeryAlgorithms::cios(&x, &C::R2, &C::MODULUS, &C::MU)
     }
+
+    // TO DO: Add tests for representatives
+    fn representative(x: Self::BaseType) -> Self::BaseType {
+        MontgomeryAlgorithms::cios(&x, &U384::from_u64(1), &C::MODULUS, &C::MU)
+    }
 }
 
 impl<C> ByteConversion for FieldElement<MontgomeryBackendPrimeField<C>>

math/src/field/fields/u64_prime_field.rs

@@ -56,6 +56,10 @@ impl<const MODULUS: u64> IsField for U64PrimeField<MODULUS> {
     fn from_base_type(x: u64) -> u64 {
         Self::from_u64(x)
     }
+
+    fn representative(x: u64) -> u64 {
+        x
+    }
 }
 
 impl<const MODULUS: u64> Copy for U64FieldElement<MODULUS> {}

math/src/field/test_fields/u64_test_field.rs

@@ -50,6 +50,10 @@ impl<const MODULUS: u64> IsField for U64TestField<MODULUS> {
     fn from_base_type(x: u64) -> u64 {
         Self::from_u64(x)
     }
+
+    fn representative(x: u64) -> u64 {
+        x
+    }
 }
 
 impl<const MODULUS: u64> IsTwoAdicField for U64TestField<MODULUS> {

math/src/field/traits.rs

@@ -93,4 +93,7 @@ pub trait IsField: Debug + Clone {
     /// Takes as input an element of BaseType and returns the internal representation
     /// of that element in the field.
     fn from_base_type(x: Self::BaseType) -> Self::BaseType;
+
+    // Returns the representative of the value stored
+    fn representative(a: Self::BaseType) -> Self::BaseType;
 }

math/src/polynomial.rs

@@ -6,7 +6,7 @@ use std::ops;
 /// as a vector of coefficients `[c_0, c_1, ... , c_n]`
 #[derive(Debug, Clone, PartialEq, Eq)]
 pub struct Polynomial<FE> {
-    coefficients: Vec<FE>,
+    pub coefficients: Vec<FE>,
 }
 
 impl<F: IsField> Polynomial<FieldElement<F>> {
@@ -160,6 +160,32 @@ impl<F: IsField> Polynomial<FieldElement<F>> {
     }
 }
 
+// TODO: This is not an optimal implementation, it should use FFT to interpolate.
+pub fn compose<F>(
+    poly_1: &Polynomial<FieldElement<F>>,
+    poly_2: &Polynomial<FieldElement<F>>,
+) -> Polynomial<FieldElement<F>>
+where
+    F: IsField,
+{
+    let max_degree: u64 = (poly_1.degree() * poly_2.degree()) as u64;
+
+    let mut interpolation_points = vec![];
+    for i in 0_u64..max_degree + 1 {
+        interpolation_points.push(FieldElement::<F>::from(i));
+    }
+
+    let values: Vec<_> = interpolation_points
+        .iter()
+        .map(|value| {
+            let intermediate_value = poly_2.evaluate(value);
+            poly_1.evaluate(&intermediate_value)
+        })
+        .collect();
+
+    Polynomial::interpolate(interpolation_points.as_slice(), values.as_slice())
+}
+
 impl<F: IsField> ops::Add<&Polynomial<FieldElement<F>>> for &Polynomial<FieldElement<F>> {
     type Output = Polynomial<FieldElement<F>>;
 
@@ -232,6 +258,21 @@ impl<F: IsField> ops::Mul<Polynomial<FieldElement<F>>> for Polynomial<FieldEleme
     }
 }
 
+impl<F: IsField> ops::Mul<FieldElement<F>> for Polynomial<FieldElement<F>> {
+    type Output = Polynomial<FieldElement<F>>;
+
+    fn mul(self, multiplicand: FieldElement<F>) -> Polynomial<FieldElement<F>> {
+        let new_coefficients = self
+            .coefficients
+            .iter()
+            .map(|value| value * &multiplicand)
+            .collect();
+        Polynomial {
+            coefficients: new_coefficients,
+        }
+    }
+}
+
 #[cfg(test)]
 mod tests {
     use crate::field::fields::u64_prime_field::U64PrimeField;
@@ -494,4 +535,14 @@ mod tests {
         let p = Polynomial::interpolate(&[FE::new(0)], &[FE::new(0)]);
         assert_eq!(FE::new(0), p.evaluate(&FE::new(0)));
     }
+
+    #[test]
+    fn composition_works() {
+        let p = Polynomial::new(&[FE::new(0), FE::new(2)]);
+        let q = Polynomial::new(&[FE::new(0), FE::new(0), FE::new(1)]);
+        assert_eq!(
+            compose(&p, &q),
+            Polynomial::new(&[FE::new(0), FE::new(0), FE::new(2)])
+        );
+    }
 }

math/src/unsigned_integer/element.rs

@@ -9,6 +9,7 @@ use std::fmt::Debug;
 
 pub type U384 = UnsignedInteger<6>;
 pub type U256 = UnsignedInteger<4>;
+pub type U128 = UnsignedInteger<2>;
 
 /// A big unsigned integer in base 2^{64} represented
 /// as fixed-size array `limbs` of `u64` components.

proving-system/stark/Cargo.toml

@@ -0,0 +1,12 @@
+[package]
+name = "lambdaworks-stark"
+version = "0.1.0"
+edition = "2021"
+
+# See more keys and their definitions at https://doc.rust-lang.org/cargo/reference/manifest.html
+
+[dependencies]
+rand = "0.8.5"
+lambdaworks-math = { path = "../../math" }
+lambdaworks-crypto = { path = "../../crypto"}
+thiserror = "1.0.38"

proving-system/stark/src/fri/fri_commitment.rs

@@ -0,0 +1,10 @@
+pub use super::{FriMerkleTree, Polynomial, F, FE};
+
+pub struct FriCommitment<FE> {
+    pub poly: Polynomial<FE>,
+    pub domain: Vec<FE>,
+    pub evaluation: Vec<FE>,
+    pub merkle_tree: FriMerkleTree,
+}
+
+pub type FriCommitmentVec<FE> = Vec<FriCommitment<FE>>;

proving-system/stark/src/fri/fri_decommit.rs

@@ -0,0 +1,94 @@
+use super::FE;
+use crate::{fri::fri_commitment::FriCommitmentVec, PrimeField};
+pub use lambdaworks_crypto::fiat_shamir::transcript::Transcript;
+use lambdaworks_crypto::merkle_tree::DefaultHasher;
+
+use lambdaworks_crypto::merkle_tree::proof::Proof;
+
+#[derive(Debug, Clone)]
+pub struct FriDecommitment {
+    pub layer_merkle_paths: Vec<(
+        Proof<PrimeField, DefaultHasher>,
+        Proof<PrimeField, DefaultHasher>,
+    )>,
+    pub last_layer_evaluation: FE,
+}
+
+// verifier chooses a randomness and get the index where
+// they want to evaluate the poly
+// TODO: encapsulate the return type of this function in a struct.
+// This returns a list of authentication paths for evaluations on points and their symmetric counterparts.
+pub fn fri_decommit_layers(
+    commit: &FriCommitmentVec<FE>,
+    index_to_verify: usize,
+) -> FriDecommitment {
+    let mut index = index_to_verify;
+
+    let mut layer_merkle_paths = vec![];
+
+    // with every element of the commit, we look for that one in
+    // the merkle tree and get the corresponding element
+    for commit_i in commit {
+        let length_i = commit_i.domain.len();
+        index %= length_i;
+        let evaluation_i = commit_i.evaluation[index].clone();
+        let auth_path = commit_i.merkle_tree.get_proof(&evaluation_i).unwrap();
+
+        // symmetrical element
+        let index_sym = (index + length_i / 2) % length_i;
+        let evaluation_i_sym = commit_i.evaluation[index_sym].clone();
+        let auth_path_sym = commit_i.merkle_tree.get_proof(&evaluation_i_sym).unwrap();
+
+        layer_merkle_paths.push((auth_path, auth_path_sym));
+    }
+
+    // send the last element of the polynomial
+    let last = commit.last().unwrap();
+    let last_evaluation = last.poly.coefficients[0].clone();
+
+    FriDecommitment {
+        layer_merkle_paths,
+        last_layer_evaluation: last_evaluation,
+    }
+}
+
+// Integration test:
+// * get an arbitrary polynomial
+// * have a domain containing roots of the unity (# is power of two)
+// p = 65_537
+// * apply FRI commitment
+// * apply FRI decommitment
+// assert:
+// * evaluations of the polynomials coincide with calculations from the decommitment
+// * show a fail example: with a monomial
+
+#[cfg(test)]
+mod tests {
+    use crate::fri::U64PrimeField;
+    use lambdaworks_math::field::element::FieldElement;
+    use std::collections::HashSet;
+    const PRIME_GENERATOR: (u64, u64) = (0xFFFF_FFFF_0000_0001_u64, 2717_u64);
+    pub type F = U64PrimeField<{ PRIME_GENERATOR.0 }>;
+    pub type FeGoldilocks = FieldElement<F>;
+
+    #[test]
+    fn test() {
+        let subgroup_size = 1024_u64;
+        let generator_field = FeGoldilocks::new(PRIME_GENERATOR.1);
+        let exp = (PRIME_GENERATOR.0 - 1) / subgroup_size;
+        let generator_of_subgroup = generator_field.pow(exp);
+        let mut numbers = HashSet::new();
+
+        let mut i = 0;
+        for exp in 0..1024_u64 {
+            i += 1;
+            let ret = generator_of_subgroup.pow(exp);
+            numbers.insert(*ret.value());
+            println!("{ret:?}");
+        }
+
+        let count = numbers.len();
+        println!("count: {count}");
+        println!("iter: {i}");
+    }
+}