Sumcheck integration (#977)

* refactor code

* refactor

* add fix error handling

* fix unreachable path error handling

* add README

* fix clippy

* fix comments

* fix typo

* fix clippy

* Update README.md

---------

Co-authored-by: Diego K <[email protected]>

Author: jotabulacios

provers/sumcheck/README.md

@@ -0,0 +1,48 @@
+# Sumcheck Protocol
+
+A naive implementation of the Sumcheck Protocol. 
+
+## Overview
+
+The Sumcheck Protocol allows a prover to convince a verifier that the sum of a multivariate polynomial over the Boolean hypercube equals a claimed value without the verifier having to compute the entire sum.
+
+It is an essential building block for many SNARK protocols, given that it reduces the complexity of computing the sum to performing $O(\nu)$ additions, plus an evaluation at a random point.
+
+The protocol proceeds in rounds, with one round per variable of the multivariate polynomial. In each round, the prover sends a univariate polynomial, and the verifier responds with a random challenge. This process reduces a claim about a multivariate polynomial to a claim about a single evaluation point.
+
+
+## Example
+
+Here's a simple example of how to use the Sumcheck Protocol:
+
+```rust
+use lambdaworks_math::field::fields::u64_prime_field::U64PrimeField;
+use lambdaworks_math::field::element::FieldElement;
+use lambdaworks_math::polynomial::dense_multilinear_poly::DenseMultilinearPolynomial;
+use lambdaworks_sumcheck::{prove, verify};
+
+// Define the field
+type F = U64PrimeField<17>;
+
+// Create a multilinear polynomial
+let evaluations = vec![
+    FieldElement::<F>::from(3),
+    FieldElement::<F>::from(4),
+    FieldElement::<F>::from(5),
+    FieldElement::<F>::from(7),
+];
+let poly = DenseMultilinearPolynomial::new(evaluations);
+
+// Generate a proof
+let (claimed_sum, proof) = prove(poly);
+
+// Verify the proof
+let result = verify(poly.num_vars(), claimed_sum, proof, Some(poly));
+assert!(result.is_ok() && result.unwrap());
+```
+
+
+## References
+
+- [Proofs, Arguments, and Zero-Knowledge. Chapter 4](https://people.cs.georgetown.edu/jthaler/ProofsArgsAndZK.pdf)
+- [Lambdaclass Blog Post: Have you checked your sums?](https://blog.lambdaclass.com/have-you-checked-your-sums/)

provers/sumcheck/src/lib.rs

@@ -8,6 +8,9 @@ use lambdaworks_math::field::element::FieldElement;
 use lambdaworks_math::field::traits::{HasDefaultTranscript, IsField};
 use lambdaworks_math::traits::ByteConversion;
 
+pub use prover::prove;
+pub use verifier::verify;
+
 pub trait Channel<F: IsField> {
     fn append_felt(&mut self, element: &FieldElement<F>);
     fn draw_felt(&mut self) -> FieldElement<F>;
@@ -26,3 +29,318 @@ where
         self.sample_field_element()
     }
 }
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+    use lambdaworks_math::field::fields::u64_prime_field::U64PrimeField;
+    use lambdaworks_math::polynomial::dense_multilinear_poly::DenseMultilinearPolynomial;
+    use verifier::VerifierRoundResult;
+
+    // Using a small prime field with modulus 101.
+    const MODULUS: u64 = 101;
+    type F = U64PrimeField<MODULUS>;
+    type FE = FieldElement<F>;
+
+    #[test]
+    fn test_protocol() {
+        let poly = DenseMultilinearPolynomial::new(vec![
+            FE::from(3),
+            FE::from(5),
+            FE::from(7),
+            FE::from(11),
+        ]);
+
+        let (claimed_sum, proof_polys) = prove(poly.clone());
+
+        let result = verify(poly.num_vars(), claimed_sum, proof_polys, Some(poly));
+
+        assert!(result.unwrap_or(false), "Valid proof should be accepted");
+    }
+
+    #[test]
+    fn test_interactive_sumcheck() {
+        let poly = DenseMultilinearPolynomial::new(vec![
+            FE::from(1),
+            FE::from(2),
+            FE::from(1),
+            FE::from(4),
+        ]);
+
+        let mut prover = prover::Prover::new(poly.clone());
+        let c_1 = prover.c_1();
+        println!("\nInitial claimed sum c₁: {:?}", c_1);
+        let mut transcript = DefaultTranscript::<F>::default();
+        let mut verifier = verifier::Verifier::new(poly.num_vars(), Some(poly), c_1);
+
+        // Round 0
+        println!("\n-- Round 0 --");
+        let univar0 = prover.poly.to_univariate();
+        println!(
+            "Univariate polynomial g₀(x) coefficients: {:?}",
+            univar0.coefficients
+        );
+        let eval_0 = univar0.evaluate(&FieldElement::<F>::zero());
+        let eval_1 = univar0.evaluate(&FieldElement::<F>::one());
+        println!(
+            "g₀(0) = {:?}, g₀(1) = {:?}, sum = {:?}",
+            eval_0,
+            eval_1,
+            eval_0 + eval_1
+        );
+        let res0 = verifier.do_round(univar0, &mut transcript).unwrap();
+        let r0 = if let VerifierRoundResult::NextRound(chal) = res0 {
+            println!("Challenge r₀: {:?}", chal);
+            chal
+        } else {
+            panic!("Expected NextRound result");
+        };
+
+        // Round 1
+        println!("\n-- Round 1 (Final) --");
+        let univar1 = prover.round(r0);
+        println!(
+            "Univariate polynomial g₁(x) coefficients: {:?}",
+            univar1.coefficients
+        );
+        let eval_0 = univar1.evaluate(&FieldElement::<F>::zero());
+        let eval_1 = univar1.evaluate(&FieldElement::<F>::one());
+        println!(
+            "g₁(0) = {:?}, g₁(1) = {:?}, sum = {:?}",
+            eval_0,
+            eval_1,
+            eval_0 + eval_1
+        );
+        let res1 = verifier.do_round(univar1, &mut transcript).unwrap();
+        if let VerifierRoundResult::Final(ok) = res1 {
+            println!(
+                "\nFinal verification result: {}",
+                if ok { "ACCEPTED" } else { "REJECTED" }
+            );
+            assert!(ok, "Final round verification failed");
+        } else {
+            panic!("Expected Final result");
+        }
+    }
+
+    /// Test based on a textbook example for a 3-variable polynomial
+    #[test]
+    fn test_from_book() {
+        // 3-variable polynomial with evaluations:
+        // (0,0,0)=1, (1,0,0)=2, (0,1,0)=3, (1,1,0)=4,
+        // (0,0,1)=5, (1,0,1)=6, (0,1,1)=7, (1,1,1)=8.
+        let poly = DenseMultilinearPolynomial::new(vec![
+            FE::from(1),
+            FE::from(2),
+            FE::from(3),
+            FE::from(4),
+            FE::from(5),
+            FE::from(6),
+            FE::from(7),
+            FE::from(8),
+        ]);
+        // Total sum (claimed sum) is 36.
+        let mut prover = prover::Prover::new(poly.clone());
+        let c_1 = prover.c_1();
+        println!("\nInitial claimed sum c₁: {:?}", c_1);
+        let mut transcript = DefaultTranscript::<F>::default();
+        let mut verifier = verifier::Verifier::new(poly.num_vars(), Some(poly), c_1);
+
+        // Round 0
+        let mut g = prover.poly.to_univariate();
+        println!("\n-- Round 0 --");
+        println!(
+            "Univariate polynomial g₀(x) coefficients: {:?}",
+            g.coefficients
+        );
+        let eval_0 = g.evaluate(&FieldElement::<F>::zero());
+        let eval_1 = g.evaluate(&FieldElement::<F>::one());
+        println!(
+            "g₀(0) = {:?}, g₀(1) = {:?}, sum = {:?}",
+            eval_0,
+            eval_1,
+            eval_0 + eval_1
+        );
+        let res0 = verifier.do_round(g, &mut transcript).unwrap();
+        let mut current_challenge = if let VerifierRoundResult::NextRound(chal) = res0 {
+            println!("Challenge r₀: {:?}", chal);
+            chal
+        } else {
+            panic!("Expected NextRound result");
+        };
+
+        // Continue rounds until final.
+        let mut round = 1;
+        while verifier.round < verifier.n {
+            println!(
+                "\n-- Round {} {}",
+                round,
+                if round == verifier.n - 1 {
+                    "(Final)"
+                } else {
+                    ""
+                }
+            );
+            g = prover.round(current_challenge);
+            println!(
+                "Univariate polynomial g{}(x) coefficients: {:?}",
+                round, g.coefficients
+            );
+            let eval_0 = g.evaluate(&FieldElement::<F>::zero());
+            let eval_1 = g.evaluate(&FieldElement::<F>::one());
+            println!(
+                "g{}(0) = {:?}, g{}(1) = {:?}, sum = {:?}",
+                round,
+                eval_0,
+                round,
+                eval_1,
+                eval_0 + eval_1
+            );
+            let res = verifier.do_round(g, &mut transcript).unwrap();
+            match res {
+                VerifierRoundResult::NextRound(chal) => {
+                    println!("Challenge r{}: {:?}", round, chal);
+                    current_challenge = chal;
+                }
+                VerifierRoundResult::Final(ok) => {
+                    println!(
+                        "\nFinal verification result: {}",
+                        if ok { "ACCEPTED" } else { "REJECTED" }
+                    );
+                    assert!(ok, "Final round verification failed");
+                    break;
+                }
+            }
+            round += 1;
+        }
+    }
+
+    #[test]
+    fn test_from_book_ported() {
+        // 3-variable polynomial: f(x₀,x₁,x₂)=2*x₀ + x₀*x₂ + x₁*x₂.
+        // Evaluations (little-endian): [0, 2, 0, 2, 0, 3, 1, 4]. Total sum = 12.
+        let poly = DenseMultilinearPolynomial::new(vec![
+            FE::from(0),
+            FE::from(2),
+            FE::from(0),
+            FE::from(2),
+            FE::from(0),
+            FE::from(3),
+            FE::from(1),
+            FE::from(4),
+        ]);
+        let mut prover = prover::Prover::new(poly.clone());
+        let c_1 = prover.c_1();
+        println!("\nInitial claimed sum c₁: {:?}", c_1);
+        let mut transcript = DefaultTranscript::<F>::default();
+        let mut verifier = verifier::Verifier::new(poly.num_vars(), Some(poly), c_1);
+
+        // Round 0:
+        println!("\n-- Round 0 --");
+        let univar0 = prover.poly.to_univariate();
+        println!(
+            "Univariate polynomial g₀(x) coefficients: {:?}",
+            univar0.coefficients
+        );
+        let eval_0 = univar0.evaluate(&FieldElement::<F>::zero());
+        let eval_1 = univar0.evaluate(&FieldElement::<F>::one());
+        println!(
+            "g₀(0) = {:?}, g₀(1) = {:?}, sum = {:?}",
+            eval_0,
+            eval_1,
+            eval_0 + eval_1
+        );
+        let res0 = verifier.do_round(univar0, &mut transcript).unwrap();
+        let r0 = if let VerifierRoundResult::NextRound(chal) = res0 {
+            println!("Challenge r₀: {:?}", chal);
+            chal
+        } else {
+            panic!("Expected NextRound result");
+        };
+
+        // Round 1:
+        println!("\n-- Round 1 --");
+        let univar1 = prover.round(r0);
+        println!(
+            "Univariate polynomial g₁(x) coefficients: {:?}",
+            univar1.coefficients
+        );
+        let eval_0 = univar1.evaluate(&FieldElement::<F>::zero());
+        let eval_1 = univar1.evaluate(&FieldElement::<F>::one());
+        println!(
+            "g₁(0) = {:?}, g₁(1) = {:?}, sum = {:?}",
+            eval_0,
+            eval_1,
+            eval_0 + eval_1
+        );
+        let res1 = verifier.do_round(univar1, &mut transcript).unwrap();
+        let r1 = if let VerifierRoundResult::NextRound(chal) = res1 {
+            println!("Challenge r₁: {:?}", chal);
+            chal
+        } else {
+            panic!("Expected NextRound result");
+        };
+
+        // Round 2 (final round):
+        println!("\n-- Round 2 (Final) --");
+        let univar2 = prover.round(r1);
+        println!(
+            "Univariate polynomial g₂(x) coefficients: {:?}",
+            univar2.coefficients
+        );
+        let eval_0 = univar2.evaluate(&FieldElement::<F>::zero());
+        let eval_1 = univar2.evaluate(&FieldElement::<F>::one());
+        println!(
+            "g₂(0) = {:?}, g₂(1) = {:?}, sum = {:?}",
+            eval_0,
+            eval_1,
+            eval_0 + eval_1
+        );
+        let res2 = verifier.do_round(univar2, &mut transcript).unwrap();
+        if let VerifierRoundResult::Final(ok) = res2 {
+            println!(
+                "\nFinal verification result: {}",
+                if ok { "ACCEPTED" } else { "REJECTED" }
+            );
+            assert!(ok, "Final round verification failed");
+        } else {
+            panic!("Expected Final result");
+        }
+    }
+
+    #[test]
+    fn failing_verification_test() {
+        let poly = DenseMultilinearPolynomial::new(vec![
+            FE::from(1),
+            FE::from(2),
+            FE::from(1),
+            FE::from(4),
+        ]);
+        let prover = prover::Prover::new(poly.clone());
+        // Deliberately use an incorrect claimed sum.
+        let incorrect_c1 = FE::from(999);
+        println!("\nInitial (incorrect) claimed sum c₁: {:?}", incorrect_c1);
+        let mut transcript = DefaultTranscript::<F>::default();
+        let mut verifier = verifier::Verifier::new(poly.num_vars(), Some(poly), incorrect_c1);
+
+        println!("\n-- Round 0 --");
+        let univar0 = prover.poly.to_univariate();
+        println!(
+            "Univariate polynomial g₀(x) coefficients: {:?}",
+            univar0.coefficients
+        );
+        let eval_0 = univar0.evaluate(&FieldElement::<F>::zero());
+        let eval_1 = univar0.evaluate(&FieldElement::<F>::one());
+        println!(
+            "g₀(0) = {:?}, g₀(1) = {:?}, sum = {:?}",
+            eval_0,
+            eval_1,
+            eval_0 + eval_1
+        );
+        let res0 = verifier.do_round(univar0, &mut transcript);
+        if let Err(e) = &res0 {
+            println!("\nExpected verification error: {:?}", e);
+        }
+        assert!(res0.is_err(), "Expected verification error");
+    }
+}