labrador/core/

garbage_polynomials.rs

use crate::ring::{rq_matrix::RqMatrix, rq_vector::RqVector};

use super::inner_product;

/// Calculate the garbage polynomials g_{ij} = <s_i, s_j>
/// Exploits symmetry by only calculating for i ≤ j since g_{ij} = g_{ji}
pub fn compute_g(witness_vector: &[RqVector]) -> RqMatrix {
    let mut g_i = Vec::new();
    for i in 0..witness_vector.len() {
        let mut g_ij = Vec::new();
        for j in 0..=i {
            // Only calculate for j ≤ i (upper triangular)
            g_ij.push(inner_product::compute_linear_combination(
                witness_vector[i].elements(),
                witness_vector[j].elements(),
            ));
        }
        g_i.push(RqVector::new(g_ij));
    }
    RqMatrix::new(g_i, true)
}

/// Calculate the h_{ij} = <φ_i, s_j> + <φ_j, s_i> garbage polynomials
/// In the paper, h_{ij} is defined with a factor of 1/2 in front
/// However, since we're using q = 2^32, division by 2 is problematic in Z_q
/// So we store h'_{ij} = 2*h_{ij} = <φ_i, s_j> + <φ_j, s_i> directly.
/// Therefore the bound for commitment scheme of h_ij should be 4 times larger than the bound specified in the paper.
///
/// Exploits symmetry by only calculating for i ≤ j since h_{ij} = h_{ji}.
pub fn compute_h(witness_vector: &[RqVector], phi: &[RqVector]) -> RqMatrix {
    let r = witness_vector.len();
    let mut h_i = Vec::with_capacity((r * (r + 1)) / 2);

    for i in 0..r {
        let mut h_ij = Vec::new();
        for j in 0..=i {
            // Only calculate for j ≤ i (upper triangular)
            let inner_phi_i_s_j = inner_product::compute_linear_combination(
                phi[i].elements(),
                witness_vector[j].elements(),
            );
            let inner_phi_j_s_i = inner_product::compute_linear_combination(
                phi[j].elements(),
                witness_vector[i].elements(),
            );
            h_ij.push(&inner_phi_i_s_j + &inner_phi_j_s_i);
        }
        h_i.push(RqVector::new(h_ij));
    }
    RqMatrix::new(h_i, true)
}

// Todo: Revise and complete the following
// Implementation of the final level optimization (Section 5.6)
// /// Uses sequentially derived challenges via Fiat-Shamir to simulate the interactive protocol
// pub fn optimize_final_level(
//     witnesses: &[PolyVector],
//     phi: &[PolyVector],
//     initial_seed: u64,
// ) -> (PolyRing, Vec<PolyRing>, Vec<PolyRing>) {
//     let r = witnesses.len();

//     // Calculate g_0 = Σ_i <s_i, s_i> (diagonal sum)
//     let g0 = (0..r)
//         .map(|i| witnesses[i].inner_product_poly_vector(&witnesses[i]))
//         .fold(
//             PolyRing::zero(witnesses[0].elements()[0].len()),
//             |acc, g| &acc + &g,
//         );

//     // Generate sequence of challenges using Fiat-Shamir
//     let mut challenges = Vec::with_capacity(r / 2);
//     let mut hasher = DefaultHasher::new();
//     initial_seed.hash(&mut hasher);
//     let mut current_seed = hasher.finish();

//     for _ in 0..r / 2 {
//         let mut rng = rand::rngs::StdRng::seed_from_u64(current_seed);
//         let challenge = PolyRing::random(&mut rng, witnesses[0].elements()[0].len());
//         challenges.push(challenge);

//         // Update seed for next challenge
//         let mut hasher = DefaultHasher::new();
//         current_seed.hash(&mut hasher);
//         current_seed = hasher.finish();
//     }

//     // Calculate selected g terms: g_{2i-1} and g_{2i}
//     let mut g_terms = Vec::new();
//     for i in 1..=r / 2 {
//         let idx1 = 2 * i - 2;
//         let idx2 = 2 * i - 1;

//         // Use unique challenge for each i
//         let challenge = &challenges[i - 1];

//         // Add g_{2i-1}
//         if idx2 < r {
//             // For g_{2i-1} = <s_{2i-2}, c_i * s_{2i-1}>
//             let s_j_scaled = witnesses[idx2]
//                 .iter()
//                 .map(|p| p * challenge)
//                 .collect::<PolyVector>();

//             let g_2i_1 = witnesses[idx1].inner_product_poly_vector(&s_j_scaled);
//             g_terms.push(g_2i_1);

//             // Add g_{2i} if we have enough witnesses
//             if 2 * i < r {
//                 // For g_{2i} = <s_{2i-1}, c_i * s_{2i}>
//                 let s_j_scaled = witnesses[2 * i]
//                     .iter()
//                     .map(|p| p * challenge)
//                     .collect::<PolyVector>();

//                 let g_2i = witnesses[idx2].inner_product_poly_vector(&s_j_scaled);
//                 g_terms.push(g_2i);
//             }
//         }
//     }

//     // Calculate selected h terms: h_{2i-1} and h_{2i}
//     let mut h_terms = Vec::new();
//     for i in 1..=r / 2 {
//         let idx1 = 2 * i - 2;
//         let idx2 = 2 * i - 1;

//         // Use unique challenge for each i
//         let challenge = &challenges[i - 1];

//         // Add h_{2i-1}
//         if idx2 < r {
//             // For h_{2i-1} = <φ_{2i-2}, c_i * s_{2i-1}> + <φ_{2i-1}, c_i * s_{2i-2}>
//             let s_j_scaled = witnesses[idx2]
//                 .iter()
//                 .map(|p| p * challenge)
//                 .collect::<PolyVector>();

//             let phi_i_s_j = phi[idx1].inner_product_poly_vector(&s_j_scaled);

//             let s_i_scaled = witnesses[idx1]
//                 .iter()
//                 .map(|p| p * challenge)
//                 .collect::<PolyVector>();

//             let phi_j_s_i = phi[idx2].inner_product_poly_vector(&s_i_scaled);

//             let h_2i_1 = &phi_i_s_j + &phi_j_s_i;
//             h_terms.push(h_2i_1);

//             // Add h_{2i} if we have enough witnesses
//             if 2 * i < r {
//                 // For h_{2i} = <φ_{2i-1}, c_i * s_{2i}> + <φ_{2i}, c_i * s_{2i-1}>
//                 let s_j_scaled = witnesses[2 * i]
//                     .iter()
//                     .map(|p| p * challenge)
//                     .collect::<PolyVector>();

//                 let phi_i_s_j = phi[idx2].inner_product_poly_vector(&s_j_scaled);

//                 let s_i_scaled = witnesses[idx2]
//                     .iter()
//                     .map(|p| p * challenge)
//                     .collect::<PolyVector>();

//                 let phi_j_s_i = phi[2 * i].inner_product_poly_vector(&s_i_scaled);

//                 let h_2i = &phi_i_s_j + &phi_j_s_i;
//                 h_terms.push(h_2i);
//             }
//         }
//     }

//     (g0, g_terms, h_terms)
// }

#[cfg(test)]
mod tests {
    use crate::ring::rq::Rq;

    use super::*;
    use rand::rng;

    const RANK: usize = 8;

    fn create_test_witnesses(count: usize) -> (Vec<RqVector>, Vec<RqVector>) {
        let witnesses = (0..count)
            .map(|_| RqVector::random(&mut rng(), RANK))
            .collect();

        let phi = (0..count)
            .map(|_| RqVector::random(&mut rng(), RANK))
            .collect();

        (witnesses, phi)
    }

    #[test]
    fn test_g_matrix_size() {
        let multiplicity = 3;
        let (witnesses, _) = create_test_witnesses(multiplicity);
        let g = compute_g(&witnesses);

        assert_eq!(g.row_len(), 3);
        // Assert that g stores half of the matrix
        for row in 0..multiplicity {
            assert_eq!(g.elements()[row].len(), row + 1);
        }
    }

    #[test]
    fn test_g_calculation() {
        let (witnesses, _) = create_test_witnesses(3);

        let g = compute_g(&witnesses);

        // Verify a few specific values
        let expected_g_01 = inner_product::compute_linear_combination(
            witnesses[0].elements(),
            witnesses[1].elements(),
        );
        let expected_g_10 = inner_product::compute_linear_combination(
            witnesses[1].elements(),
            witnesses[0].elements(),
        );
        assert_eq!(expected_g_01, expected_g_10);

        let expected_g_22 = inner_product::compute_linear_combination(
            witnesses[2].elements(),
            witnesses[2].elements(),
        );

        assert_eq!(*g.get_cell(0, 1), expected_g_01);
        assert_eq!(*g.get_cell(1, 0), expected_g_10);
        assert_eq!(*g.get_cell(2, 2), expected_g_22);
    }

    #[test]
    fn test_h_matrix_size() {
        let multiplicity = 3;
        let (witnesses, phi) = create_test_witnesses(multiplicity);
        let h = compute_h(&witnesses, &phi);

        assert_eq!(h.row_len(), 3);
        // Assert that g stores half of the matrix
        for row in 0..multiplicity {
            assert_eq!(h.elements()[row].len(), row + 1);
        }
    }

    #[test]
    fn test_h_calculation() {
        let (witnesses, phi) = create_test_witnesses(3);
        let h = compute_h(&witnesses, &phi);

        // Verify a specific value
        let phi_0_s_1 =
            inner_product::compute_linear_combination(phi[0].elements(), witnesses[1].elements());
        let phi_1_s_0 =
            inner_product::compute_linear_combination(phi[1].elements(), witnesses[0].elements());
        let expected_h_01 = &phi_0_s_1 + &phi_1_s_0;

        assert_eq!(h.get_cell(0, 1), h.get_cell(1, 0));
        assert_eq!(expected_h_01, *h.get_cell(0, 1));
    }

    #[test]
    fn test_g_computation_with_zero_vectors() {
        let witness_vector = vec![RqVector::zero(100); 50];
        let g = compute_g(&witness_vector);

        for row in g.elements() {
            for cell in row.elements() {
                assert_eq!(*cell, Rq::zero());
            }
        }
    }

    #[test]
    fn test_h_computation_with_zero_vectors() {
        let witness_vector = vec![RqVector::zero(100); 50];
        let phi = vec![RqVector::zero(100); 50];
        let h = compute_h(&witness_vector, &phi);

        for row in h.elements() {
            for cell in row.elements() {
                assert_eq!(*cell, Rq::zero());
            }
        }
    }

    // #[test]
    // fn test_commit_recursive() {
    //     let commitment_scheme = create_test_commitment();
    //     let (witnesses, phi) = create_test_witnesses(3);

    //     // Create mock inner commitment parts (t and z)
    //     let t_parts = create_test_parts(5);
    //     let z_parts = create_test_parts(5);

    //     let (recursive_commitment, recursive_witness) = commitment_scheme
    //         .commit_recursive(&witnesses, &phi, &t_parts, &z_parts)
    //         .unwrap();

    //     // Check the output structure
    //     assert!(!recursive_commitment.nu1.as_slice().is_empty());
    //     assert!(!recursive_commitment.nu2.as_slice().is_empty());

    //     // Check witness has appropriate parts
    //     assert_eq!(recursive_witness.t_parts.len(), t_parts.len());
    //     assert_eq!(recursive_witness.z_parts.len(), z_parts.len());
    //     assert!(!recursive_witness.g_parts.is_empty());
    //     assert!(!recursive_witness.h_parts.is_empty());
    // }

    // #[test]
    // fn test_commit_recursive_correctness() {
    //     let commitment_scheme = create_test_commitment();
    //     let (witnesses, phi) = create_test_witnesses(3);

    //     // Create test parts for inner commitment
    //     let t_parts = create_test_parts(5);
    //     let z_parts = create_test_parts(5);

    //     // Get the recursive commitment and witness
    //     let (recursive_commitment, recursive_witness) = commitment_scheme
    //         .commit_recursive(&witnesses, &phi, &t_parts, &z_parts)
    //         .unwrap();

    //     // Manually compute the expected commitments:

    //     // 1. For nu1, combine t_parts and g_parts
    //     let mut combined_parts = recursive_witness.t_parts.clone();
    //     combined_parts.extend(recursive_witness.g_parts.clone());

    //     // 2. Create expected witnesses
    //     let expected_nu1_witness = commitment_scheme.create_witness_from_parts(&combined_parts);
    //     let expected_nu2_witness =
    //         commitment_scheme.create_witness_from_parts(&recursive_witness.h_parts);

    //     // 3. Create AjtaiCommitment instances with the correct matrices
    //     let nu1_commitment = AjtaiCommitment::new(
    //         commitment_scheme.params.clone(),
    //         commitment_scheme.nu1_matrix.clone(),
    //     )
    //     .unwrap();

    //     let nu2_commitment = AjtaiCommitment::new(
    //         commitment_scheme.params.clone(),
    //         commitment_scheme.nu2_matrix.clone(),
    //     )
    //     .unwrap();

    //     // 4. Compute expected commitments
    //     let (expected_nu1, _) = nu1_commitment.commit(expected_nu1_witness).unwrap();
    //     let (expected_nu2, _) = nu2_commitment.commit(expected_nu2_witness).unwrap();

    //     // 5. Compare expected with actual
    //     assert_eq!(
    //         recursive_commitment.nu1, expected_nu1,
    //         "nu1 commitment does not match expected value"
    //     );
    //     assert_eq!(
    //         recursive_commitment.nu2, expected_nu2,
    //         "nu2 commitment does not match expected value"
    //     );
    // }

    // #[test]
    // fn test_decomposition_reconstruction() {
    //     let commitment_scheme = create_test_commitment();
    //     let mut rng = rand::rng();

    //     // Create a random polynomial
    //     let original_poly = PolyRing::random(&mut rng, TEST_D);
    //     let original_rq: Rq<TEST_D> = original_poly.clone().into();

    //     // Test g decomposition parameters
    //     let g_parts = commitment_scheme.decompose_polynomial(&original_poly, true);
    //     let g_base = commitment_scheme.g_decomp_params.base();

    //     // Reconstruct the polynomial from parts
    //     let mut reconstructed_g = Rq::<TEST_D>::zero();
    //     let mut current_base_power = Zq::ONE; // Base^0

    //     for part in &g_parts {
    //         // Add part * base^k
    //         reconstructed_g = reconstructed_g.clone() + part.clone().scalar_mul(current_base_power);
    //         // Multiply by base for next iteration
    //         current_base_power *= g_base;
    //     }

    //     assert_eq!(
    //         reconstructed_g, original_rq,
    //         "G decomposition reconstruction failed"
    //     );

    //     // Test h decomposition parameters
    //     let h_parts = commitment_scheme.decompose_polynomial(&original_poly, false);
    //     let h_base = commitment_scheme.h_decomp_params.base();

    //     // Reconstruct the polynomial from parts
    //     let mut reconstructed_h = Rq::<TEST_D>::zero();
    //     let mut current_base_power = Zq::ONE; // Base^0

    //     for part in &h_parts {
    //         // Add part * base^k
    //         reconstructed_h = reconstructed_h.clone() + part.clone().scalar_mul(current_base_power);
    //         // Multiply by base for next iteration
    //         current_base_power *= h_base;
    //     }

    //     assert_eq!(
    //         reconstructed_h, original_rq,
    //         "H decomposition reconstruction failed"
    //     );
    // }

    // #[test]
    // fn test_create_witness_from_parts_edge_cases() {
    //     let commitment_scheme = create_test_commitment();
    //     let mut rng = rand::rng();

    //     // Test case 1: parts.len() < N (should pad with zeros)
    //     let few_parts: Vec<Rq<TEST_D>> = (0..TEST_N - 2)
    //         .map(|_| Rq::<TEST_D>::random(&mut rng))
    //         .collect();

    //     let witness_few = commitment_scheme.create_witness_from_parts(&few_parts);

    //     // Check length is exactly N
    //     assert_eq!(witness_few.as_slice().len(), TEST_N);

    //     // Check that last elements are zero
    //     for i in few_parts.len()..TEST_N {
    //         assert_eq!(witness_few[i], Rq::<TEST_D>::zero());
    //     }

    //     // Check original parts are preserved (with possible bounding applied)
    //     let witness_bound = commitment_scheme.params.witness_bound();
    //     for (i, part) in few_parts.iter().enumerate() {
    //         let mut bounded_part_coeffs = [Zq::ZERO; TEST_D];
    //         for (j, coeff) in part.get_coefficients().iter().enumerate().take(TEST_D) {
    //             bounded_part_coeffs[j] = coeff.centered_mod(witness_bound);
    //         }
    //         let bounded_part = Rq::<TEST_D>::new(bounded_part_coeffs);
    //         assert_eq!(witness_few[i], bounded_part);
    //     }

    //     // Test case 2: parts.len() > N (should truncate to first N)
    //     let many_parts: Vec<Rq<TEST_D>> = (0..TEST_N + 3)
    //         .map(|_| Rq::<TEST_D>::random(&mut rng))
    //         .collect();

    //     let witness_many = commitment_scheme.create_witness_from_parts(&many_parts);

    //     // Check length is exactly N
    //     assert_eq!(witness_many.as_slice().len(), TEST_N);

    //     // Check only first N parts are included (with possible bounding applied)
    //     let witness_bound = commitment_scheme.params.witness_bound();
    //     for i in 0..TEST_N {
    //         let mut bounded_part_coeffs = [Zq::ZERO; TEST_D];
    //         for (j, coeff) in many_parts[i]
    //             .get_coefficients()
    //             .iter()
    //             .enumerate()
    //             .take(TEST_D)
    //         {
    //             bounded_part_coeffs[j] = coeff.centered_mod(witness_bound);
    //         }
    //         let bounded_part = Rq::<TEST_D>::new(bounded_part_coeffs);
    //         assert_eq!(witness_many[i], bounded_part);
    //     }

    //     // Test case 3: Coefficient bounding
    //     // Create parts with large coefficients
    //     let large_coeff_parts: Vec<Rq<TEST_D>> = (0..TEST_N)
    //         .map(|_| {
    //             let mut large_part = Rq::<TEST_D>::random(&mut rng);
    //             // Set first coefficient to a large value beyond the witness bound
    //             if let Some(c) = large_part.iter_mut().next() {
    //                 *c = Zq::MAX - Zq::ONE;
    //             }
    //             large_part
    //         })
    //         .collect();

    //     let witness_large = commitment_scheme.create_witness_from_parts(&large_coeff_parts);

    //     // Check coefficients are properly bounded
    //     for i in 0..TEST_N {
    //         let mut bounded_part_coeffs = [Zq::ZERO; TEST_D];
    //         for (j, coeff) in large_coeff_parts[i]
    //             .get_coefficients()
    //             .iter()
    //             .enumerate()
    //             .take(TEST_D)
    //         {
    //             bounded_part_coeffs[j] = coeff.centered_mod(witness_bound);
    //         }
    //         let bounded_part = Rq::<TEST_D>::new(bounded_part_coeffs);

    //         assert_eq!(witness_large[i], bounded_part);

    //         // Also check that large coefficients were properly bounded
    //         for (j, coeff) in witness_large[i].get_coefficients().iter().enumerate() {
    //             let original_coeff = large_coeff_parts[i].get_coefficients()[j];
    //             if original_coeff > witness_bound {
    //                 assert!(*coeff <= witness_bound);
    //             }
    //         }
    //     }
    // }

    // #[test]
    // #[allow(clippy::as_conversions)]
    // fn test_optimal_parameters_accuracy() {
    //     // Choose small, simple values for manual calculation
    //     let n = 4; // Small dimension
    //     let d = 4; // Small degree
    //     let s = 2.0; // Simple standard deviation
    //     let beta = 1.0; // Simple beta value

    //     // Manually calculate the expected values according to the paper's formulas
    //     let n_d_sqrt = (n * d) as f64; // = 4.0

    //     // s_g = sqrt(n*d) * s^2 = 4.0 * 4.0 = 16.0
    //     let s_g = n_d_sqrt * s * s;

    //     // s_h = beta * sqrt(n*d) * s = 1.0 * 4.0 * 2.0 = 8.0
    //     let s_h = beta * n_d_sqrt * s;

    //     // b2 ≈ sqrt(12 * s_g) = sqrt(12 * 16.0) = sqrt(192) ≈ 13.856... => 13
    //     let expected_b2 = (12.0 * s_g).sqrt() as u32;

    //     // b1 ≈ sqrt(12 * s_h) = sqrt(12 * 8.0) = sqrt(96) ≈ 9.798... => 9
    //     let expected_b1 = (12.0 * s_h).sqrt() as u32;

    //     // For q = 2^32:
    //     // t2 ≈ log_b2(q) = log_13(2^32) = 32/log_2(13) ≈ 32/3.7 ≈ 8.65 => 9
    //     let expected_t2 = ((32.0 / (expected_b2 as f64).log2()).ceil() as usize).max(2);

    //     // t1 ≈ log_b1(q) = log_9(2^32) = 32/log_2(9) ≈ 32/3.17 ≈ 10.09 => 11
    //     let expected_t1 = ((32.0 / (expected_b1 as f64).log2()).ceil() as usize).max(2);

    //     // Call the function under test
    //     let params =
    //         GarbagePolynomialCommitment::<TEST_M, TEST_N, TEST_D>::calculate_optimal_parameters(
    //             n, d, s, beta,
    //         );

    //     // Check results
    //     assert!(
    //         params.g_base.to_u128() >= expected_b2 as u128 - 1
    //             && params.g_base.to_u128() <= expected_b2 as u128 + 1,
    //         "g_base {}, expected {}",
    //         params.g_base.to_u128(),
    //         expected_b2
    //     );

    //     assert!(
    //         params.h_base.to_u128() >= expected_b1 as u128 - 1
    //             && params.h_base.to_u128() <= expected_b1 as u128 + 1,
    //         "h_base {}, expected {}",
    //         params.h_base.to_u128(),
    //         expected_b1
    //     );

    //     // For part counts, use approximate comparison due to potential floating point differences
    //     assert!(
    //         params.g_parts >= expected_t2 - 1 && params.g_parts <= expected_t2 + 1,
    //         "g_parts {}, expected {}",
    //         params.g_parts,
    //         expected_t2
    //     );

    //     assert!(
    //         params.h_parts >= expected_t1 - 1 && params.h_parts <= expected_t1 + 1,
    //         "h_parts {}, expected {}",
    //         params.h_parts,
    //         expected_t1
    //     );
    // }

    // #[test]
    // fn test_error_handling() {
    //     let params = AjtaiParameters::new(Zq::ONE, Zq::ONE).unwrap();
    //     let mut rng = rand::rng();
    //     let nu1_matrix = RqMatrix::<TEST_M, TEST_N, TEST_D>::random(&mut rng);
    //     let nu2_matrix = RqMatrix::<TEST_M, TEST_N, TEST_D>::random(&mut rng);

    //     // Test invalid g_base (≤ 1)
    //     let invalid_g_base = GarbageParameters {
    //         g_base: Zq::ONE, // Invalid: base must be > 1
    //         g_parts: 2,
    //         h_base: Zq::new(4),
    //         h_parts: 3,
    //     };

    //     let result = GarbagePolynomialCommitment::<TEST_M, TEST_N, TEST_D>::new(
    //         params.clone(),
    //         nu1_matrix.clone(),
    //         nu2_matrix.clone(),
    //         invalid_g_base,
    //     );

    //     assert!(result.is_err(), "Should reject g_base ≤ 1");
    //     match result {
    //         Err(HierarchicalError::InvalidBase(_)) => {} // Expected error
    //         _ => panic!("Wrong error type for invalid g_base"),
    //     }

    //     // Test invalid g_parts (0)
    //     let invalid_g_parts = GarbageParameters {
    //         g_base: Zq::new(8),
    //         g_parts: 0, // Invalid: parts must be > 0
    //         h_base: Zq::new(4),
    //         h_parts: 3,
    //     };

    //     let result = GarbagePolynomialCommitment::<TEST_M, TEST_N, TEST_D>::new(
    //         params.clone(),
    //         nu1_matrix.clone(),
    //         nu2_matrix.clone(),
    //         invalid_g_parts,
    //     );

    //     assert!(result.is_err(), "Should reject g_parts = 0");
    //     match result {
    //         Err(HierarchicalError::InvalidPartCount(_)) => {} // Expected error
    //         _ => panic!("Wrong error type for invalid g_parts"),
    //     }

    //     // Test invalid h_base (≤ 1)
    //     let invalid_h_base = GarbageParameters {
    //         g_base: Zq::new(8),
    //         g_parts: 2,
    //         h_base: Zq::ZERO, // Invalid: base must be > 0
    //         h_parts: 3,
    //     };

    //     let result = GarbagePolynomialCommitment::<TEST_M, TEST_N, TEST_D>::new(
    //         params.clone(),
    //         nu1_matrix.clone(),
    //         nu2_matrix.clone(),
    //         invalid_h_base,
    //     );

    //     assert!(result.is_err(), "Should reject h_base ≤ 1");
    //     match result {
    //         Err(HierarchicalError::InvalidBase(_)) => {} // Expected error
    //         _ => panic!("Wrong error type for invalid h_base"),
    //     }

    //     // Test invalid h_parts (0)
    //     let invalid_h_parts = GarbageParameters {
    //         g_base: Zq::new(8),
    //         g_parts: 2,
    //         h_base: Zq::new(4),
    //         h_parts: 0, // Invalid: parts must be > 0
    //     };

    //     let result = GarbagePolynomialCommitment::<TEST_M, TEST_N, TEST_D>::new(
    //         params.clone(),
    //         nu1_matrix.clone(),
    //         nu2_matrix,
    //         invalid_h_parts,
    //     );

    //     assert!(result.is_err(), "Should reject h_parts = 0");
    //     match result {
    //         Err(HierarchicalError::InvalidPartCount(_)) => {} // Expected error
    //         _ => panic!("Wrong error type for invalid h_parts"),
    //     }
    // }
}