diff --git a/tachyon/crypto/commitments/univariate_polynomial_commitment_scheme.h b/tachyon/crypto/commitments/univariate_polynomial_commitment_scheme.h
index f9c85b265..250b4e558 100644
--- a/tachyon/crypto/commitments/univariate_polynomial_commitment_scheme.h
+++ b/tachyon/crypto/commitments/univariate_polynomial_commitment_scheme.h
@@ -22,6 +22,11 @@ class UnivariatePolynomialCommitmentScheme
   using Evals = math::UnivariateEvaluations<Field, kMaxDegree>;
   using Domain = math::UnivariateEvaluationDomain<Field, kMaxDegree>;
 
+  size_t D() const {
+    const Derived* derived = static_cast<const Derived*>(this);
+    return derived->N() - 1;
+  }
+
   // Commit to |poly| and populates |result| with the commitment.
   // Return false if the degree of |poly| exceeds |kMaxDegree|.
   [[nodiscard]] bool Commit(const Poly& poly, Commitment* result) const {
diff --git a/tachyon/math/polynomials/univariate/univariate_evaluation_domain.h b/tachyon/math/polynomials/univariate/univariate_evaluation_domain.h
index 4915f32c7..ff129c66f 100644
--- a/tachyon/math/polynomials/univariate/univariate_evaluation_domain.h
+++ b/tachyon/math/polynomials/univariate/univariate_evaluation_domain.h
@@ -99,6 +99,16 @@ class UnivariateEvaluationDomain : public EvaluationDomain<F, MaxDegree> {
     return t;
   }
 
+  template <typename T>
+  constexpr T Empty() const {
+    return T::UnsafeZero(size_ - 1);
+  }
+
+  template <typename T>
+  constexpr T Random() const {
+    return T::Random(size_ - 1);
+  }
+
   // Compute a FFT.
   [[nodiscard]] constexpr virtual Evals FFT(const DensePoly& poly) const = 0;
 
diff --git a/tachyon/math/polynomials/univariate/univariate_polynomial.h b/tachyon/math/polynomials/univariate/univariate_polynomial.h
index 556cafa7d..152f9698e 100644
--- a/tachyon/math/polynomials/univariate/univariate_polynomial.h
+++ b/tachyon/math/polynomials/univariate/univariate_polynomial.h
@@ -52,6 +52,15 @@ class UnivariatePolynomial final
     return UnivariatePolynomial(Coefficients::Zero());
   }
 
+  // NOTE(chokobole): This doesn't call |RemoveHighDegreeZeros()| internally.
+  // So when the returned evaluations is called with |IsZero()|, it returns
+  // false. So please use it carefully!
+  constexpr static UnivariatePolynomial UnsafeZero(size_t degree) {
+    UnivariatePolynomial ret;
+    ret.coefficients_ = Coefficients::UnsafeZero(degree);
+    return ret;
+  }
+
   constexpr static UnivariatePolynomial One() {
     return UnivariatePolynomial(Coefficients::One());
   }
@@ -269,15 +278,6 @@ class UnivariatePolynomial final
   friend class Radix2EvaluationDomain<Field, kMaxDegree>;
   friend class MixedRadixEvaluationDomain<Field, kMaxDegree>;
 
-  // NOTE(chokobole): This doesn't call |RemoveHighDegreeZeros()| internally.
-  // So when the returned evaluations is called with |IsZero()|, it returns
-  // false. So please use it carefully!
-  constexpr static UnivariatePolynomial UnsafeZero(size_t degree) {
-    UnivariatePolynomial ret;
-    ret.coefficients_ = Coefficients::UnsafeZero(degree);
-    return ret;
-  }
-
   Coefficients coefficients_;
 };
 
diff --git a/tachyon/zk/base/commitments/shplonk_extension.h b/tachyon/zk/base/commitments/shplonk_extension.h
index 6d7a35182..db7702792 100644
--- a/tachyon/zk/base/commitments/shplonk_extension.h
+++ b/tachyon/zk/base/commitments/shplonk_extension.h
@@ -36,6 +36,8 @@ class SHPlonkExtension
 
   size_t N() const { return shplonk_.N(); }
 
+  size_t D() const { return N() - 1; }
+
   [[nodiscard]] bool DoUnsafeSetup(size_t size) {
     return shplonk_.DoUnsafeSetup(size);
   }
diff --git a/tachyon/zk/base/entities/prover_unittest.cc b/tachyon/zk/base/entities/prover_unittest.cc
index df0918798..6ab48eb0d 100644
--- a/tachyon/zk/base/entities/prover_unittest.cc
+++ b/tachyon/zk/base/entities/prover_unittest.cc
@@ -11,8 +11,9 @@ class ProverTest : public Halo2ProverTest {};
 }  // namespace
 
 TEST_F(ProverTest, CommitEvalsWithBlind) {
+  const Domain* domain = prover_->domain();
   // setting random polynomial
-  Evals evals = Evals::Random(prover_->pcs().N() - 1);
+  Evals evals = domain->Random<Evals>();
 
   // setting struct to get output
   BlindedPolynomial<Poly> out;
diff --git a/tachyon/zk/lookup/compress_expression.h b/tachyon/zk/lookup/compress_expression.h
index c36840903..a52f5b700 100644
--- a/tachyon/zk/lookup/compress_expression.h
+++ b/tachyon/zk/lookup/compress_expression.h
@@ -15,13 +15,13 @@
 
 namespace tachyon::zk {
 
-template <typename Evals, typename F = typename Evals::Field>
+template <typename Domain, typename Evals, typename F>
 bool CompressExpressions(
+    const Domain* domain,
     const std::vector<std::unique_ptr<Expression<F>>>& expressions,
-    size_t domain_size, const F& theta,
-    const SimpleEvaluator<Evals>& evaluator_tpl, Evals* out) {
-  Evals compressed_value = Evals::UnsafeZero(domain_size - 1);
-  Evals values = Evals::UnsafeZero(domain_size - 1);
+    const F& theta, const SimpleEvaluator<Evals>& evaluator_tpl, Evals* out) {
+  Evals compressed_value = domain->template Empty<Evals>();
+  Evals values = domain->template Empty<Evals>();
 
   for (size_t expr_idx = 0; expr_idx < expressions.size(); ++expr_idx) {
     base::Parallelize(
diff --git a/tachyon/zk/lookup/compress_expression_unittest.cc b/tachyon/zk/lookup/compress_expression_unittest.cc
index 137666c66..7084c9684 100644
--- a/tachyon/zk/lookup/compress_expression_unittest.cc
+++ b/tachyon/zk/lookup/compress_expression_unittest.cc
@@ -38,7 +38,8 @@ TEST_F(CompressExpressionTest, CompressExpressions) {
   }
 
   Evals out;
-  ASSERT_TRUE(CompressExpressions(expressions, n, theta_, evaluator_, &out));
+  ASSERT_TRUE(CompressExpressions(prover_->domain(), expressions, theta_,
+                                  evaluator_, &out));
   EXPECT_EQ(out, Evals(std::move(expected)));
 }
 
diff --git a/tachyon/zk/lookup/lookup_argument_runner_impl.h b/tachyon/zk/lookup/lookup_argument_runner_impl.h
index 8a8dcc2a7..5fefee28b 100644
--- a/tachyon/zk/lookup/lookup_argument_runner_impl.h
+++ b/tachyon/zk/lookup/lookup_argument_runner_impl.h
@@ -24,14 +24,14 @@ LookupPermuted<Poly, Evals> LookupArgumentRunner<Poly, Evals>::PermuteArgument(
     const SimpleEvaluator<Evals>& evaluator_tpl) {
   // A_compressed(X) = θᵐ⁻¹A₀(X) + θᵐ⁻²A₁(X) + ... + θAₘ₋₂(X) + Aₘ₋₁(X)
   Evals compressed_input_expression;
-  CHECK(CompressExpressions(argument.input_expressions(),
-                            prover->domain()->size(), theta, evaluator_tpl,
+  CHECK(CompressExpressions(prover->domain(), argument.input_expressions(),
+                            theta, evaluator_tpl,
                             &compressed_input_expression));
 
   // S_compressed(X) = θᵐ⁻¹S₀(X) + θᵐ⁻²S₁(X) + ... + θSₘ₋₂(X) + Sₘ₋₁(X)
   Evals compressed_table_expression;
-  CHECK(CompressExpressions(argument.table_expressions(),
-                            prover->domain()->size(), theta, evaluator_tpl,
+  CHECK(CompressExpressions(prover->domain(), argument.table_expressions(),
+                            theta, evaluator_tpl,
                             &compressed_table_expression));
 
   // Permute compressed (InputExpression, TableExpression) pair.
diff --git a/tachyon/zk/lookup/lookup_argument_runner_unittest.cc b/tachyon/zk/lookup/lookup_argument_runner_unittest.cc
index f0c82d4b3..f8df2ebc0 100644
--- a/tachyon/zk/lookup/lookup_argument_runner_unittest.cc
+++ b/tachyon/zk/lookup/lookup_argument_runner_unittest.cc
@@ -37,11 +37,11 @@ TEST_F(LookupArgumentRunnerTest, ComputePermutationProduct) {
   }
 
   Evals compressed_input_expression;
-  ASSERT_TRUE(CompressExpressions(input_expressions, n, theta_, evaluator_,
-                                  &compressed_input_expression));
+  ASSERT_TRUE(CompressExpressions(prover_->domain(), input_expressions, theta_,
+                                  evaluator_, &compressed_input_expression));
   Evals compressed_table_expression;
-  ASSERT_TRUE(CompressExpressions(table_expressions, n, theta_, evaluator_,
-                                  &compressed_table_expression));
+  ASSERT_TRUE(CompressExpressions(prover_->domain(), table_expressions, theta_,
+                                  evaluator_, &compressed_table_expression));
 
   LookupPair<Evals> compressed_evals_pair(
       std::move(compressed_input_expression),
diff --git a/tachyon/zk/plonk/circuit/examples/simple_circuit_unittest.cc b/tachyon/zk/plonk/circuit/examples/simple_circuit_unittest.cc
index 9e4b911fa..b29f420f3 100644
--- a/tachyon/zk/plonk/circuit/examples/simple_circuit_unittest.cc
+++ b/tachyon/zk/plonk/circuit/examples/simple_circuit_unittest.cc
@@ -134,12 +134,13 @@ TEST_F(SimpleCircuitTest, Synthesize) {
   size_t n = 16;
   CHECK(prover_->pcs().UnsafeSetup(n, F(2)));
   prover_->set_domain(Domain::Create(n));
+  const Domain* domain = prover_->domain();
 
   ConstraintSystem<F> constraint_system;
   FieldConfig<math::bn254::Fr> config =
       SimpleCircuit<math::bn254::Fr>::Configure(constraint_system);
   Assembly<PCS> assembly =
-      VerifyingKey<PCS>::CreateAssembly(prover_->pcs(), constraint_system);
+      VerifyingKey<PCS>::CreateAssembly(domain, constraint_system);
 
   F constant(7);
   F a(2);
@@ -148,9 +149,8 @@ TEST_F(SimpleCircuitTest, Synthesize) {
   SimpleCircuit<math::bn254::Fr>::FloorPlanner::Synthesize(
       &assembly, circuit, std::move(config), constraint_system.constants());
 
-  EXPECT_EQ(assembly.k(), 4);
   std::vector<RationalEvals> expected_fixed_columns;
-  RationalEvals evals = RationalEvals::UnsafeZero(n - 1);
+  RationalEvals evals = domain->Empty<RationalEvals>();
   *evals[0] = math::RationalField<F>(constant);
   expected_fixed_columns.push_back(std::move(evals));
   EXPECT_EQ(assembly.fixed_columns(), expected_fixed_columns);
diff --git a/tachyon/zk/plonk/keys/assembly.h b/tachyon/zk/plonk/keys/assembly.h
index 46d67127a..c46aee37c 100644
--- a/tachyon/zk/plonk/keys/assembly.h
+++ b/tachyon/zk/plonk/keys/assembly.h
@@ -26,17 +26,15 @@ class Assembly : public Assignment<typename PCSTy::Field> {
   using AssignCallback = typename Assignment<F>::AssignCallback;
 
   Assembly() = default;
-  Assembly(uint32_t k, std::vector<RationalEvals>&& fixed_columns,
+  Assembly(std::vector<RationalEvals>&& fixed_columns,
            PermutationAssembly<PCSTy>&& permutation,
            std::vector<std::vector<bool>>&& selectors,
            base::Range<size_t> usable_rows)
-      : k_(k),
-        fixed_columns_(std::move(fixed_columns)),
+      : fixed_columns_(std::move(fixed_columns)),
         permutation_(std::move(permutation)),
         selectors_(std::move(selectors)),
         usable_rows_(usable_rows) {}
 
-  uint32_t k() const { return k_; }
   const std::vector<RationalEvals>& fixed_columns() const {
     return fixed_columns_;
   }
@@ -80,7 +78,6 @@ class Assembly : public Assignment<typename PCSTy::Field> {
   }
 
  private:
-  uint32_t k_ = 0;
   std::vector<RationalEvals> fixed_columns_;
   PermutationAssembly<PCSTy> permutation_;
   std::vector<std::vector<bool>> selectors_;
diff --git a/tachyon/zk/plonk/keys/key.h b/tachyon/zk/plonk/keys/key.h
index 6bb613a04..121880a9f 100644
--- a/tachyon/zk/plonk/keys/key.h
+++ b/tachyon/zk/plonk/keys/key.h
@@ -21,22 +21,23 @@ template <typename PCSTy>
 class Key {
  public:
   using F = typename PCSTy::Field;
+  using Domain = typename PCSTy::Domain;
   using Evals = typename PCSTy::Evals;
 
   static Assembly<PCSTy> CreateAssembly(
-      const PCSTy& pcs, const ConstraintSystem<F>& constraint_system) {
+      const Domain* domain, const ConstraintSystem<F>& constraint_system) {
     using RationalEvals = typename Assembly<PCSTy>::RationalEvals;
+    size_t n = domain->size();
     return {
-        static_cast<uint32_t>(pcs.K()),
         base::CreateVector(constraint_system.num_fixed_columns(),
-                           RationalEvals::UnsafeZero(pcs.N() - 1)),
-        PermutationAssembly<PCSTy>(constraint_system.permutation(), pcs.N()),
+                           domain->template Empty<RationalEvals>()),
+        PermutationAssembly<PCSTy>(constraint_system.permutation(), n),
         base::CreateVector(constraint_system.num_selectors(),
-                           base::CreateVector(pcs.N(), false)),
+                           base::CreateVector(n, false)),
         // NOTE(chokobole): Considering that this is called from a verifier,
         // then you can't load this number through |prover->GetUsableRows()|.
         base::Range<size_t>::Until(
-            pcs.N() - (constraint_system.ComputeBlindingFactors() + 1))};
+            n - (constraint_system.ComputeBlindingFactors() + 1))};
   }
 
  protected:
@@ -67,7 +68,7 @@ class Key {
     entity->set_extended_domain(
         ExtendedDomain::Create(size_t{1} << extended_k));
 
-    result->assembly = CreateAssembly(pcs, constraint_system);
+    result->assembly = CreateAssembly(entity->domain(), constraint_system);
     Assembly<PCSTy>& assembly = result->assembly;
     FloorPlanner::Synthesize(&assembly, circuit, std::move(config),
                              constraint_system.constants());
diff --git a/tachyon/zk/plonk/keys/proving_key.h b/tachyon/zk/plonk/keys/proving_key.h
index 126131c95..3db942975 100644
--- a/tachyon/zk/plonk/keys/proving_key.h
+++ b/tachyon/zk/plonk/keys/proving_key.h
@@ -83,8 +83,7 @@ class ProvingKey : public Key<PCSTy> {
       permutations = std::move(vk_load_result->permutations);
     } else {
       permutations =
-          pre_load_result.assembly.permutation().GeneratePermutations(
-              prover->domain());
+          pre_load_result.assembly.permutation().GeneratePermutations(domain);
     }
 
     permutation_proving_key_ =
@@ -104,8 +103,7 @@ class ProvingKey : public Key<PCSTy> {
     // | 5 | 0          |
     // | 6 | 0          |
     // | 7 | 0          |
-    const PCSTy& pcs = prover->pcs();
-    Evals evals = Evals::UnsafeZero(pcs.N() - 1);
+    Evals evals = domain->template Empty<Evals>();
     *evals[0] = F::One();
     l_first_ = domain->IFFT(evals);
     *evals[0] = F::Zero();
diff --git a/tachyon/zk/plonk/permutation/permutation_argument_unittest.cc b/tachyon/zk/plonk/permutation/permutation_argument_unittest.cc
index 383353f66..7d274cda6 100644
--- a/tachyon/zk/plonk/permutation/permutation_argument_unittest.cc
+++ b/tachyon/zk/plonk/permutation/permutation_argument_unittest.cc
@@ -21,13 +21,15 @@ class PermutationArgumentTest : public Halo2ProverTest {
   void SetUp() override {
     Halo2ProverTest::SetUp();
 
-    const size_t n = prover_->pcs().N();
-    const size_t d = n - 1;
+    const Domain* domain = prover_->domain();
 
-    Evals cycled_column = Evals::Random(d);
-    fixed_columns_ = {cycled_column, Evals::Random(d), Evals::Random(d)};
-    advice_columns_ = {Evals::Random(d), cycled_column, Evals::Random(d)};
-    instance_columns_ = {cycled_column, Evals::Random(d), Evals::Random(d)};
+    Evals cycled_column = domain->Random<Evals>();
+    fixed_columns_ = {cycled_column, domain->Random<Evals>(),
+                      domain->Random<Evals>()};
+    advice_columns_ = {domain->Random<Evals>(), cycled_column,
+                       domain->Random<Evals>()};
+    instance_columns_ = {cycled_column, domain->Random<Evals>(),
+                         domain->Random<Evals>()};
 
     table_ = Table<Evals>(absl::MakeConstSpan(fixed_columns_),
                           absl::MakeConstSpan(advice_columns_),
@@ -40,8 +42,8 @@ class PermutationArgumentTest : public Halo2ProverTest {
     };
     argument_ = PermutationArgument(column_keys_);
 
-    unpermuted_table_ = UnpermutedTable<Evals>::Construct(column_keys_.size(),
-                                                          n, prover_->domain());
+    unpermuted_table_ = UnpermutedTable<Evals>::Construct(
+        column_keys_.size(), prover_->pcs().N(), prover_->domain());
   }
 
  protected:
@@ -92,7 +94,7 @@ TEST_F(PermutationArgumentTest, Commit) {
   F gamma = F::Random();
 
   PermutationArgumentRunner<Poly, Evals>::CommitArgument(
-      prover_.get(), argument_, table_, prover_->pcs().N(), pk, beta, gamma);
+      prover_.get(), argument_, table_, n, pk, beta, gamma);
 }
 
 }  // namespace tachyon::zk
diff --git a/tachyon/zk/plonk/permutation/permutation_assembly.h b/tachyon/zk/plonk/permutation/permutation_assembly.h
index c62893243..ccd59a5a2 100644
--- a/tachyon/zk/plonk/permutation/permutation_assembly.h
+++ b/tachyon/zk/plonk/permutation/permutation_assembly.h
@@ -114,12 +114,13 @@ class PermutationAssembly {
   // permutations. Note that the permutation polynomials are in evaluation
   // form.
   std::vector<Evals> GeneratePermutations(const Domain* domain) const {
+    CHECK_EQ(domain->size(), rows_);
     UnpermutedTable<Evals> unpermuted_table =
         UnpermutedTable<Evals>::Construct(columns_.size(), rows_, domain);
 
     // Init evaluation formed polynomials with all-zero coefficients.
     std::vector<Evals> permutations =
-        base::CreateVector(columns_.size(), Evals::UnsafeZero(rows_ - 1));
+        base::CreateVector(columns_.size(), domain->template Empty<Evals>());
 
     // Assign |unpermuted_table| to |permutations|.
     base::Parallelize(permutations, [&unpermuted_table, this](
diff --git a/tachyon/zk/plonk/permutation/permutation_proving_key_unittest.cc b/tachyon/zk/plonk/permutation/permutation_proving_key_unittest.cc
index ed2a5d9bc..875675a54 100644
--- a/tachyon/zk/plonk/permutation/permutation_proving_key_unittest.cc
+++ b/tachyon/zk/plonk/permutation/permutation_proving_key_unittest.cc
@@ -23,8 +23,8 @@ class PermutationProvingKeyTest : public Halo2ProverTest {
 }  // namespace
 
 TEST_F(PermutationProvingKeyTest, Copyable) {
-  ProvingKey expected({Evals::Random(prover_->pcs().N() - 1)},
-                      {Poly::Random(5)});
+  const Domain* domain = prover_->domain();
+  ProvingKey expected({domain->Random<Evals>()}, {domain->Random<Poly>()});
   ProvingKey value;
 
   base::VectorBuffer write_buf;
diff --git a/tachyon/zk/plonk/permutation/permutation_table_store_unittest.cc b/tachyon/zk/plonk/permutation/permutation_table_store_unittest.cc
index b70f4b5e4..099a487a8 100644
--- a/tachyon/zk/plonk/permutation/permutation_table_store_unittest.cc
+++ b/tachyon/zk/plonk/permutation/permutation_table_store_unittest.cc
@@ -17,11 +17,13 @@ class PermutationTableStoreTest : public Halo2ProverTest {
   void SetUp() override {
     Halo2ProverTest::SetUp();
 
-    size_t n = prover_->pcs().N();
-    size_t d = n - 1;
-    fixed_columns_ = {Evals::Random(d), Evals::Random(d), Evals::Random(d)};
-    advice_columns_ = {Evals::Random(d), Evals::Random(d), Evals::Random(d)};
-    instance_columns_ = {Evals::Random(d), Evals::Random(d), Evals::Random(d)};
+    const Domain* domain = prover_->domain();
+    fixed_columns_ =
+        base::CreateVector(3, [domain]() { return domain->Random<Evals>(); });
+    advice_columns_ =
+        base::CreateVector(3, [domain]() { return domain->Random<Evals>(); });
+    instance_columns_ =
+        base::CreateVector(3, [domain]() { return domain->Random<Evals>(); });
 
     table_ = Table<Evals>(absl::MakeConstSpan(fixed_columns_),
                           absl::MakeConstSpan(advice_columns_),
@@ -32,8 +34,8 @@ class PermutationTableStoreTest : public Halo2ProverTest {
         AdviceColumnKey(1), FixedColumnKey(1),    FixedColumnKey(2),
         AdviceColumnKey(2), InstanceColumnKey(1), InstanceColumnKey(2)};
 
-    unpermuted_table_ = UnpermutedTable<Evals>::Construct(column_keys_.size(),
-                                                          n, prover_->domain());
+    unpermuted_table_ = UnpermutedTable<Evals>::Construct(
+        column_keys_.size(), prover_->pcs().N(), prover_->domain());
     for (const Evals& column : unpermuted_table_.table()) {
       permutations_.push_back(column);
     }
diff --git a/tachyon/zk/plonk/prover/argument_unittest.cc b/tachyon/zk/plonk/prover/argument_unittest.cc
index 0841f6c8c..e910c1d01 100644
--- a/tachyon/zk/plonk/prover/argument_unittest.cc
+++ b/tachyon/zk/plonk/prover/argument_unittest.cc
@@ -18,26 +18,26 @@ namespace {
 
 class ArgumentTest : public Halo2ProverTest {
  public:
-  using F = typename PCS::Field;
-  using Poly = typename PCS::Poly;
-  using Evals = typename PCS::Evals;
-
   void InitColumns() {
-    size_t d = prover_->pcs().N() - 1;
+    const Domain* domain = prover_->domain();
     num_circuits_ = 2;
     expected_fixed_columns_ =
-        base::CreateVector(1, [d]() { return Evals::Random(d); });
+        base::CreateVector(1, [domain]() { return domain->Random<Evals>(); });
     expected_fixed_polys_ =
-        base::CreateVector(1, [d]() { return Poly::Random(d); });
-    expected_advice_columns_vec_ = base::CreateVector(num_circuits_, [d]() {
-      return base::CreateVector(2, [d]() { return Evals::Random(d); });
-    });
+        base::CreateVector(1, [domain]() { return domain->Random<Poly>(); });
+    expected_advice_columns_vec_ =
+        base::CreateVector(num_circuits_, [domain]() {
+          return base::CreateVector(
+              2, [domain]() { return domain->Random<Evals>(); });
+        });
     expected_advice_blinds_vec_ = base::CreateVector(num_circuits_, []() {
       return base::CreateVector(2, []() { return F::Random(); });
     });
-    expected_instance_columns_vec_ = base::CreateVector(num_circuits_, [d]() {
-      return base::CreateVector(1, [d]() { return Evals::Random(d); });
-    });
+    expected_instance_columns_vec_ =
+        base::CreateVector(num_circuits_, [domain]() {
+          return base::CreateVector(
+              1, [domain]() { return domain->Random<Evals>(); });
+        });
     expected_challenges_ = {F::Random()};
   }
 
diff --git a/tachyon/zk/plonk/prover/synthesizer.h b/tachyon/zk/plonk/prover/synthesizer.h
index 0cbea0028..6073169e9 100644
--- a/tachyon/zk/plonk/prover/synthesizer.h
+++ b/tachyon/zk/plonk/prover/synthesizer.h
@@ -108,7 +108,7 @@ class Synthesizer {
     // number of blinding factors and an extra row for use in the
     // permutation argument.
     WitnessCollection<PCSTy> witness(
-        prover->pcs().K(), constraint_system_->num_advice_columns(),
+        prover->domain(), constraint_system_->num_advice_columns(),
         prover->GetUsableRows(), phase, challenges_, instance_columns);
 
     CircuitTy::FloorPlanner::Synthesize(&witness, circuit, config.Clone(),
diff --git a/tachyon/zk/plonk/prover/synthesizer_unittest.cc b/tachyon/zk/plonk/prover/synthesizer_unittest.cc
index c5dd1bbcd..218560776 100644
--- a/tachyon/zk/plonk/prover/synthesizer_unittest.cc
+++ b/tachyon/zk/plonk/prover/synthesizer_unittest.cc
@@ -44,7 +44,7 @@ class SynthesizerTest : public Halo2ProverTest {
 TEST_F(SynthesizerTest, GenerateAdviceColumns) {
   std::vector<std::vector<Evals>> instance_columns_vec =
       base::CreateVector(circuits_.size(), [this]() {
-        return base::CreateVector(1, Evals::Random(prover_->pcs().N() - 1));
+        return base::CreateVector(1, prover_->domain()->Random<Evals>());
       });
   synthesizer_.GenerateAdviceColumns(prover_.get(), circuits_,
                                      instance_columns_vec);
diff --git a/tachyon/zk/plonk/prover/witness_collection.h b/tachyon/zk/plonk/prover/witness_collection.h
index 1ed7c7166..da0af0037 100644
--- a/tachyon/zk/plonk/prover/witness_collection.h
+++ b/tachyon/zk/plonk/prover/witness_collection.h
@@ -24,24 +24,23 @@ template <typename PCSTy>
 class WitnessCollection : public Assignment<typename PCSTy::Field> {
  public:
   using F = typename PCSTy::Field;
+  using Domain = typename PCSTy::Domain;
   using Evals = typename PCSTy::Evals;
   using RationalEvals = typename PCSTy::RationalEvals;
   using AssignCallback = typename Assignment<F>::AssignCallback;
 
   WitnessCollection() = default;
-  WitnessCollection(size_t k, size_t num_advice_columns, size_t usable_rows,
-                    const Phase current_phase,
+  WitnessCollection(const Domain* domain, size_t num_advice_columns,
+                    size_t usable_rows, const Phase current_phase,
                     const absl::btree_map<size_t, F>& challenges,
                     const std::vector<Evals>& instance_columns)
-      : k_(k),
-        advices_(base::CreateVector(num_advice_columns,
-                                    RationalEvals::UnsafeZero(size_t{1} << k))),
+      : advices_(base::CreateVector(num_advice_columns,
+                                    domain->template Empty<RationalEvals>())),
         usable_rows_(base::Range<size_t>::Until(usable_rows)),
         current_phase_(current_phase),
         challenges_(challenges),
         instance_columns_(instance_columns) {}
 
-  size_t k() const { return k_; }
   // NOTE(dongchangYoo): This getter of |advices| transfers ownership as well.
   // That's why, |WitnessCollection| will be released as soon as emitting it.
   std::vector<RationalEvals>&& advices() && { return std::move(advices_); }
@@ -76,7 +75,6 @@ class WitnessCollection : public Assignment<typename PCSTy::Field> {
   }
 
  private:
-  size_t k_ = 0;
   std::vector<RationalEvals> advices_;
   base::Range<size_t> usable_rows_;
   Phase current_phase_;
diff --git a/tachyon/zk/plonk/prover/witness_collection_unittest.cc b/tachyon/zk/plonk/prover/witness_collection_unittest.cc
index a274b1b3e..79cb17848 100644
--- a/tachyon/zk/plonk/prover/witness_collection_unittest.cc
+++ b/tachyon/zk/plonk/prover/witness_collection_unittest.cc
@@ -23,16 +23,17 @@ class WitnessCollectionTest : public Halo2ProverTest {
   void SetUp() override {
     Halo2ProverTest::SetUp();
 
+    const Domain* domain = prover_->domain();
     prover_->blinder().set_blinding_factors(5);
 
     // There is a single challenge in |challenges_|.
     expected_challenges_[0] = F::Random();
-    expected_instance_columns_ = {Evals::Random(prover_->pcs().N() - 1)};
+    expected_instance_columns_ = {domain->Random<Evals>()};
 
     Phase current_phase(0);
     witness_collection_ = WitnessCollection<PCS>(
-        5, 3, prover_->GetUsableRows(), current_phase, expected_challenges_,
-        expected_instance_columns_);
+        domain, 3, prover_->GetUsableRows(), current_phase,
+        expected_challenges_, expected_instance_columns_);
   }
 
  protected: