diff --git a/libs/marshalling/zk/include/nil/crypto3/marshalling/zk/detail/random_test_data_generation.hpp b/libs/marshalling/zk/include/nil/crypto3/marshalling/zk/detail/random_test_data_generation.hpp
index 9a535d523..7c714b9d9 100644
--- a/libs/marshalling/zk/include/nil/crypto3/marshalling/zk/detail/random_test_data_generation.hpp
+++ b/libs/marshalling/zk/include/nil/crypto3/marshalling/zk/detail/random_test_data_generation.hpp
@@ -48,7 +48,7 @@
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
diff --git a/libs/marshalling/zk/test/fri_commitment.cpp b/libs/marshalling/zk/test/fri_commitment.cpp
index 34093cff8..afeb0ae26 100644
--- a/libs/marshalling/zk/test/fri_commitment.cpp
+++ b/libs/marshalling/zk/test/fri_commitment.cpp
@@ -50,7 +50,7 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/mnt4.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
diff --git a/libs/marshalling/zk/test/kzg_commitment.cpp b/libs/marshalling/zk/test/kzg_commitment.cpp
index 398d07bf8..8ba0164a4 100644
--- a/libs/marshalling/zk/test/kzg_commitment.cpp
+++ b/libs/marshalling/zk/test/kzg_commitment.cpp
@@ -51,7 +51,7 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/alt_bn128.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
diff --git a/libs/marshalling/zk/test/lpc_commitment.cpp b/libs/marshalling/zk/test/lpc_commitment.cpp
index d3fd7c352..fd0c67f3c 100644
--- a/libs/marshalling/zk/test/lpc_commitment.cpp
+++ b/libs/marshalling/zk/test/lpc_commitment.cpp
@@ -52,7 +52,7 @@
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
diff --git a/libs/marshalling/zk/test/placeholder_common_data.cpp b/libs/marshalling/zk/test/placeholder_common_data.cpp
index 72a9f9ac0..6986269f9 100644
--- a/libs/marshalling/zk/test/placeholder_common_data.cpp
+++ b/libs/marshalling/zk/test/placeholder_common_data.cpp
@@ -50,7 +50,7 @@
 #include <nil/crypto3/zk/snark/systems/plonk/placeholder/detail/profiling.hpp>
 
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/calculate_domain_set.hpp>
 
 #include <nil/crypto3/marshalling/zk/types/commitments/eval_storage.hpp>
diff --git a/libs/marshalling/zk/test/placeholder_preprocessed_public_data.cpp b/libs/marshalling/zk/test/placeholder_preprocessed_public_data.cpp
index dc3f710f8..e539f21ee 100644
--- a/libs/marshalling/zk/test/placeholder_preprocessed_public_data.cpp
+++ b/libs/marshalling/zk/test/placeholder_preprocessed_public_data.cpp
@@ -48,7 +48,7 @@
 #include <nil/crypto3/zk/snark/systems/plonk/placeholder/detail/profiling.hpp>
 
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/calculate_domain_set.hpp>
 
 #include <nil/crypto3/marshalling/zk/types/commitments/eval_storage.hpp>
diff --git a/libs/marshalling/zk/test/polys_evaluator.cpp b/libs/marshalling/zk/test/polys_evaluator.cpp
index f013b7024..6fed8bba4 100644
--- a/libs/marshalling/zk/test/polys_evaluator.cpp
+++ b/libs/marshalling/zk/test/polys_evaluator.cpp
@@ -50,7 +50,7 @@
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
diff --git a/libs/math/docs/concepts.md b/libs/math/docs/concepts.md
index 900c39b55..c8f74fa9f 100644
--- a/libs/math/docs/concepts.md
+++ b/libs/math/docs/concepts.md
@@ -98,7 +98,7 @@ canonical storage, arithmetic operators, or alias-safe operations.
 
 The polynomial multiplication backend concept is declared in:
 
-    <nil/crypto3/math/polynomial/polynomial_backend.hpp>
+    <nil/crypto3/math/polynomial/backends/polynomial_backend.hpp>
 
 `polynomial_arithmetic::PolynomialBackend<Backend>` requires an associated `polynomial_type` that satisfies
 `CoefficientPolynomial` and three operations:
diff --git a/libs/math/docs/polynomial_arithmetic.md b/libs/math/docs/polynomial_arithmetic.md
index 044ecec91..10cd0d454 100644
--- a/libs/math/docs/polynomial_arithmetic.md
+++ b/libs/math/docs/polynomial_arithmetic.md
@@ -23,15 +23,15 @@ The main dependency chain is:
 | Facility | Header |
 |---|---|
 | Representation concepts | `<nil/crypto3/math/polynomial/concepts.hpp>` |
-| Backend concept and arithmetic context | `<nil/crypto3/math/polynomial/polynomial_backend.hpp>` |
-| Schoolbook and mixed-radix backends | `<nil/crypto3/math/polynomial/schoolbook_backend.hpp>`, `<nil/crypto3/math/polynomial/mixed_radix_backend.hpp>` |
-| Power-series inversion | `<nil/crypto3/math/polynomial/power_series.hpp>` |
-| Divisor context and division | `<nil/crypto3/math/polynomial/polynomial_division.hpp>` |
-| GCD | `<nil/crypto3/math/polynomial/gcd.hpp>` |
-| Quotient-ring multiplication | `<nil/crypto3/math/polynomial/polynomial_modular_arithmetic.hpp>` |
-| Quotient-ring exponentiation | `<nil/crypto3/math/polynomial/polynomial_exponentiation.hpp>` |
-| Modular composition | `<nil/crypto3/math/polynomial/polynomial_composition.hpp>` |
-| Frobenius maps | `<nil/crypto3/math/polynomial/polynomial_frobenius.hpp>` |
+| Backend concept and arithmetic context | `<nil/crypto3/math/polynomial/backends/polynomial_backend.hpp>` |
+| Schoolbook and mixed-radix backends | `<nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>`, `<nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp>` |
+| Power-series inversion | `<nil/crypto3/math/polynomial/arithmetic/power_series.hpp>` |
+| Divisor context and division | `<nil/crypto3/math/polynomial/arithmetic/polynomial_division.hpp>` |
+| GCD | `<nil/crypto3/math/polynomial/arithmetic/gcd.hpp>` |
+| Quotient-ring multiplication | `<nil/crypto3/math/polynomial/quotient_ring/polynomial_modular_arithmetic.hpp>` |
+| Quotient-ring exponentiation | `<nil/crypto3/math/polynomial/quotient_ring/polynomial_exponentiation.hpp>` |
+| Modular composition | `<nil/crypto3/math/polynomial/quotient_ring/polynomial_composition.hpp>` |
+| Frobenius maps | `<nil/crypto3/math/polynomial/quotient_ring/polynomial_frobenius.hpp>` |
 
 ## Multiplication backends
 
diff --git a/libs/math/docs/polynomial_factorization.md b/libs/math/docs/polynomial_factorization.md
index ce701113e..510e83264 100644
--- a/libs/math/docs/polynomial_factorization.md
+++ b/libs/math/docs/polynomial_factorization.md
@@ -42,12 +42,12 @@ maps used by these stages.
 
 | Facility | Header |
 |---|---|
-| Result and callback types | `<nil/crypto3/math/polynomial/polynomial_factorization.hpp>` |
-| Square-free factorization | `<nil/crypto3/math/polynomial/square_free_factorization.hpp>` |
-| Reference distinct-degree factorization | `<nil/crypto3/math/polynomial/distinct_degree_factorization.hpp>` |
-| Kaltofen-Shoup distinct-degree factorization | `<nil/crypto3/math/polynomial/kaltofen_shoup_distinct_degree_factorization.hpp>` |
-| Equal-degree factorization | `<nil/crypto3/math/polynomial/equal_degree_factorization.hpp>` |
-| Complete factorization | `<nil/crypto3/math/polynomial/complete_factorization.hpp>` |
+| Result and callback types | `<nil/crypto3/math/polynomial/factorization/polynomial_factorization.hpp>` |
+| Square-free factorization | `<nil/crypto3/math/polynomial/factorization/square_free_factorization.hpp>` |
+| Reference distinct-degree factorization | `<nil/crypto3/math/polynomial/factorization/distinct_degree_factorization.hpp>` |
+| Kaltofen-Shoup distinct-degree factorization | `<nil/crypto3/math/polynomial/factorization/kaltofen_shoup_distinct_degree_factorization.hpp>` |
+| Equal-degree factorization | `<nil/crypto3/math/polynomial/factorization/equal_degree_factorization.hpp>` |
+| Complete factorization | `<nil/crypto3/math/polynomial/factorization/complete_factorization.hpp>` |
 
 ## Complete factorization
 
@@ -55,8 +55,8 @@ The simplest entry point takes a polynomial arithmetic context and a caller-owne
 
 ```cpp
 #include <nil/crypto3/algebra/fields/babybear/base_field.hpp>
-#include <nil/crypto3/math/polynomial/complete_factorization.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/factorization/complete_factorization.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 #include <nil/crypto3/random/algebraic_engine.hpp>
 
 namespace math = nil::crypto3::math;
diff --git a/libs/math/docs/polynomial_recovery.md b/libs/math/docs/polynomial_recovery.md
index 13ef8f0cc..4df8901ac 100644
--- a/libs/math/docs/polynomial_recovery.md
+++ b/libs/math/docs/polynomial_recovery.md
@@ -20,8 +20,8 @@ bounds, random sources, and any policy for combining or rejecting recovered repr
 |---|---|
 | Field orders and multiplicative-group decomposition | `<nil/crypto3/algebra/fields/field_order.hpp>` |
 | Coefficient-field square-root helpers | `<nil/crypto3/algebra/fields/field_algorithms.hpp>` |
-| Quotient-field square testing and roots | `<nil/crypto3/math/polynomial/polynomial_square_root.hpp>` |
-| Bounded rational reconstruction | `<nil/crypto3/math/polynomial/polynomial_rational_reconstruction.hpp>` |
+| Quotient-field square testing and roots | `<nil/crypto3/math/polynomial/quotient_ring/polynomial_square_root.hpp>` |
+| Bounded rational reconstruction | `<nil/crypto3/math/polynomial/reconstruction/polynomial_rational_reconstruction.hpp>` |
 
 ## Field orders and coefficient square roots
 
@@ -70,7 +70,7 @@ characterize squares if the quotient has zero divisors.
 
 ```cpp
 #include <algorithm>
-#include <nil/crypto3/math/polynomial/polynomial_square_root.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_square_root.hpp>
 
 // B must be irreducible. Its degree is d.
 const std::size_t d = B.size() - 1;
@@ -115,7 +115,7 @@ numerator bound, while tracking the corresponding coefficient of `R`. The return
 numerator is scaled by the same field element.
 
 ```cpp
-#include <nil/crypto3/math/polynomial/polynomial_rational_reconstruction.hpp>
+#include <nil/crypto3/math/polynomial/reconstruction/polynomial_rational_reconstruction.hpp>
 
 polynomial_type numerator;
 polynomial_type denominator;
diff --git a/libs/math/example/polynomials.cpp b/libs/math/example/polynomials.cpp
index 165096271..783bd8930 100644
--- a/libs/math/example/polynomials.cpp
+++ b/libs/math/example/polynomials.cpp
@@ -27,8 +27,8 @@
 
 #include <nil/crypto3/algebra/fields/arithmetic_params/bls12.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
-#include <nil/crypto3/math/polynomial/xgcd.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/xgcd.hpp>
 #include <nil/crypto3/algebra/fields/bls12/scalar_field.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
diff --git a/libs/math/example/polynomials_dfs.cpp b/libs/math/example/polynomials_dfs.cpp
index 62c02a94d..f7501f6cb 100644
--- a/libs/math/example/polynomials_dfs.cpp
+++ b/libs/math/example/polynomials_dfs.cpp
@@ -27,8 +27,8 @@
 
 #include <nil/crypto3/algebra/fields/arithmetic_params/bls12.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
-#include <nil/crypto3/math/polynomial/xgcd.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/xgcd.hpp>
 #include <nil/crypto3/algebra/fields/bls12/scalar_field.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
diff --git a/libs/math/include/nil/crypto3/math/domains/arithmetic_sequence_domain.hpp b/libs/math/include/nil/crypto3/math/domains/arithmetic_sequence_domain.hpp
index 24f830e6a..f54c1b6d5 100644
--- a/libs/math/include/nil/crypto3/math/domains/arithmetic_sequence_domain.hpp
+++ b/libs/math/include/nil/crypto3/math/domains/arithmetic_sequence_domain.hpp
@@ -30,7 +30,7 @@
 
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 
-#include <nil/crypto3/math/polynomial/basis_change.hpp>
+#include <nil/crypto3/math/polynomial/operations/basis_change.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 
 namespace nil {
diff --git a/libs/math/include/nil/crypto3/math/domains/geometric_sequence_domain.hpp b/libs/math/include/nil/crypto3/math/domains/geometric_sequence_domain.hpp
index 8dfbc1efc..a6bed5a53 100644
--- a/libs/math/include/nil/crypto3/math/domains/geometric_sequence_domain.hpp
+++ b/libs/math/include/nil/crypto3/math/domains/geometric_sequence_domain.hpp
@@ -32,7 +32,7 @@
 #include <nil/crypto3/math/algorithms/batch_inverse.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 
-#include <nil/crypto3/math/polynomial/basis_change.hpp>
+#include <nil/crypto3/math/polynomial/operations/basis_change.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 
 namespace nil {
diff --git a/libs/math/include/nil/crypto3/math/polynomial/gcd.hpp b/libs/math/include/nil/crypto3/math/polynomial/arithmetic/gcd.hpp
similarity index 98%
rename from libs/math/include/nil/crypto3/math/polynomial/gcd.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/arithmetic/gcd.hpp
index a11b9a4cd..ebe9b8d22 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/gcd.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/arithmetic/gcd.hpp
@@ -30,7 +30,7 @@
 #include <cstddef>
 #include <utility>
 
-#include <nil/crypto3/math/polynomial/half_gcd.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/half_gcd.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/half_gcd.hpp b/libs/math/include/nil/crypto3/math/polynomial/arithmetic/half_gcd.hpp
similarity index 99%
rename from libs/math/include/nil/crypto3/math/polynomial/half_gcd.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/arithmetic/half_gcd.hpp
index 4da4b43bf..650c693c4 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/half_gcd.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/arithmetic/half_gcd.hpp
@@ -29,8 +29,8 @@
 #include <stdexcept>
 #include <utility>
 
-#include <nil/crypto3/math/polynomial/polynomial_division.hpp>
-#include <nil/crypto3/math/polynomial/shift.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/polynomial_division.hpp>
+#include <nil/crypto3/math/polynomial/operations/shift.hpp>
 
 namespace nil::crypto3::math::detail {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_division.hpp b/libs/math/include/nil/crypto3/math/polynomial/arithmetic/polynomial_division.hpp
similarity index 99%
rename from libs/math/include/nil/crypto3/math/polynomial/polynomial_division.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/arithmetic/polynomial_division.hpp
index 080a88e54..326eee707 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial_division.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/arithmetic/polynomial_division.hpp
@@ -31,7 +31,7 @@
 #include <stdexcept>
 #include <utility>
 
-#include <nil/crypto3/math/polynomial/power_series.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/power_series.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/power_series.hpp b/libs/math/include/nil/crypto3/math/polynomial/arithmetic/power_series.hpp
similarity index 98%
rename from libs/math/include/nil/crypto3/math/polynomial/power_series.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/arithmetic/power_series.hpp
index e0bd2f4bc..3ffe617fb 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/power_series.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/arithmetic/power_series.hpp
@@ -31,7 +31,7 @@
 #include <stdexcept>
 #include <utility>
 
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/xgcd.hpp b/libs/math/include/nil/crypto3/math/polynomial/arithmetic/xgcd.hpp
similarity index 98%
rename from libs/math/include/nil/crypto3/math/polynomial/xgcd.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/arithmetic/xgcd.hpp
index 85b493bd1..d9a7cfd11 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/xgcd.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/arithmetic/xgcd.hpp
@@ -33,7 +33,7 @@
 #include <vector>
 
 #include <nil/crypto3/algebra/type_traits.hpp>
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 
 namespace nil {
     namespace crypto3 {
diff --git a/libs/math/include/nil/crypto3/math/polynomial/mixed_radix_backend.hpp b/libs/math/include/nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp
similarity index 98%
rename from libs/math/include/nil/crypto3/math/polynomial/mixed_radix_backend.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp
index d6ae017c0..b70b5041d 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/mixed_radix_backend.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp
@@ -32,9 +32,9 @@
 #include <vector>
 
 #include <nil/crypto3/math/algorithms/mixed_radix_fft.hpp>
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/polynomial_backend.hpp>
 
 namespace nil::crypto3::math::polynomial_arithmetic {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_backend.hpp b/libs/math/include/nil/crypto3/math/polynomial/backends/polynomial_backend.hpp
similarity index 100%
rename from libs/math/include/nil/crypto3/math/polynomial/polynomial_backend.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/backends/polynomial_backend.hpp
diff --git a/libs/math/include/nil/crypto3/math/polynomial/schoolbook_backend.hpp b/libs/math/include/nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp
similarity index 96%
rename from libs/math/include/nil/crypto3/math/polynomial/schoolbook_backend.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp
index f07939636..f1f2b4851 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/schoolbook_backend.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp
@@ -29,9 +29,9 @@
 #include <cstddef>
 #include <utility>
 
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/polynomial_backend.hpp>
 
 namespace nil::crypto3::math::polynomial_arithmetic {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/complete_factorization.hpp b/libs/math/include/nil/crypto3/math/polynomial/factorization/complete_factorization.hpp
similarity index 95%
rename from libs/math/include/nil/crypto3/math/polynomial/complete_factorization.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/factorization/complete_factorization.hpp
index 827c3b641..0c4fada6a 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/complete_factorization.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/factorization/complete_factorization.hpp
@@ -29,9 +29,9 @@
 #include <utility>
 #include <vector>
 
-#include <nil/crypto3/math/polynomial/equal_degree_factorization.hpp>
-#include <nil/crypto3/math/polynomial/kaltofen_shoup_distinct_degree_factorization.hpp>
-#include <nil/crypto3/math/polynomial/square_free_factorization.hpp>
+#include <nil/crypto3/math/polynomial/factorization/equal_degree_factorization.hpp>
+#include <nil/crypto3/math/polynomial/factorization/kaltofen_shoup_distinct_degree_factorization.hpp>
+#include <nil/crypto3/math/polynomial/factorization/square_free_factorization.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/distinct_degree_factorization.hpp b/libs/math/include/nil/crypto3/math/polynomial/factorization/distinct_degree_factorization.hpp
similarity index 97%
rename from libs/math/include/nil/crypto3/math/polynomial/distinct_degree_factorization.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/factorization/distinct_degree_factorization.hpp
index 428049a7d..aae8d646c 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/distinct_degree_factorization.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/factorization/distinct_degree_factorization.hpp
@@ -30,9 +30,9 @@
 #include <stdexcept>
 #include <utility>
 
-#include <nil/crypto3/math/polynomial/gcd.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_factorization.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_frobenius.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/gcd.hpp>
+#include <nil/crypto3/math/polynomial/factorization/polynomial_factorization.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_frobenius.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/equal_degree_factorization.hpp b/libs/math/include/nil/crypto3/math/polynomial/factorization/equal_degree_factorization.hpp
similarity index 99%
rename from libs/math/include/nil/crypto3/math/polynomial/equal_degree_factorization.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/factorization/equal_degree_factorization.hpp
index 594353f2a..c2651cbf9 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/equal_degree_factorization.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/factorization/equal_degree_factorization.hpp
@@ -35,8 +35,8 @@
 
 #include <nil/crypto3/algebra/fields/field_order.hpp>
 
-#include <nil/crypto3/math/polynomial/polynomial_factorization.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_exponentiation.hpp>
+#include <nil/crypto3/math/polynomial/factorization/polynomial_factorization.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_exponentiation.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/kaltofen_shoup_distinct_degree_factorization.hpp b/libs/math/include/nil/crypto3/math/polynomial/factorization/kaltofen_shoup_distinct_degree_factorization.hpp
similarity index 98%
rename from libs/math/include/nil/crypto3/math/polynomial/kaltofen_shoup_distinct_degree_factorization.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/factorization/kaltofen_shoup_distinct_degree_factorization.hpp
index 460563e61..1e238eee9 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/kaltofen_shoup_distinct_degree_factorization.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/factorization/kaltofen_shoup_distinct_degree_factorization.hpp
@@ -33,10 +33,10 @@
 #include <vector>
 
 #include <nil/crypto3/math/detail/integer_sqrt.hpp>
-#include <nil/crypto3/math/polynomial/distinct_degree_factorization.hpp>
-#include <nil/crypto3/math/polynomial/gcd.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_factorization.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_frobenius.hpp>
+#include <nil/crypto3/math/polynomial/factorization/distinct_degree_factorization.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/gcd.hpp>
+#include <nil/crypto3/math/polynomial/factorization/polynomial_factorization.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_frobenius.hpp>
 
 namespace nil::crypto3::math::detail {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_factorization.hpp b/libs/math/include/nil/crypto3/math/polynomial/factorization/polynomial_factorization.hpp
similarity index 98%
rename from libs/math/include/nil/crypto3/math/polynomial/polynomial_factorization.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/factorization/polynomial_factorization.hpp
index b7513ab7f..2d70e80db 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial_factorization.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/factorization/polynomial_factorization.hpp
@@ -31,8 +31,8 @@
 #include <vector>
 
 #include <nil/crypto3/math/polynomial/concepts.hpp>
-#include <nil/crypto3/math/polynomial/gcd.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_division.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/gcd.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/polynomial_division.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/square_free_factorization.hpp b/libs/math/include/nil/crypto3/math/polynomial/factorization/square_free_factorization.hpp
similarity index 98%
rename from libs/math/include/nil/crypto3/math/polynomial/square_free_factorization.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/factorization/square_free_factorization.hpp
index d60f98586..d56ebd6bb 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/square_free_factorization.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/factorization/square_free_factorization.hpp
@@ -32,8 +32,8 @@
 
 #include <nil/crypto3/algebra/fields/field_order.hpp>
 
-#include <nil/crypto3/math/polynomial/gcd.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_factorization.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/gcd.hpp>
+#include <nil/crypto3/math/polynomial/factorization/polynomial_factorization.hpp>
 
 namespace nil::crypto3::math {
     /**
diff --git a/libs/math/include/nil/crypto3/math/polynomial/basic_operations.hpp b/libs/math/include/nil/crypto3/math/polynomial/operations/basic_operations.hpp
similarity index 99%
rename from libs/math/include/nil/crypto3/math/polynomial/basic_operations.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/operations/basic_operations.hpp
index 9ec71a4e2..d1e894a0e 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/basic_operations.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/operations/basic_operations.hpp
@@ -37,7 +37,7 @@
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
 #include <nil/crypto3/math/domains/detail/basic_radix2_domain_aux.hpp>
 #include <nil/crypto3/math/detail/field_utils.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/polynomial_backend.hpp>
 
 namespace nil {
     namespace crypto3 {
diff --git a/libs/math/include/nil/crypto3/math/polynomial/basis_change.hpp b/libs/math/include/nil/crypto3/math/polynomial/operations/basis_change.hpp
similarity index 99%
rename from libs/math/include/nil/crypto3/math/polynomial/basis_change.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/operations/basis_change.hpp
index a1e702721..3e653f5ba 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/basis_change.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/operations/basis_change.hpp
@@ -32,8 +32,8 @@
 #include <vector>
 
 #include <nil/crypto3/algebra/type_traits.hpp>
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
-#include <nil/crypto3/math/polynomial/xgcd.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/xgcd.hpp>
 
 namespace nil {
     namespace crypto3 {
diff --git a/libs/math/include/nil/crypto3/math/polynomial/cyclotomic.hpp b/libs/math/include/nil/crypto3/math/polynomial/operations/cyclotomic.hpp
similarity index 100%
rename from libs/math/include/nil/crypto3/math/polynomial/cyclotomic.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/operations/cyclotomic.hpp
diff --git a/libs/math/include/nil/crypto3/math/polynomial/evaluate.hpp b/libs/math/include/nil/crypto3/math/polynomial/operations/evaluate.hpp
similarity index 100%
rename from libs/math/include/nil/crypto3/math/polynomial/evaluate.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/operations/evaluate.hpp
diff --git a/libs/math/include/nil/crypto3/math/polynomial/lagrange_interpolation.hpp b/libs/math/include/nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp
similarity index 100%
rename from libs/math/include/nil/crypto3/math/polynomial/lagrange_interpolation.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp
diff --git a/libs/math/include/nil/crypto3/math/polynomial/shift.hpp b/libs/math/include/nil/crypto3/math/polynomial/operations/shift.hpp
similarity index 99%
rename from libs/math/include/nil/crypto3/math/polynomial/shift.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/operations/shift.hpp
index 15ba86d3d..8484a57a7 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/shift.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/operations/shift.hpp
@@ -34,7 +34,7 @@
 #include <stdexcept>
 
 #include <nil/crypto3/algebra/type_traits.hpp>
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial.hpp b/libs/math/include/nil/crypto3/math/polynomial/polynomial.hpp
index 43a6c6a9e..a549edddf 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/polynomial.hpp
@@ -32,7 +32,7 @@
 #include <ranges>
 #include <vector>
 
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 #include <nil/crypto3/math/polynomial/concepts.hpp>
 
 #include <nil/crypto3/algebra/type_traits.hpp>
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_dfs.hpp b/libs/math/include/nil/crypto3/math/polynomial/polynomial_dfs.hpp
index 353702a0d..c25dabd14 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial_dfs.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/polynomial_dfs.hpp
@@ -37,7 +37,7 @@
 
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 #include <nil/crypto3/math/polynomial/concepts.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_composition.hpp b/libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_composition.hpp
similarity index 99%
rename from libs/math/include/nil/crypto3/math/polynomial/polynomial_composition.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_composition.hpp
index 7a8700dba..7da858649 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial_composition.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_composition.hpp
@@ -32,7 +32,7 @@
 #include <vector>
 
 #include <nil/crypto3/math/detail/integer_sqrt.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_modular_arithmetic.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_modular_arithmetic.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_exponentiation.hpp b/libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_exponentiation.hpp
similarity index 98%
rename from libs/math/include/nil/crypto3/math/polynomial/polynomial_exponentiation.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_exponentiation.hpp
index bfa448814..fddd981f4 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial_exponentiation.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_exponentiation.hpp
@@ -30,7 +30,7 @@
 #include <type_traits>
 #include <utility>
 
-#include <nil/crypto3/math/polynomial/polynomial_modular_arithmetic.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_modular_arithmetic.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_frobenius.hpp b/libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_frobenius.hpp
similarity index 97%
rename from libs/math/include/nil/crypto3/math/polynomial/polynomial_frobenius.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_frobenius.hpp
index 302809532..8a72aae07 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial_frobenius.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_frobenius.hpp
@@ -31,8 +31,8 @@
 
 #include <nil/crypto3/algebra/fields/field_order.hpp>
 
-#include <nil/crypto3/math/polynomial/polynomial_composition.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_exponentiation.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_composition.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_exponentiation.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_modular_arithmetic.hpp b/libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_modular_arithmetic.hpp
similarity index 98%
rename from libs/math/include/nil/crypto3/math/polynomial/polynomial_modular_arithmetic.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_modular_arithmetic.hpp
index 8bf7df7da..3f29a5976 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial_modular_arithmetic.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_modular_arithmetic.hpp
@@ -25,7 +25,7 @@
 #ifndef CRYPTO3_MATH_POLYNOMIAL_MODULAR_ARITHMETIC_HPP
 #define CRYPTO3_MATH_POLYNOMIAL_MODULAR_ARITHMETIC_HPP
 
-#include <nil/crypto3/math/polynomial/polynomial_division.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/polynomial_division.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_square_root.hpp b/libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_square_root.hpp
similarity index 99%
rename from libs/math/include/nil/crypto3/math/polynomial/polynomial_square_root.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_square_root.hpp
index 93b4c5b4f..2fd072b0b 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial_square_root.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/quotient_ring/polynomial_square_root.hpp
@@ -35,7 +35,7 @@
 #include <nil/crypto3/algebra/fields/field_order.hpp>
 #include <nil/crypto3/algebra/type_traits.hpp>
 
-#include <nil/crypto3/math/polynomial/polynomial_exponentiation.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_exponentiation.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_rational_reconstruction.hpp b/libs/math/include/nil/crypto3/math/polynomial/reconstruction/polynomial_rational_reconstruction.hpp
similarity index 99%
rename from libs/math/include/nil/crypto3/math/polynomial/polynomial_rational_reconstruction.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/reconstruction/polynomial_rational_reconstruction.hpp
index 1d635f464..7f102fd1e 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial_rational_reconstruction.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/reconstruction/polynomial_rational_reconstruction.hpp
@@ -30,7 +30,7 @@
 #include <stdexcept>
 #include <utility>
 
-#include <nil/crypto3/math/polynomial/half_gcd.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/half_gcd.hpp>
 
 namespace nil::crypto3::math {
 
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polymorphic_polynomial.hpp b/libs/math/include/nil/crypto3/math/polynomial/types/polymorphic_polynomial.hpp
similarity index 100%
rename from libs/math/include/nil/crypto3/math/polynomial/polymorphic_polynomial.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/types/polymorphic_polynomial.hpp
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polymorphic_polynomial_dfs.hpp b/libs/math/include/nil/crypto3/math/polynomial/types/polymorphic_polynomial_dfs.hpp
similarity index 98%
rename from libs/math/include/nil/crypto3/math/polynomial/polymorphic_polynomial_dfs.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/types/polymorphic_polynomial_dfs.hpp
index fb919eb95..2a2efd67e 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polymorphic_polynomial_dfs.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/types/polymorphic_polynomial_dfs.hpp
@@ -34,8 +34,8 @@
 #include <variant>
 #include <vector>
 
-#include "polymorphic_polynomial.hpp"
-#include "polynomial_dfs.hpp"
+#include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
+#include <nil/crypto3/math/polynomial/types/polymorphic_polynomial.hpp>
 
 #include <nil/crypto3/algebra/type_traits.hpp>
 #include <nil/crypto3/bench/scoped_profiler.hpp>
diff --git a/libs/math/include/nil/crypto3/math/polynomial/static_simd_vector.hpp b/libs/math/include/nil/crypto3/math/polynomial/types/static_simd_vector.hpp
similarity index 100%
rename from libs/math/include/nil/crypto3/math/polynomial/static_simd_vector.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/types/static_simd_vector.hpp
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_dfs_view.hpp b/libs/math/include/nil/crypto3/math/polynomial/views/polynomial_dfs_view.hpp
similarity index 99%
rename from libs/math/include/nil/crypto3/math/polynomial/polynomial_dfs_view.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/views/polynomial_dfs_view.hpp
index 0dd72dcdc..a93a3b398 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial_dfs_view.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/views/polynomial_dfs_view.hpp
@@ -30,7 +30,7 @@
 #include <algorithm>
 #include <vector>
 
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 #include <string_view>
 
 namespace nil {
diff --git a/libs/math/include/nil/crypto3/math/polynomial/polynomial_view.hpp b/libs/math/include/nil/crypto3/math/polynomial/views/polynomial_view.hpp
similarity index 99%
rename from libs/math/include/nil/crypto3/math/polynomial/polynomial_view.hpp
rename to libs/math/include/nil/crypto3/math/polynomial/views/polynomial_view.hpp
index 335106fe3..ed061e24d 100644
--- a/libs/math/include/nil/crypto3/math/polynomial/polynomial_view.hpp
+++ b/libs/math/include/nil/crypto3/math/polynomial/views/polynomial_view.hpp
@@ -30,7 +30,7 @@
 #include <algorithm>
 #include <vector>
 
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 
 namespace nil {
     namespace crypto3 {
diff --git a/libs/math/test/basic_radix2_domain.cpp b/libs/math/test/basic_radix2_domain.cpp
index 9e2f3894c..20c91cb04 100644
--- a/libs/math/test/basic_radix2_domain.cpp
+++ b/libs/math/test/basic_radix2_domain.cpp
@@ -35,7 +35,7 @@
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
-#include <nil/crypto3/math/polynomial/shift.hpp>
+#include <nil/crypto3/math/polynomial/operations/shift.hpp>
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
 #include <nil/crypto3/math/domains/detail/basic_radix2_domain_aux.hpp>
 
diff --git a/libs/math/test/bench_test/mixed_radix_benchmark.cpp b/libs/math/test/bench_test/mixed_radix_benchmark.cpp
index cb0c8977d..e6da8be90 100644
--- a/libs/math/test/bench_test/mixed_radix_benchmark.cpp
+++ b/libs/math/test/bench_test/mixed_radix_benchmark.cpp
@@ -37,8 +37,8 @@
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 #include <nil/crypto3/algebra/random_element.hpp>
 #include <nil/crypto3/math/algorithms/mixed_radix_fft.hpp>
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
-#include <nil/crypto3/math/polynomial/mixed_radix_backend.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp>
 
 namespace {
 
diff --git a/libs/math/test/complete_factorization.cpp b/libs/math/test/complete_factorization.cpp
index dee55fd9d..8ee4289e0 100644
--- a/libs/math/test/complete_factorization.cpp
+++ b/libs/math/test/complete_factorization.cpp
@@ -34,9 +34,9 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/alt_bn128.hpp>
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 
-#include <nil/crypto3/math/polynomial/complete_factorization.hpp>
-#include <nil/crypto3/math/polynomial/mixed_radix_backend.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/factorization/complete_factorization.hpp>
+#include <nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 #include <nil/crypto3/random/algebraic_engine.hpp>
 
 namespace {
diff --git a/libs/math/test/distinct_degree_factorization.cpp b/libs/math/test/distinct_degree_factorization.cpp
index e0e969ffd..8cac7e1e6 100644
--- a/libs/math/test/distinct_degree_factorization.cpp
+++ b/libs/math/test/distinct_degree_factorization.cpp
@@ -33,10 +33,10 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/alt_bn128.hpp>
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 
-#include <nil/crypto3/math/polynomial/distinct_degree_factorization.hpp>
-#include <nil/crypto3/math/polynomial/kaltofen_shoup_distinct_degree_factorization.hpp>
-#include <nil/crypto3/math/polynomial/mixed_radix_backend.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/factorization/distinct_degree_factorization.hpp>
+#include <nil/crypto3/math/polynomial/factorization/kaltofen_shoup_distinct_degree_factorization.hpp>
+#include <nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 
 namespace {
     namespace math = nil::crypto3::math;
diff --git a/libs/math/test/equal_degree_factorization.cpp b/libs/math/test/equal_degree_factorization.cpp
index bb438080f..c5d09c910 100644
--- a/libs/math/test/equal_degree_factorization.cpp
+++ b/libs/math/test/equal_degree_factorization.cpp
@@ -36,8 +36,8 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/alt_bn128.hpp>
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 
-#include <nil/crypto3/math/polynomial/equal_degree_factorization.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/factorization/equal_degree_factorization.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 #include <nil/crypto3/random/algebraic_engine.hpp>
 
 namespace {
diff --git a/libs/math/test/evaluation_domain.cpp b/libs/math/test/evaluation_domain.cpp
index 2954e6c97..353e61b72 100644
--- a/libs/math/test/evaluation_domain.cpp
+++ b/libs/math/test/evaluation_domain.cpp
@@ -67,7 +67,7 @@
 
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 
-#include <nil/crypto3/math/polynomial/evaluate.hpp>
+#include <nil/crypto3/math/polynomial/operations/evaluate.hpp>
 
 #include <typeinfo>
 
diff --git a/libs/math/test/kronecker_substitution.cpp b/libs/math/test/kronecker_substitution.cpp
index 334a0a5cd..8a021f211 100755
--- a/libs/math/test/kronecker_substitution.cpp
+++ b/libs/math/test/kronecker_substitution.cpp
@@ -35,7 +35,7 @@
 #include <nil/crypto3/algebra/fields/bls12/base_field.hpp>
 #include <nil/crypto3/algebra/fields/arithmetic_params/bls12.hpp>
 
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 #include <nil/crypto3/math/kronecker_substitution.hpp>
 
 using namespace nil::crypto3::algebra;
diff --git a/libs/math/test/lagrange_interpolation.cpp b/libs/math/test/lagrange_interpolation.cpp
index cce6c5443..f476c8740 100644
--- a/libs/math/test/lagrange_interpolation.cpp
+++ b/libs/math/test/lagrange_interpolation.cpp
@@ -35,7 +35,7 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/bls12.hpp>
 #include <nil/crypto3/algebra/random_element.hpp>
 
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 
 using namespace nil::crypto3::algebra;
 using namespace nil::crypto3::math;
diff --git a/libs/math/test/polynomial.cpp b/libs/math/test/polynomial.cpp
index a1b9d092b..039e77f8e 100644
--- a/libs/math/test/polynomial.cpp
+++ b/libs/math/test/polynomial.cpp
@@ -33,7 +33,7 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/bls12.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/shift.hpp>
+#include <nil/crypto3/math/polynomial/operations/shift.hpp>
 
 using namespace nil::crypto3::algebra;
 using namespace nil::crypto3::math;
diff --git a/libs/math/test/polynomial_algorithm_constraints.cpp b/libs/math/test/polynomial_algorithm_constraints.cpp
index 6bd54ca03..9bb0e09ef 100644
--- a/libs/math/test/polynomial_algorithm_constraints.cpp
+++ b/libs/math/test/polynomial_algorithm_constraints.cpp
@@ -28,12 +28,12 @@
 #include <vector>
 
 #include <nil/crypto3/algebra/fields/babybear/base_field.hpp>
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
-#include <nil/crypto3/math/polynomial/basis_change.hpp>
-#include <nil/crypto3/math/polynomial/evaluate.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
-#include <nil/crypto3/math/polynomial/shift.hpp>
-#include <nil/crypto3/math/polynomial/xgcd.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basis_change.hpp>
+#include <nil/crypto3/math/polynomial/operations/evaluate.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/shift.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/xgcd.hpp>
 
 namespace math = nil::crypto3::math;
 namespace fields = nil::crypto3::algebra::fields;
diff --git a/libs/math/test/polynomial_arithmetic.cpp b/libs/math/test/polynomial_arithmetic.cpp
index 59ea8f7a1..b8eeaccbd 100644
--- a/libs/math/test/polynomial_arithmetic.cpp
+++ b/libs/math/test/polynomial_arithmetic.cpp
@@ -35,8 +35,8 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/bls12.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
-#include <nil/crypto3/math/polynomial/xgcd.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/xgcd.hpp>
 
 using namespace nil::crypto3::algebra;
 using namespace nil::crypto3::math;
diff --git a/libs/math/test/polynomial_backend.cpp b/libs/math/test/polynomial_backend.cpp
index d5c01b5fe..b1de72a77 100644
--- a/libs/math/test/polynomial_backend.cpp
+++ b/libs/math/test/polynomial_backend.cpp
@@ -34,9 +34,9 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/alt_bn128.hpp>
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 
-#include <nil/crypto3/math/polynomial/mixed_radix_backend.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_backend.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/polynomial_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 
 namespace {
     namespace math = nil::crypto3::math;
diff --git a/libs/math/test/polynomial_composition.cpp b/libs/math/test/polynomial_composition.cpp
index dde6161e0..35d91af72 100644
--- a/libs/math/test/polynomial_composition.cpp
+++ b/libs/math/test/polynomial_composition.cpp
@@ -32,9 +32,9 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/alt_bn128.hpp>
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 
-#include <nil/crypto3/math/polynomial/mixed_radix_backend.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_composition.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_composition.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 
 namespace {
     namespace math = nil::crypto3::math;
diff --git a/libs/math/test/polynomial_concepts.cpp b/libs/math/test/polynomial_concepts.cpp
index 74b32855e..47d7d09ab 100644
--- a/libs/math/test/polynomial_concepts.cpp
+++ b/libs/math/test/polynomial_concepts.cpp
@@ -27,8 +27,8 @@
 
 #include <nil/crypto3/algebra/fields/babybear/base_field.hpp>
 #include <nil/crypto3/math/polynomial/concepts.hpp>
-#include <nil/crypto3/math/polynomial/polymorphic_polynomial.hpp>
-#include <nil/crypto3/math/polynomial/polymorphic_polynomial_dfs.hpp>
+#include <nil/crypto3/math/polynomial/types/polymorphic_polynomial.hpp>
+#include <nil/crypto3/math/polynomial/types/polymorphic_polynomial_dfs.hpp>
 
 namespace math = nil::crypto3::math;
 namespace fields = nil::crypto3::algebra::fields;
diff --git a/libs/math/test/polynomial_dfs.cpp b/libs/math/test/polynomial_dfs.cpp
index 3711ac551..674489888 100644
--- a/libs/math/test/polynomial_dfs.cpp
+++ b/libs/math/test/polynomial_dfs.cpp
@@ -38,7 +38,7 @@
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
-#include <nil/crypto3/math/polynomial/shift.hpp>
+#include <nil/crypto3/math/polynomial/operations/shift.hpp>
 
 using namespace nil::crypto3::algebra;
 using namespace nil::crypto3::math;
diff --git a/libs/math/test/polynomial_dfs_view.cpp b/libs/math/test/polynomial_dfs_view.cpp
index b2e22911a..d770d1915 100644
--- a/libs/math/test/polynomial_dfs_view.cpp
+++ b/libs/math/test/polynomial_dfs_view.cpp
@@ -35,7 +35,7 @@
 
 #include <nil/crypto3/algebra/fields/arithmetic_params/bls12.hpp>
 
-#include <nil/crypto3/math/polynomial/polynomial_dfs_view.hpp>
+#include <nil/crypto3/math/polynomial/views/polynomial_dfs_view.hpp>
 
 using namespace nil::crypto3::algebra;
 using namespace nil::crypto3::math;
diff --git a/libs/math/test/polynomial_division.cpp b/libs/math/test/polynomial_division.cpp
index 120e04805..709d3c1a4 100644
--- a/libs/math/test/polynomial_division.cpp
+++ b/libs/math/test/polynomial_division.cpp
@@ -33,10 +33,10 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/alt_bn128.hpp>
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 
-#include <nil/crypto3/math/polynomial/mixed_radix_backend.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_division.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_modular_arithmetic.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/polynomial_division.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_modular_arithmetic.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 
 namespace {
     namespace math = nil::crypto3::math;
diff --git a/libs/math/test/polynomial_exponentiation.cpp b/libs/math/test/polynomial_exponentiation.cpp
index f3817a710..43c77b02a 100644
--- a/libs/math/test/polynomial_exponentiation.cpp
+++ b/libs/math/test/polynomial_exponentiation.cpp
@@ -35,9 +35,9 @@
 #include <nil/crypto3/algebra/fields/field_order.hpp>
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 
-#include <nil/crypto3/math/polynomial/mixed_radix_backend.hpp>
-#include <nil/crypto3/math/polynomial/polynomial_exponentiation.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_exponentiation.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 
 namespace {
     namespace math = nil::crypto3::math;
diff --git a/libs/math/test/polynomial_frobenius.cpp b/libs/math/test/polynomial_frobenius.cpp
index 9397b8fe9..0f754f5b0 100644
--- a/libs/math/test/polynomial_frobenius.cpp
+++ b/libs/math/test/polynomial_frobenius.cpp
@@ -34,8 +34,8 @@
 #include <nil/crypto3/algebra/fields/field_order.hpp>
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 
-#include <nil/crypto3/math/polynomial/polynomial_frobenius.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_frobenius.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 
 namespace {
     namespace math = nil::crypto3::math;
diff --git a/libs/math/test/polynomial_gcd.cpp b/libs/math/test/polynomial_gcd.cpp
index 42149532d..37b895a91 100644
--- a/libs/math/test/polynomial_gcd.cpp
+++ b/libs/math/test/polynomial_gcd.cpp
@@ -35,9 +35,9 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/alt_bn128.hpp>
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 
-#include <nil/crypto3/math/polynomial/gcd.hpp>
-#include <nil/crypto3/math/polynomial/mixed_radix_backend.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/gcd.hpp>
+#include <nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 
 namespace {
     namespace math = nil::crypto3::math;
diff --git a/libs/math/test/polynomial_rational_reconstruction.cpp b/libs/math/test/polynomial_rational_reconstruction.cpp
index c9b64ab10..2dd3ec0ec 100644
--- a/libs/math/test/polynomial_rational_reconstruction.cpp
+++ b/libs/math/test/polynomial_rational_reconstruction.cpp
@@ -34,8 +34,8 @@
 #include <nil/crypto3/algebra/fields/babybear/base_field.hpp>
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 
-#include <nil/crypto3/math/polynomial/polynomial_rational_reconstruction.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/reconstruction/polynomial_rational_reconstruction.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 
 namespace {
     namespace fields = nil::crypto3::algebra::fields;
diff --git a/libs/math/test/polynomial_square_root.cpp b/libs/math/test/polynomial_square_root.cpp
index 7a48d4419..46b75752c 100644
--- a/libs/math/test/polynomial_square_root.cpp
+++ b/libs/math/test/polynomial_square_root.cpp
@@ -36,8 +36,8 @@
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 #include <nil/crypto3/algebra/random_element.hpp>
 
-#include <nil/crypto3/math/polynomial/polynomial_square_root.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/quotient_ring/polynomial_square_root.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 
 namespace {
     namespace math = nil::crypto3::math;
diff --git a/libs/math/test/polynomial_view.cpp b/libs/math/test/polynomial_view.cpp
index 019510b10..bc0d76353 100644
--- a/libs/math/test/polynomial_view.cpp
+++ b/libs/math/test/polynomial_view.cpp
@@ -34,7 +34,7 @@
 
 #include <nil/crypto3/algebra/fields/arithmetic_params/bls12.hpp>
 
-#include <nil/crypto3/math/polynomial/polynomial_view.hpp>
+#include <nil/crypto3/math/polynomial/views/polynomial_view.hpp>
 
 using namespace nil::crypto3::algebra;
 using namespace nil::crypto3::math;
diff --git a/libs/math/test/power_series.cpp b/libs/math/test/power_series.cpp
index 516da2c26..9ec77edce 100644
--- a/libs/math/test/power_series.cpp
+++ b/libs/math/test/power_series.cpp
@@ -33,9 +33,9 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/alt_bn128.hpp>
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 
-#include <nil/crypto3/math/polynomial/mixed_radix_backend.hpp>
-#include <nil/crypto3/math/polynomial/power_series.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp>
+#include <nil/crypto3/math/polynomial/arithmetic/power_series.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
 
 namespace {
     namespace math = nil::crypto3::math;
diff --git a/libs/math/test/square_free_factorization.cpp b/libs/math/test/square_free_factorization.cpp
index 0c0efbb86..a09c5c1b4 100644
--- a/libs/math/test/square_free_factorization.cpp
+++ b/libs/math/test/square_free_factorization.cpp
@@ -35,9 +35,9 @@
 #include <nil/crypto3/algebra/fields/fp12_2over3over2.hpp>
 #include <nil/crypto3/algebra/fields/params.hpp>
 
-#include <nil/crypto3/math/polynomial/mixed_radix_backend.hpp>
-#include <nil/crypto3/math/polynomial/schoolbook_backend.hpp>
-#include <nil/crypto3/math/polynomial/square_free_factorization.hpp>
+#include <nil/crypto3/math/polynomial/backends/mixed_radix_backend.hpp>
+#include <nil/crypto3/math/polynomial/backends/schoolbook_backend.hpp>
+#include <nil/crypto3/math/polynomial/factorization/square_free_factorization.hpp>
 
 namespace {
     namespace math = nil::crypto3::math;
diff --git a/libs/zk/example/fri.cpp b/libs/zk/example/fri.cpp
index 7dc74af31..17631aead 100644
--- a/libs/zk/example/fri.cpp
+++ b/libs/zk/example/fri.cpp
@@ -31,7 +31,7 @@
 #include <nil/crypto3/algebra/random_element.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
diff --git a/libs/zk/include/nil/crypto3/zk/commitments/batched_commitment.hpp b/libs/zk/include/nil/crypto3/zk/commitments/batched_commitment.hpp
index 37b4f87e0..193dbad77 100644
--- a/libs/zk/include/nil/crypto3/zk/commitments/batched_commitment.hpp
+++ b/libs/zk/include/nil/crypto3/zk/commitments/batched_commitment.hpp
@@ -37,7 +37,7 @@
 #include <boost/property_tree/json_parser.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 
 #include <nil/crypto3/zk/transcript/fiat_shamir.hpp>
 #include <nil/crypto3/zk/commitments/type_traits.hpp>
diff --git a/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_batched_fri_compile_time_size.hpp b/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_batched_fri_compile_time_size.hpp
index 8a20a31d4..313fcbe69 100644
--- a/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_batched_fri_compile_time_size.hpp
+++ b/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_batched_fri_compile_time_size.hpp
@@ -30,7 +30,7 @@
 #include <nil/crypto3/marshalling/algebra/types/field_element.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 
diff --git a/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_batched_fri_runtime_size.hpp b/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_batched_fri_runtime_size.hpp
index a642c4447..fa386a47f 100644
--- a/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_batched_fri_runtime_size.hpp
+++ b/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_batched_fri_runtime_size.hpp
@@ -30,7 +30,7 @@
 #include <nil/crypto3/marshalling/algebra/types/field_element.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 
diff --git a/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_fri.hpp b/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_fri.hpp
index acd97a7c9..a455a2ecd 100644
--- a/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_fri.hpp
+++ b/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/basic_fri.hpp
@@ -41,9 +41,9 @@
 #include <nil/crypto3/math/algorithms/calculate_domain_set.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/polynomial/concepts.hpp>
-#include <nil/crypto3/math/polynomial/polymorphic_polynomial_dfs.hpp>
+#include <nil/crypto3/math/polynomial/types/polymorphic_polynomial_dfs.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
 
diff --git a/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/fold_polynomial.hpp b/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/fold_polynomial.hpp
index c1d836c9f..7cb98c85a 100644
--- a/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/fold_polynomial.hpp
+++ b/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/fold_polynomial.hpp
@@ -31,8 +31,8 @@
 
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
-#include <nil/crypto3/math/polynomial/polymorphic_polynomial_dfs.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/types/polymorphic_polynomial_dfs.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
 
diff --git a/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/powers_of_tau/result.hpp b/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/powers_of_tau/result.hpp
index 322514094..67f78c2c6 100644
--- a/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/powers_of_tau/result.hpp
+++ b/libs/zk/include/nil/crypto3/zk/commitments/detail/polynomial/powers_of_tau/result.hpp
@@ -29,7 +29,7 @@
 
 #include <nil/crypto3/zk/commitments/detail/polynomial/powers_of_tau/accumulator.hpp>
 
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 
 namespace nil {
diff --git a/libs/zk/include/nil/crypto3/zk/commitments/polynomial/fri.hpp b/libs/zk/include/nil/crypto3/zk/commitments/polynomial/fri.hpp
index 3b6709f45..6f71a42b5 100644
--- a/libs/zk/include/nil/crypto3/zk/commitments/polynomial/fri.hpp
+++ b/libs/zk/include/nil/crypto3/zk/commitments/polynomial/fri.hpp
@@ -34,7 +34,7 @@
 
 #include <nil/crypto3/math/polynomial/concepts.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 
 #include <nil/crypto3/container/merkle/tree.hpp>
 #include <nil/crypto3/container/merkle/proof.hpp>
diff --git a/libs/zk/include/nil/crypto3/zk/commitments/polynomial/kzg.hpp b/libs/zk/include/nil/crypto3/zk/commitments/polynomial/kzg.hpp
index 81e9d40dc..b004c9223 100644
--- a/libs/zk/include/nil/crypto3/zk/commitments/polynomial/kzg.hpp
+++ b/libs/zk/include/nil/crypto3/zk/commitments/polynomial/kzg.hpp
@@ -40,7 +40,7 @@
 #include <boost/accumulators/accumulators.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/algebra/type_traits.hpp>
 #include <nil/crypto3/algebra/algorithms/pair.hpp>
 #include <nil/crypto3/algebra/multiexp/multiexp.hpp>
diff --git a/libs/zk/include/nil/crypto3/zk/commitments/polynomial/kzg_v2.hpp b/libs/zk/include/nil/crypto3/zk/commitments/polynomial/kzg_v2.hpp
index 9cd4770f1..abced9602 100644
--- a/libs/zk/include/nil/crypto3/zk/commitments/polynomial/kzg_v2.hpp
+++ b/libs/zk/include/nil/crypto3/zk/commitments/polynomial/kzg_v2.hpp
@@ -40,7 +40,7 @@
 #include <boost/accumulators/accumulators.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/algebra/type_traits.hpp>
 #include <nil/crypto3/algebra/algorithms/pair.hpp>
 #include <nil/crypto3/algebra/multiexp/multiexp.hpp>
diff --git a/libs/zk/include/nil/crypto3/zk/commitments/polynomial/lpc.hpp b/libs/zk/include/nil/crypto3/zk/commitments/polynomial/lpc.hpp
index a6ff11ebd..eb9c05889 100644
--- a/libs/zk/include/nil/crypto3/zk/commitments/polynomial/lpc.hpp
+++ b/libs/zk/include/nil/crypto3/zk/commitments/polynomial/lpc.hpp
@@ -33,14 +33,14 @@
 #include <queue>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 
 #include <nil/crypto3/container/merkle/tree.hpp>
 #include <nil/crypto3/container/merkle/proof.hpp>
 
 #include <nil/crypto3/zk/commitments/batched_commitment.hpp>
 #include <nil/crypto3/zk/commitments/detail/polynomial/basic_fri.hpp>
-#include <nil/crypto3/math/polynomial/polymorphic_polynomial_dfs.hpp>
+#include <nil/crypto3/math/polynomial/types/polymorphic_polynomial_dfs.hpp>
 
 namespace nil {
     namespace crypto3 {
diff --git a/libs/zk/include/nil/crypto3/zk/math/centralized_expression_evaluator.hpp b/libs/zk/include/nil/crypto3/zk/math/centralized_expression_evaluator.hpp
index 234a0770d..3f8466473 100644
--- a/libs/zk/include/nil/crypto3/zk/math/centralized_expression_evaluator.hpp
+++ b/libs/zk/include/nil/crypto3/zk/math/centralized_expression_evaluator.hpp
@@ -33,7 +33,7 @@
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
-#include <nil/crypto3/math/polynomial/shift.hpp>
+#include <nil/crypto3/math/polynomial/operations/shift.hpp>
 
 #include <nil/crypto3/zk/math/cached_assignment_table.hpp>
 #include <nil/crypto3/zk/math/expression.hpp>
diff --git a/libs/zk/include/nil/crypto3/zk/math/dag_expression_evaluator.hpp b/libs/zk/include/nil/crypto3/zk/math/dag_expression_evaluator.hpp
index a85677bb6..9e852edb0 100644
--- a/libs/zk/include/nil/crypto3/zk/math/dag_expression_evaluator.hpp
+++ b/libs/zk/include/nil/crypto3/zk/math/dag_expression_evaluator.hpp
@@ -34,7 +34,7 @@
 #include <boost/bimap/unordered_set_of.hpp>
 #include <boost/container/small_vector.hpp>
 
-#include <nil/crypto3/math/polynomial/static_simd_vector.hpp>
+#include <nil/crypto3/math/polynomial/types/static_simd_vector.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
 
 #include <nil/crypto3/zk/math/expression.hpp>
diff --git a/libs/zk/include/nil/crypto3/zk/snark/arithmetization/plonk/assignment.hpp b/libs/zk/include/nil/crypto3/zk/snark/arithmetization/plonk/assignment.hpp
index 38a7a75ed..dde20db1d 100644
--- a/libs/zk/include/nil/crypto3/zk/snark/arithmetization/plonk/assignment.hpp
+++ b/libs/zk/include/nil/crypto3/zk/snark/arithmetization/plonk/assignment.hpp
@@ -32,7 +32,7 @@
 #include <memory>
 #include <nil/crypto3/zk/snark/arithmetization/plonk/padding.hpp>
 #include <nil/crypto3/random/algebraic_engine.hpp>
-#include <nil/crypto3/math/polynomial/shift.hpp>
+#include <nil/crypto3/math/polynomial/operations/shift.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
 #include <nil/crypto3/zk/snark/arithmetization/plonk/variable.hpp>
 #include <nil/crypto3/zk/snark/arithmetization/plonk/table_description.hpp>
diff --git a/libs/zk/include/nil/crypto3/zk/snark/arithmetization/plonk/constraint.hpp b/libs/zk/include/nil/crypto3/zk/snark/arithmetization/plonk/constraint.hpp
index 1f3cde1c1..49d7243e1 100644
--- a/libs/zk/include/nil/crypto3/zk/snark/arithmetization/plonk/constraint.hpp
+++ b/libs/zk/include/nil/crypto3/zk/snark/arithmetization/plonk/constraint.hpp
@@ -28,7 +28,7 @@
 #define CRYPTO3_ZK_PLONK_CONSTRAINT_HPP
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/shift.hpp>
+#include <nil/crypto3/math/polynomial/operations/shift.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 
 #include <nil/crypto3/zk/snark/arithmetization/plonk/variable.hpp>
diff --git a/libs/zk/include/nil/crypto3/zk/snark/systems/plonk/placeholder/lookup_argument.hpp b/libs/zk/include/nil/crypto3/zk/snark/systems/plonk/placeholder/lookup_argument.hpp
index 881fc519e..d34887615 100644
--- a/libs/zk/include/nil/crypto3/zk/snark/systems/plonk/placeholder/lookup_argument.hpp
+++ b/libs/zk/include/nil/crypto3/zk/snark/systems/plonk/placeholder/lookup_argument.hpp
@@ -39,8 +39,8 @@
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/shift.hpp>
-#include <nil/crypto3/math/polynomial/static_simd_vector.hpp>
+#include <nil/crypto3/math/polynomial/operations/shift.hpp>
+#include <nil/crypto3/math/polynomial/types/static_simd_vector.hpp>
 
 #include <nil/crypto3/hash/sha2.hpp>
 
diff --git a/libs/zk/include/nil/crypto3/zk/snark/systems/plonk/placeholder/permutation_argument.hpp b/libs/zk/include/nil/crypto3/zk/snark/systems/plonk/placeholder/permutation_argument.hpp
index 555f4493e..e5dc97cf9 100644
--- a/libs/zk/include/nil/crypto3/zk/snark/systems/plonk/placeholder/permutation_argument.hpp
+++ b/libs/zk/include/nil/crypto3/zk/snark/systems/plonk/placeholder/permutation_argument.hpp
@@ -32,7 +32,7 @@
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
-#include <nil/crypto3/math/polynomial/shift.hpp>
+#include <nil/crypto3/math/polynomial/operations/shift.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
 
diff --git a/libs/zk/include/nil/crypto3/zk/snark/systems/ppzksnark/r1cs_gg_ppzksnark/ipp2/prover.hpp b/libs/zk/include/nil/crypto3/zk/snark/systems/ppzksnark/r1cs_gg_ppzksnark/ipp2/prover.hpp
index 0987f8232..61543fbe6 100644
--- a/libs/zk/include/nil/crypto3/zk/snark/systems/ppzksnark/r1cs_gg_ppzksnark/ipp2/prover.hpp
+++ b/libs/zk/include/nil/crypto3/zk/snark/systems/ppzksnark/r1cs_gg_ppzksnark/ipp2/prover.hpp
@@ -38,7 +38,7 @@
 #include <nil/crypto3/hash/sha2.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/basic_operations.hpp>
+#include <nil/crypto3/math/polynomial/operations/basic_operations.hpp>
 
 #include <nil/crypto3/algebra/multiexp/multiexp.hpp>
 #include <nil/crypto3/algebra/multiexp/policies.hpp>
diff --git a/libs/zk/test/commitment/fold_polynomial.cpp b/libs/zk/test/commitment/fold_polynomial.cpp
index 89ba489a2..d572627bd 100644
--- a/libs/zk/test/commitment/fold_polynomial.cpp
+++ b/libs/zk/test/commitment/fold_polynomial.cpp
@@ -40,7 +40,7 @@
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
 #include <nil/crypto3/math/polynomial/polynomial_dfs.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/calculate_domain_set.hpp>
 
 #include <nil/crypto3/zk/commitments/detail/polynomial/fold_polynomial.hpp>
diff --git a/libs/zk/test/commitment/fri.cpp b/libs/zk/test/commitment/fri.cpp
index 4db5127ea..3710d153a 100644
--- a/libs/zk/test/commitment/fri.cpp
+++ b/libs/zk/test/commitment/fri.cpp
@@ -40,7 +40,7 @@
 #include <nil/crypto3/algebra/random_element.hpp>
 
 #include <nil/crypto3/math/polynomial/polynomial.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
 #include <nil/crypto3/math/domains/evaluation_domain.hpp>
 #include <nil/crypto3/math/algorithms/make_evaluation_domain.hpp>
diff --git a/libs/zk/test/systems/plonk/placeholder/placeholder_lookup_argument.cpp b/libs/zk/test/systems/plonk/placeholder/placeholder_lookup_argument.cpp
index d75fa130a..78fb5a50d 100644
--- a/libs/zk/test/systems/plonk/placeholder/placeholder_lookup_argument.cpp
+++ b/libs/zk/test/systems/plonk/placeholder/placeholder_lookup_argument.cpp
@@ -39,7 +39,7 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/pallas.hpp>
 
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/calculate_domain_set.hpp>
 
 #include <nil/crypto3/hash/algorithm/hash.hpp>
diff --git a/libs/zk/test/systems/plonk/placeholder/placeholder_permutation_argument.cpp b/libs/zk/test/systems/plonk/placeholder/placeholder_permutation_argument.cpp
index 6e51b26ae..4427da632 100644
--- a/libs/zk/test/systems/plonk/placeholder/placeholder_permutation_argument.cpp
+++ b/libs/zk/test/systems/plonk/placeholder/placeholder_permutation_argument.cpp
@@ -41,7 +41,7 @@
 #include <nil/crypto3/algebra/fields/arithmetic_params/bls12.hpp>
 
 #include <nil/crypto3/math/algorithms/unity_root.hpp>
-#include <nil/crypto3/math/polynomial/lagrange_interpolation.hpp>
+#include <nil/crypto3/math/polynomial/operations/lagrange_interpolation.hpp>
 #include <nil/crypto3/math/algorithms/calculate_domain_set.hpp>
 
 #include <nil/crypto3/hash/algorithm/hash.hpp>