diff --git a/heu/library/algorithms/paillier_zahlen/public_key.h b/heu/library/algorithms/paillier_zahlen/public_key.h
index 0b936e2..dd6a01e 100644
--- a/heu/library/algorithms/paillier_zahlen/public_key.h
+++ b/heu/library/algorithms/paillier_zahlen/public_key.h
@@ -11,84 +11,66 @@
 // WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 // See the License for the specific language governing permissions and
 // limitations under the License.
-
 #pragma once
-
 #include "heu/library/algorithms/util/he_object.h"
 #include "heu/library/algorithms/util/mp_int.h"
-
 namespace heu::lib::algorithms::paillier_z {
 // The density parameter of each participant can be different, so density is
 // a local configuration and will not be automatically passed to other parties
 // through the protocol
 void SetCacheTableDensity(size_t density);
-
 class PublicKey : public HeObject<PublicKey> {
-  public:
-    MPInt n_; // public modulus n = p * q
-    MPInt n_square_; // n_ * n_
-    MPInt n_half_; // n_ / 2
-    MPInt h_s_; // h^n mod n^2
-
-    size_t key_size_;
-
-    std::shared_ptr<MontgomerySpace> m_space_; // m-space for mod n^2
-    std::shared_ptr<BaseTable> hs_table_; // h_s_ table mod n^2
-
-    // Init pk based on n_
-    void Init();
-    [[nodiscard]] std::string ToString() const override;
-
-    bool operator==(const PublicKey &other) const {
-      return n_ == other.n_ && h_s_ == other.h_s_;
-    }
-
-    bool operator!=(const PublicKey &other) const {
-      return !this->operator==(other);
-    }
-
-    // Valid plaintext range: [n_half_, -n_half]
-    [[nodiscard]] inline const MPInt &PlaintextBound() const & { return n_half_; }
+ public:
+  MPInt n_;         // public modulus n = p * q
+  MPInt n_square_;  // n_ * n_
+  MPInt n_half_;    // n_ / 2
+  MPInt h_s_;       // h^n mod n^2
+  size_t key_size_;
+  std::shared_ptr<MontgomerySpace> m_space_;  // m-space for mod n^2
+  std::shared_ptr<BaseTable> hs_table_;       // h_s_ table mod n^2
+  // Init pk based on n_
+  void Init();
+  [[nodiscard]] std::string ToString() const override;
+  bool operator==(const PublicKey &other) const {
+    return n_ == other.n_ && h_s_ == other.h_s_;
+  }
+  bool operator!=(const PublicKey &other) const {
+    return !this->operator==(other);
+  }
+  // Valid plaintext range: [n_half_, -n_half]
+  [[nodiscard]] inline const MPInt &PlaintextBound() const & { return n_half_; }
 };
-} // namespace heu::lib::algorithms::paillier_z
-
+}  // namespace heu::lib::algorithms::paillier_z
 // clang-format off
 namespace msgpack {
-MSGPACK_API_VERSION_NAMESPACE (MSGPACK_DEFAULT_API_NS) {
+MSGPACK_API_VERSION_NAMESPACE(MSGPACK_DEFAULT_API_NS) {
 namespace adaptor {
-    template
-    <
-    >
-    struct pack<heu::lib::algorithms::paillier_z::PublicKey> {
-      template<typename Stream>
-      packer<Stream> &operator()(msgpack::packer<Stream> &o,
-                                 const heu::lib::algorithms::paillier_z::PublicKey &pk) const {
-        // packing member variables as an array.
-        o.pack_array(2);
-        o.pack(pk.n_);
-        o.pack(pk.h_s_);
-        return o;
-      }
-    };
-
-    template
-    <
-    >
-    struct convert<heu::lib::algorithms::paillier_z::PublicKey> {
-      msgpack::object const &operator()(const msgpack::object &object,
-                                        heu::lib::algorithms::paillier_z::PublicKey &pk) const {
-        if (object.type != msgpack::type::ARRAY) { throw msgpack::type_error(); }
-        if (object.via.array.size != 2) { throw msgpack::type_error(); }
-
-        // The order here corresponds to the packer above
-        pk.n_ = object.via.array.ptr[0].as<heu::lib::algorithms::MPInt>();
-        pk.h_s_ = object.via.array.ptr[1].as<heu::lib::algorithms::MPInt>();
-        pk.Init();
-        return object;
-      }
-    };
-  } // namespace adaptor
-} // namespace msgpack
-} // namespace msgpack
-
+template<>
+struct pack<heu::lib::algorithms::paillier_z::PublicKey> {
+  template<typename Stream>
+  packer<Stream> &operator()(msgpack::packer<Stream> &o,
+      const heu::lib::algorithms::paillier_z::PublicKey &pk) const {
+    // packing member variables as an array.
+    o.pack_array(2);
+    o.pack(pk.n_);
+    o.pack(pk.h_s_);
+    return o;
+  }
+};
+template<>
+struct convert<heu::lib::algorithms::paillier_z::PublicKey> {
+  msgpack::object const &operator()(const msgpack::object &object,
+      heu::lib::algorithms::paillier_z::PublicKey &pk) const {
+    if (object.type != msgpack::type::ARRAY) { throw msgpack::type_error(); }
+    if (object.via.array.size != 2) { throw msgpack::type_error(); }
+    // The order here corresponds to the packer above
+    pk.n_ = object.via.array.ptr[0].as<heu::lib::algorithms::MPInt>();
+    pk.h_s_ = object.via.array.ptr[1].as<heu::lib::algorithms::MPInt>();
+    pk.Init();
+    return object;
+  }
+};
+}  // namespace adaptor
+}  // namespace msgpack
+}  // namespace msgpack
 // clang-format on