diff --git a/BGL/include/CGAL/boost/graph/parameters_interface.h b/BGL/include/CGAL/boost/graph/parameters_interface.h
index 780fc10cb0a..92d8d87f6e3 100644
--- a/BGL/include/CGAL/boost/graph/parameters_interface.h
+++ b/BGL/include/CGAL/boost/graph/parameters_interface.h
@@ -128,6 +128,7 @@ CGAL_add_named_parameter(match_faces_t, match_faces, match_faces)
 CGAL_add_named_parameter(face_epsilon_map_t, face_epsilon_map, face_epsilon_map)
 CGAL_add_named_parameter(maximum_number_t, maximum_number, maximum_number)
 CGAL_add_named_parameter(use_one_sided_hausdorff_t, use_one_sided_hausdorff, use_one_sided_hausdorff)
+CGAL_add_named_parameter(random_generator_f, random_generator, random_generator)
 
 // List of named parameters that we use in the package 'Surface Mesh Simplification'
 CGAL_add_named_parameter(get_cost_policy_t, get_cost_policy, get_cost)
diff --git a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
index 4b5a96c9669..cb9df43f839 100644
--- a/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
+++ b/Polygon_mesh_processing/include/CGAL/Polygon_mesh_processing/distance.h
@@ -438,6 +438,7 @@ struct Triangle_structure_sampler_for_triangle_mesh
   Vpm pmap;
   double min_sq_edge_length;
   const Mesh& tm;
+  CGAL::Random rnd;
 
   Triangle_structure_sampler_for_triangle_mesh(const Mesh& m,
                                                PointOutputIterator& out,
@@ -449,6 +450,8 @@ struct Triangle_structure_sampler_for_triangle_mesh
 
     pmap = choose_parameter(get_parameter(np, internal_np::vertex_point),
                             get_const_property_map(vertex_point, tm));
+    rnd = choose_parameter(get_parameter(np, internal_np::random_generator),
+                           get_default_random());
     min_sq_edge_length = (std::numeric_limits<double>::max)();
   }
 
@@ -549,7 +552,7 @@ struct Triangle_structure_sampler_for_triangle_mesh
 
   Randomizer get_randomizer()
   {
-    return Randomizer(tm, pmap);
+    return Randomizer(tm, pmap, rnd);
   }
 
   void internal_sample_triangles(double grid_spacing_, bool smpl_fcs, bool smpl_dgs)
@@ -609,6 +612,7 @@ struct Triangle_structure_sampler_for_triangle_soup
   double min_sq_edge_length;
   const PointRange& points;
   const TriangleRange& triangles;
+  Random rnd;
 
   Triangle_structure_sampler_for_triangle_soup(const PointRange& pts,
                                                const TriangleRange& trs,
@@ -616,7 +620,12 @@ struct Triangle_structure_sampler_for_triangle_soup
                                                const NamedParameters& np)
     : Base(out, np), points(pts), triangles(trs)
   {
+    using parameters::choose_parameter;
+    using parameters::get_parameter;
+
     min_sq_edge_length = (std::numeric_limits<double>::max)();
+    rnd = choose_parameter(get_parameter(np, internal_np::random_generator),
+                           get_default_random());
   }
 
   std::pair<TriangleIterator, TriangleIterator> get_range()
@@ -681,7 +690,7 @@ struct Triangle_structure_sampler_for_triangle_soup
 
   Randomizer get_randomizer()
   {
-    return Randomizer(triangles, points);
+    return Randomizer(triangles, points, rnd);
   }
 
   void internal_sample_triangles(double distance, bool, bool)
@@ -737,6 +746,12 @@ struct Triangle_structure_sampler_for_triangle_soup
  *     \cgalParamExtra{The geometric traits class must be compatible with the vertex point type.}
  *   \cgalParamNEnd
  *
+ *   \cgalParamNBegin{random_generator}
+ *     \cgalParamDescription{An instance of `CGAL::Random` used for generating random numbers.}
+ *     \cgalParamType{`CGAL::Random`}
+ *     \cgalParamType{`CGAL::get_default_random()`}
+ *   \cgalParamNEnd
+ *
  *   \cgalParamNBegin{use_random_uniform_sampling}
  *     \cgalParamDescription{If `true` is passed, points are generated in a random and uniform way
  *                           on the surface of `tm`, and/or on edges of `tm`.}
@@ -896,6 +911,12 @@ sample_triangle_mesh(const TriangleMesh& tm,
  *     \cgalParamExtra{The geometric traits class must be compatible with the point range's point type.}
  *   \cgalParamNEnd
  *
+ *   \cgalParamNBegin{random_generator}
+ *     \cgalParamDescription{An instance of `CGAL::Random` used for generating random numbers.}
+ *     \cgalParamType{`CGAL::Random`}
+ *     \cgalParamType{`CGAL::get_default_random()`}
+ *   \cgalParamNEnd
+ *
  *   \cgalParamNBegin{use_random_uniform_sampling}
  *     \cgalParamDescription{If `true` is passed, points are generated in a random and uniform way
  *                           over the triangles of the soup.}