diff --git a/rest_framework/pagination.py b/rest_framework/pagination.py
index 5938063af..2fd375500 100644
--- a/rest_framework/pagination.py
+++ b/rest_framework/pagination.py
@@ -503,15 +503,10 @@ class CursorPagination(BasePagination):
         self.base_url = request.build_absolute_uri()
         self.ordering = self.get_ordering(request, queryset, view)
 
-        # Determine if we have a cursor, and if so then decode it.
-        encoded = request.query_params.get(self.cursor_query_param)
-        if encoded is None:
-            self.cursor = None
+        self.cursor = self.decode_cursor(request)
+        if self.cursor is None:
             (offset, reverse, current_position) = (0, False, None)
         else:
-            self.cursor = _decode_cursor(encoded)
-            if self.cursor is None:
-                raise NotFound(self.invalid_cursor_message)
             (offset, reverse, current_position) = self.cursor
 
         # Cursor pagination always enforces an ordering.
@@ -623,8 +618,7 @@ class CursorPagination(BasePagination):
                 position = self.previous_position
 
         cursor = Cursor(offset=offset, reverse=False, position=position)
-        encoded = _encode_cursor(cursor)
-        return replace_query_param(self.base_url, self.cursor_query_param, encoded)
+        return self.encode_cursor(cursor)
 
     def get_previous_link(self):
         if not self.has_previous:
@@ -672,8 +666,7 @@ class CursorPagination(BasePagination):
                 position = self.next_position
 
         cursor = Cursor(offset=offset, reverse=True, position=position)
-        encoded = _encode_cursor(cursor)
-        return replace_query_param(self.base_url, self.cursor_query_param, encoded)
+        return self.encode_cursor(cursor)
 
     def get_ordering(self, request, queryset, view):
         """
@@ -715,6 +708,19 @@ class CursorPagination(BasePagination):
             return (ordering,)
         return tuple(ordering)
 
+    def decode_cursor(self, request):
+        # Determine if we have a cursor, and if so then decode it.
+        encoded = request.query_params.get(self.cursor_query_param)
+        if encoded is not None:
+            cursor = _decode_cursor(encoded)
+            if cursor is None:
+                raise NotFound(self.invalid_cursor_message)
+            return cursor
+
+    def encode_cursor(self, cursor):
+        encoded = _encode_cursor(cursor)
+        return replace_query_param(self.base_url, self.cursor_query_param, encoded)
+
     def _get_position_from_instance(self, instance, ordering):
         attr = getattr(instance, ordering[0].lstrip('-'))
         return six.text_type(attr)