step 5 : add public key, login try using public and failed

pubspec.yaml

@@ -46,6 +46,8 @@ dependencies:
   flutter_map: ^6.1.0
   latlong2: ^0.9.0
   google_sign_in: ^6.1.6
+  crypton: ^2.2.1
+  path_provider: ^2.0.2
 
 dev_dependencies:
   flutter_test:
@@ -72,6 +74,7 @@ flutter:
   # To add assets to your application, add an assets section, like this:
   assets:
     - images/
+    - publickey/
   #   - images/a_dot_ham.jpeg
 
   # An image asset can refer to one or more resolution-specific "variants", see