WIP: event signature validation

lib/nostrex/events/event.ex

@@ -6,6 +6,7 @@ defmodule Nostrex.Events.Event do
   use Ecto.Schema
   import Ecto.Changeset
   alias Nostrex.Events.Tag
+  alias Bitcoinex.Secp256k1.{Point, Signature, Schnorr, PrivateKey}
 
   @primary_key {:id, :string, autogenerate: false}
   # @primary_key false
@@ -86,8 +87,7 @@ defmodule Nostrex.Events.Event do
       event.pubkey,
       event.created_at,
       event.kind,
-      # TODO: add tag functionality next
-      [],
+      event.tags,
       event.content
     ])
   end
@@ -98,18 +98,66 @@ defmodule Nostrex.Events.Event do
   """
   def calculate_id(event) do
     {:ok, serialized_event} = serialize(event)
-
-    :crypto.hash(:sha256, serialized_event)
+    serialized_event
+    |> Bitcoinex.Utils.sha256()
     |> Base.encode16(case: :lower)
   end
 
-  # TODO
-  # defp validate(event) do
-  # validate event ID
-  # validate signature
-  # end
+  def validate(%__MODULE__{pubkey: pubkey, id: id, sig: signature} = event) do
+    # validate event ID
+    if id != calculate_id(event) do
+      {:error, "incorrect event id"}
+    else
+      # validate signature
+      validate_signature(pubkey, id, signature)
+    end
+  end
 
-  # TODO
-  # defp validate_signature(pubkey, event_id, sig) do
-  # end
+  defp validate_signature(pubkey, event_id, signature) do
+    {:ok, pk} = Point.lift_x(pubkey)
+    {:ok, sig} = Signature.parse_signature(signature)
+
+    z =
+      event_id
+      |> Base.decode16!(case: :lower)
+      |> :binary.decode_unsigned()
+
+    case {pk, sig} do
+      {{:error, msg}, _} ->
+        {:error, "failed to read event pubkey: #{msg}"}
+
+      {_, {:error, msg}} ->
+        {:error, "failed to read event signature: #{msg}"}
+
+      {%Point{} = pk, %Signature{} = sig} ->
+        Schnorr.verify_signature(pk, z, sig)
+    end
+  end
+
+  def sign(%__MODULE__{} = event, %PrivateKey{} = sk) do
+    id = calculate_id(event)
+    z =
+      id
+      |> Base.decode16!(case: :lower)
+      |> :binary.decode_unsigned()
+
+    aux = get_rand_uint(32)
+
+    {:ok, signature} = Schnorr.sign(sk, z, aux)
+    sig = serialize_signature(signature)
+
+    %__MODULE__{event | id: id, sig: sig}
+  end
+
+  defp get_rand_uint(len) do
+    len
+    |> :crypto.strong_rand_bytes()
+    |> :binary.decode_unsigned()
+  end
+
+  defp serialize_signature(%Signature{} = sig) do
+    sig
+    |> Signature.serialize_signature()
+    |> Base.encode16(case: :lower)
+  end
 end

lib/nostrex/events/events.ex

@@ -5,6 +5,7 @@ defmodule Nostrex.Events do
 
   alias Nostrex.Repo
   alias Nostrex.Events.{Event, Filter}
+  alias Bitcoinex.Secp256k1.PrivateKey
   import Ecto.Changeset
   import Ecto.Query
   alias Phoenix.PubSub
@@ -16,6 +17,17 @@ defmodule Nostrex.Events do
     |> Repo.insert()
   end
 
+  @doc """
+  Only to be used for testing purposes. This makes it easy to test
+  serialization, signature verification, and signing
+  """
+  def create_and_sign_event(params, %PrivateKey{} = sk) do
+    %Event{}
+    |> Event.test_only_changeset_no_validation( params)
+    |> Event.sign(e, sk)
+    |> Repo.insert()
+  end
+
   @doc """
   Only to be used for testing purposes. This makes it easy to test
   filter logic with simple, human readable identifiers

mix.exs

@@ -48,7 +48,8 @@ defmodule Nostrex.MixProject do
       {:gettext, "~> 0.18"},
       {:jason, "~> 1.2"},
       {:plug_cowboy, "~> 2.5"},
-      {:credo, "~> 1.6", only: [:dev, :test], runtime: false}
+      {:credo, "~> 1.6", only: [:dev, :test], runtime: false},
+      {:bitcoinex, "~> 0.1.7"}
     ]
   end
 

mix.lock

@@ -1,6 +1,9 @@
 %{
+  "bitcoinex": {:hex, :bitcoinex, "0.1.7", "2357049df10ba79e701138481692326863553476fd902c1c5a6e918d7f93b721", [:mix], [{:decimal, "~> 1.0 or ~> 2.0", [hex: :decimal, repo: "hexpm", optional: false]}, {:timex, "~> 3.1", [hex: :timex, repo: "hexpm", optional: false]}], "hexpm", "06f2d2c84b98ada2cf87106e54b7cc309497281f2bbf601e86b8528cfbd6e9fd"},
   "bunt": {:hex, :bunt, "0.2.1", "e2d4792f7bc0ced7583ab54922808919518d0e57ee162901a16a1b6664ef3b14", [:mix], [], "hexpm", "a330bfb4245239787b15005e66ae6845c9cd524a288f0d141c148b02603777a5"},
   "castore": {:hex, :castore, "0.1.20", "62a0126cbb7cb3e259257827b9190f88316eb7aa3fdac01fd6f2dfd64e7f46e9", [:mix], [], "hexpm", "a020b7650529c986c454a4035b6b13a328e288466986307bea3aadb4c95ac98a"},
+  "certifi": {:hex, :certifi, "2.9.0", "6f2a475689dd47f19fb74334859d460a2dc4e3252a3324bd2111b8f0429e7e21", [:rebar3], [], "hexpm", "266da46bdb06d6c6d35fde799bcb28d36d985d424ad7c08b5bb48f5b5cdd4641"},
+  "combine": {:hex, :combine, "0.10.0", "eff8224eeb56498a2af13011d142c5e7997a80c8f5b97c499f84c841032e429f", [:mix], [], "hexpm", "1b1dbc1790073076580d0d1d64e42eae2366583e7aecd455d1215b0d16f2451b"},
   "connection": {:hex, :connection, "1.1.0", "ff2a49c4b75b6fb3e674bfc5536451607270aac754ffd1bdfe175abe4a6d7a68", [:mix], [], "hexpm", "722c1eb0a418fbe91ba7bd59a47e28008a189d47e37e0e7bb85585a016b2869c"},
   "cowboy": {:hex, :cowboy, "2.9.0", "865dd8b6607e14cf03282e10e934023a1bd8be6f6bacf921a7e2a96d800cd452", [:make, :rebar3], [{:cowlib, "2.11.0", [hex: :cowlib, repo: "hexpm", optional: false]}, {:ranch, "1.8.0", [hex: :ranch, repo: "hexpm", optional: false]}], "hexpm", "2c729f934b4e1aa149aff882f57c6372c15399a20d54f65c8d67bef583021bde"},
   "cowboy_telemetry": {:hex, :cowboy_telemetry, "0.4.0", "f239f68b588efa7707abce16a84d0d2acf3a0f50571f8bb7f56a15865aae820c", [:rebar3], [{:cowboy, "~> 2.7", [hex: :cowboy, repo: "hexpm", optional: false]}, {:telemetry, "~> 1.0", [hex: :telemetry, repo: "hexpm", optional: false]}], "hexpm", "7d98bac1ee4565d31b62d59f8823dfd8356a169e7fcbb83831b8a5397404c9de"},
@@ -14,12 +17,17 @@
   "file_system": {:hex, :file_system, "0.2.10", "fb082005a9cd1711c05b5248710f8826b02d7d1784e7c3451f9c1231d4fc162d", [:mix], [], "hexpm", "41195edbfb562a593726eda3b3e8b103a309b733ad25f3d642ba49696bf715dc"},
   "floki": {:hex, :floki, "0.34.0", "002d0cc194b48794d74711731db004fafeb328fe676976f160685262d43706a8", [:mix], [], "hexpm", "9c3a9f43f40dde00332a589bd9d389b90c1f518aef500364d00636acc5ebc99c"},
   "gettext": {:hex, :gettext, "0.20.0", "75ad71de05f2ef56991dbae224d35c68b098dd0e26918def5bb45591d5c8d429", [:mix], [], "hexpm", "1c03b177435e93a47441d7f681a7040bd2a816ece9e2666d1c9001035121eb3d"},
+  "hackney": {:hex, :hackney, "1.18.1", "f48bf88f521f2a229fc7bae88cf4f85adc9cd9bcf23b5dc8eb6a1788c662c4f6", [:rebar3], [{:certifi, "~> 2.9.0", [hex: :certifi, repo: "hexpm", optional: false]}, {:idna, "~> 6.1.0", [hex: :idna, repo: "hexpm", optional: false]}, {:metrics, "~> 1.0.0", [hex: :metrics, repo: "hexpm", optional: false]}, {:mimerl, "~> 1.1", [hex: :mimerl, repo: "hexpm", optional: false]}, {:parse_trans, "3.3.1", [hex: :parse_trans, repo: "hexpm", optional: false]}, {:ssl_verify_fun, "~> 1.1.0", [hex: :ssl_verify_fun, repo: "hexpm", optional: false]}, {:unicode_util_compat, "~> 0.7.0", [hex: :unicode_util_compat, repo: "hexpm", optional: false]}], "hexpm", "a4ecdaff44297e9b5894ae499e9a070ea1888c84afdd1fd9b7b2bc384950128e"},
   "hammer": {:hex, :hammer, "6.1.0", "f263e3c3e9946bd410ea0336b2abe0cb6260af4afb3a221e1027540706e76c55", [:make, :mix], [{:poolboy, "~> 1.5", [hex: :poolboy, repo: "hexpm", optional: false]}], "hexpm", "b47e415a562a6d072392deabcd58090d8a41182cf9044cdd6b0d0faaaf68ba57"},
   "hpax": {:hex, :hpax, "0.1.2", "09a75600d9d8bbd064cdd741f21fc06fc1f4cf3d0fcc335e5aa19be1a7235c84", [:mix], [], "hexpm", "2c87843d5a23f5f16748ebe77969880e29809580efdaccd615cd3bed628a8c13"},
+  "idna": {:hex, :idna, "6.1.1", "8a63070e9f7d0c62eb9d9fcb360a7de382448200fbbd1b106cc96d3d8099df8d", [:rebar3], [{:unicode_util_compat, "~> 0.7.0", [hex: :unicode_util_compat, repo: "hexpm", optional: false]}], "hexpm", "92376eb7894412ed19ac475e4a86f7b413c1b9fbb5bd16dccd57934157944cea"},
   "jason": {:hex, :jason, "1.4.0", "e855647bc964a44e2f67df589ccf49105ae039d4179db7f6271dfd3843dc27e6", [:mix], [{:decimal, "~> 1.0 or ~> 2.0", [hex: :decimal, repo: "hexpm", optional: true]}], "hexpm", "79a3791085b2a0f743ca04cec0f7be26443738779d09302e01318f97bdb82121"},
+  "metrics": {:hex, :metrics, "1.0.1", "25f094dea2cda98213cecc3aeff09e940299d950904393b2a29d191c346a8486", [:rebar3], [], "hexpm", "69b09adddc4f74a40716ae54d140f93beb0fb8978d8636eaded0c31b6f099f16"},
   "mime": {:hex, :mime, "2.0.3", "3676436d3d1f7b81b5a2d2bd8405f412c677558c81b1c92be58c00562bb59095", [:mix], [], "hexpm", "27a30bf0db44d25eecba73755acf4068cbfe26a4372f9eb3e4ea3a45956bff6b"},
+  "mimerl": {:hex, :mimerl, "1.2.0", "67e2d3f571088d5cfd3e550c383094b47159f3eee8ffa08e64106cdf5e981be3", [:rebar3], [], "hexpm", "f278585650aa581986264638ebf698f8bb19df297f66ad91b18910dfc6e19323"},
   "mint": {:hex, :mint, "1.4.2", "50330223429a6e1260b2ca5415f69b0ab086141bc76dc2fbf34d7c389a6675b2", [:mix], [{:castore, "~> 0.1.0", [hex: :castore, repo: "hexpm", optional: true]}, {:hpax, "~> 0.1.1", [hex: :hpax, repo: "hexpm", optional: false]}], "hexpm", "ce75a5bbcc59b4d7d8d70f8b2fc284b1751ffb35c7b6a6302b5192f8ab4ddd80"},
   "mint_web_socket": {:hex, :mint_web_socket, "1.0.2", "0933a4c82f2376e35569b2255cdce94f2e3f993c0d5b04c360460cb8beda7154", [:mix], [{:mint, ">= 1.4.0", [hex: :mint, repo: "hexpm", optional: false]}], "hexpm", "067c5e15439be060f2ab57c468ee4ab29e39cb20b498ed990cb94f62db0efc3a"},
+  "parse_trans": {:hex, :parse_trans, "3.3.1", "16328ab840cc09919bd10dab29e431da3af9e9e7e7e6f0089dd5a2d2820011d8", [:rebar3], [], "hexpm", "07cd9577885f56362d414e8c4c4e6bdf10d43a8767abb92d24cbe8b24c54888b"},
   "phoenix": {:git, "https://github.com/phoenixframework/phoenix.git", "7f1085472662d96479a9969d6e94c3738a56e5e7", []},
   "phoenix_ecto": {:hex, :phoenix_ecto, "4.4.0", "0672ed4e4808b3fbed494dded89958e22fb882de47a97634c0b13e7b0b5f7720", [:mix], [{:ecto, "~> 3.3", [hex: :ecto, repo: "hexpm", optional: false]}, {:phoenix_html, "~> 2.14.2 or ~> 3.0", [hex: :phoenix_html, repo: "hexpm", optional: true]}, {:plug, "~> 1.9", [hex: :plug, repo: "hexpm", optional: false]}], "hexpm", "09864e558ed31ee00bd48fcc1d4fc58ae9678c9e81649075431e69dbabb43cc1"},
   "phoenix_html": {:hex, :phoenix_html, "3.2.0", "1c1219d4b6cb22ac72f12f73dc5fad6c7563104d083f711c3fcd8551a1f4ae11", [:mix], [{:plug, "~> 1.5", [hex: :plug, repo: "hexpm", optional: true]}], "hexpm", "36ec97ba56d25c0136ef1992c37957e4246b649d620958a1f9fa86165f8bc54f"},
@@ -35,10 +43,14 @@
   "poolboy": {:hex, :poolboy, "1.5.2", "392b007a1693a64540cead79830443abf5762f5d30cf50bc95cb2c1aaafa006b", [:rebar3], [], "hexpm", "dad79704ce5440f3d5a3681c8590b9dc25d1a561e8f5a9c995281012860901e3"},
   "postgrex": {:hex, :postgrex, "0.16.5", "fcc4035cc90e23933c5d69a9cd686e329469446ef7abba2cf70f08e2c4b69810", [:mix], [{:connection, "~> 1.1", [hex: :connection, repo: "hexpm", optional: false]}, {:db_connection, "~> 2.1", [hex: :db_connection, repo: "hexpm", optional: false]}, {:decimal, "~> 1.5 or ~> 2.0", [hex: :decimal, repo: "hexpm", optional: false]}, {:jason, "~> 1.0", [hex: :jason, repo: "hexpm", optional: true]}, {:table, "~> 0.1.0", [hex: :table, repo: "hexpm", optional: true]}], "hexpm", "edead639dc6e882618c01d8fc891214c481ab9a3788dfe38dd5e37fd1d5fb2e8"},
   "ranch": {:hex, :ranch, "1.8.0", "8c7a100a139fd57f17327b6413e4167ac559fbc04ca7448e9be9057311597a1d", [:make, :rebar3], [], "hexpm", "49fbcfd3682fab1f5d109351b61257676da1a2fdbe295904176d5e521a2ddfe5"},
+  "ssl_verify_fun": {:hex, :ssl_verify_fun, "1.1.6", "cf344f5692c82d2cd7554f5ec8fd961548d4fd09e7d22f5b62482e5aeaebd4b0", [:make, :mix, :rebar3], [], "hexpm", "bdb0d2471f453c88ff3908e7686f86f9be327d065cc1ec16fa4540197ea04680"},
   "swoosh": {:hex, :swoosh, "1.9.0", "23b0678abc29158d3881970d2264724ecf960ac12b8657b657a717445ac01a8f", [:mix], [{:cowboy, "~> 1.1 or ~> 2.4", [hex: :cowboy, repo: "hexpm", optional: true]}, {:ex_aws, "~> 2.1", [hex: :ex_aws, repo: "hexpm", optional: true]}, {:finch, "~> 0.6", [hex: :finch, repo: "hexpm", optional: true]}, {:gen_smtp, "~> 0.13 or ~> 1.0", [hex: :gen_smtp, repo: "hexpm", optional: true]}, {:hackney, "~> 1.9", [hex: :hackney, repo: "hexpm", optional: true]}, {:jason, "~> 1.0", [hex: :jason, repo: "hexpm", optional: false]}, {:mail, "~> 0.2", [hex: :mail, repo: "hexpm", optional: true]}, {:mime, "~> 1.1 or ~> 2.0", [hex: :mime, repo: "hexpm", optional: false]}, {:plug_cowboy, ">= 1.0.0", [hex: :plug_cowboy, repo: "hexpm", optional: true]}, {:telemetry, "~> 0.4.2 or ~> 1.0", [hex: :telemetry, repo: "hexpm", optional: false]}], "hexpm", "548e8f680182064e94354264065275d424eb60bc207fcd1891bcdc3d40845704"},
   "telemetry": {:hex, :telemetry, "1.2.0", "a8ce551485a9a3dac8d523542de130eafd12e40bbf76cf0ecd2528f24e812a44", [:rebar3], [], "hexpm", "1427e73667b9a2002cf1f26694c422d5c905df889023903c4518921d53e3e883"},
   "telemetry_metrics": {:hex, :telemetry_metrics, "0.6.1", "315d9163a1d4660aedc3fee73f33f1d355dcc76c5c3ab3d59e76e3edf80eef1f", [:mix], [{:telemetry, "~> 0.4 or ~> 1.0", [hex: :telemetry, repo: "hexpm", optional: false]}], "hexpm", "7be9e0871c41732c233be71e4be11b96e56177bf15dde64a8ac9ce72ac9834c6"},
   "telemetry_poller": {:hex, :telemetry_poller, "1.0.0", "db91bb424e07f2bb6e73926fcafbfcbcb295f0193e0a00e825e589a0a47e8453", [:rebar3], [{:telemetry, "~> 1.0", [hex: :telemetry, repo: "hexpm", optional: false]}], "hexpm", "b3a24eafd66c3f42da30fc3ca7dda1e9d546c12250a2d60d7b81d264fbec4f6e"},
+  "timex": {:hex, :timex, "3.7.9", "790cdfc4acfce434e442f98c02ea6d84d0239073bfd668968f82ac63e9a6788d", [:mix], [{:combine, "~> 0.10", [hex: :combine, repo: "hexpm", optional: false]}, {:gettext, "~> 0.10", [hex: :gettext, repo: "hexpm", optional: false]}, {:tzdata, "~> 1.1", [hex: :tzdata, repo: "hexpm", optional: false]}], "hexpm", "64691582e5bb87130f721fc709acfb70f24405833998fabf35be968984860ce1"},
+  "tzdata": {:hex, :tzdata, "1.1.1", "20c8043476dfda8504952d00adac41c6eda23912278add38edc140ae0c5bcc46", [:mix], [{:hackney, "~> 1.17", [hex: :hackney, repo: "hexpm", optional: false]}], "hexpm", "a69cec8352eafcd2e198dea28a34113b60fdc6cb57eb5ad65c10292a6ba89787"},
+  "unicode_util_compat": {:hex, :unicode_util_compat, "0.7.0", "bc84380c9ab48177092f43ac89e4dfa2c6d62b40b8bd132b1059ecc7232f9a78", [:rebar3], [], "hexpm", "25eee6d67df61960cf6a794239566599b09e17e668d3700247bc498638152521"},
   "websock": {:hex, :websock, "0.4.3", "184ac396bdcd3dfceb5b74c17d221af659dd559a95b1b92041ecb51c9b728093", [:mix], [], "hexpm", "5e4dd85f305f43fd3d3e25d70bec4a45228dfed60f0f3b072d8eddff335539cf"},
   "websock_adapter": {:hex, :websock_adapter, "0.4.5", "30038a3715067f51a9580562c05a3a8d501126030336ffc6edb53bf57d6d2d26", [:mix], [{:bandit, "~> 0.6", [hex: :bandit, repo: "hexpm", optional: true]}, {:plug, "~> 1.14", [hex: :plug, repo: "hexpm", optional: false]}, {:plug_cowboy, "~> 2.6", [hex: :plug_cowboy, repo: "hexpm", optional: true]}, {:websock, "~> 0.4", [hex: :websock, repo: "hexpm", optional: false]}], "hexpm", "1d9812dc7e703c205049426fd4fe0852a247a825f91b099e53dc96f68bafe4c8"},
 }

test/nostrex/events/events_test.exs

@@ -5,6 +5,32 @@ defmodule Nostrex.EventsTest do
   alias Nostrex.Events.Event
   alias Nostrex.FixtureFactory
 
+  @valid_events [
+    %Event{
+      id: "bfe9a9f57c61d04493c74189dc6ffa73f54522d0bf470b6194dcf33c323eb3c0",
+      pubkey: "f7b642493ed5a462c2faebb5d6cd208e42b8ea36f0b479f2aa2f5f5bf6f67aa7",
+      created_at: 1673931680,
+      kind: 1,
+      tags: [],
+      content: "running bitcoin",
+      sig: "6815aaa87665e68a43639631d9dbac7c3f6b825ff14e6689a100eef2d307f54701ec6b28fa9ab9c9ea01215f07db4e507d8e06a0e01527035f0b0ae9e4c2779c"
+    },
+    %Event{
+      # TODO(sachin): incorrect ID
+      id: "035c202e0f98df0ca71ef0167a0d00bccc88cf290481a8c8f21be40e65f6da5f",
+      pubkey: "b0448252cddc47798e5e726b5c6de25f3c486a01427d736915071f6d320abaab",
+      created_at: 1673931868,
+      kind: 1,
+      tags: [
+        ["p", "f7b642493ed5a462c2faebb5d6cd208e42b8ea36f0b479f2aa2f5f5bf6f67aa7", "random"],
+        ["e", "bfe9a9f57c61d04493c74189dc6ffa73f54522d0bf470b6194dcf33c323eb3c0", "other"]
+      ],
+      content: "It might make sense just to get some in case it catches on.",
+      # TODO(sachin): incorrect sig
+      sig: "f0f6d65f6a2257b3af1a8e1760a697ed1dd2ad8839e3fb708e33555ad1d01206d7a68f9a944387c6505a7fd8cbfac29fc8151bf9109e62b5efbb1479893a8bca"
+    },
+  ]
+
   defp sample_event_params do
     map = %{
       id: "75b79351140f7f0002b050d9b2fef4d1f2d5f4ade7a3b04ed24604672d326009",
@@ -106,6 +132,18 @@ defmodule Nostrex.EventsTest do
   test "ensure kind value is valid" do
   end
 
+  describe "ensure signatures validation works" do
+    test "valid signatures pass check" do
+      for e <- @valid_events do
+        assert Event.validate(e)
+      end
+    end
+
+    test "invalid signatures fail check" do
+
+    end
+  end
+
   test "ensure invalid signature events don't get persisted" do
   end
 

test/support/fixture_factory.ex

@@ -8,7 +8,24 @@ defmodule Nostrex.FixtureFactory do
 
   import Ecto.Changeset
 
+  def create_signed_event(opts \\ []) do
+    # Event.sign will overwrite the random id and sig
+    {:ok, event} =
+      opts
+      |> populate_default_event_params()
+      |> Events.create_and_sign_event()
+    event
+  end
+
   def create_event_no_validation(opts \\ []) do
+    {:ok, event} =
+      opts
+      |> populate_default_event_params()
+      |> Events.create_event_no_validation()
+    event
+  end
+
+  defp populate_default_event_params(opts \\ []) do
     defaults = %{
       id: rand_identifier(),
       pubkey: rand_identifier(),
@@ -47,10 +64,7 @@ defmodule Nostrex.FixtureFactory do
 
     raw = Jason.encode!(params)
 
-    params = Map.put(params, :raw, raw)
-
-    {:ok, event} = Events.create_event_no_validation(params)
-    event
+    Map.put(params, :raw, raw)
   end
 
   def create_filter(opts \\ []) do
@@ -86,7 +100,6 @@ defmodule Nostrex.FixtureFactory do
 
   defp rand_identifier do
     :crypto.hash(:sha256, Integer.to_string(:rand.uniform(99_999_999_999)))
-    |> Base.encode16()
-    |> String.downcase()
+    |> Base.encode16(case: :lower)
   end
 end