diff --git a/src/proto_alpha/lib_protocol/sc_rollup_errors.ml b/src/proto_alpha/lib_protocol/sc_rollup_errors.ml
index 2dde9a810fb32bf3419581fe96e0a4f1eca19cb9..47d9df611560b8aaf6a11a1dcd4626b48d57c094 100644
--- a/src/proto_alpha/lib_protocol/sc_rollup_errors.ml
+++ b/src/proto_alpha/lib_protocol/sc_rollup_errors.ml
@@ -71,6 +71,7 @@ type error +=
   | (* `Temporary *) Sc_rollup_bad_commitment_serialization
   | (* `Permanent *) Sc_rollup_address_generation
   | (* `Permanent *) Sc_rollup_zero_tick_commitment
+  | (* `Permanent *) Sc_rollup_commitment_past_curfew
 
 let () =
   register_error_kind
@@ -448,6 +449,18 @@ let () =
     Data_encoding.empty
     (function Sc_rollup_bad_commitment_serialization -> Some () | _ -> None)
     (fun () -> Sc_rollup_bad_commitment_serialization) ;
+  let description = "Commitment is past the curfew for this level." in
+  register_error_kind
+    `Permanent
+    ~id:"Sc_rollup_commitment_past_curfew"
+    ~title:"Commitment past curfew."
+    ~description:
+      "A commitment exists for this inbox level for longer than the curfew \
+       period."
+    ~pp:(fun ppf () -> Format.fprintf ppf "%s" description)
+    Data_encoding.empty
+    (function Sc_rollup_commitment_past_curfew -> Some () | _ -> None)
+    (fun () -> Sc_rollup_commitment_past_curfew) ;
   let description = "Error while generating rollup address" in
   register_error_kind
     `Permanent
diff --git a/src/proto_alpha/lib_protocol/sc_rollup_stake_storage.ml b/src/proto_alpha/lib_protocol/sc_rollup_stake_storage.ml
index 8d28d386a77ac1234c26d715babf4d0deec284ed..8784830939faf674661305c9b6e73c5dfbd9efe9 100644
--- a/src/proto_alpha/lib_protocol/sc_rollup_stake_storage.ml
+++ b/src/proto_alpha/lib_protocol/sc_rollup_stake_storage.ml
@@ -169,8 +169,40 @@ let assert_commitment_period ctxt rollup commitment =
   in
   return ctxt
 
-(** Check invariants on [inbox_level], enforcing overallocation of storage and
-    regularity of block production.
+(** [assert_commitment_is_not_past_curfew ctxt rollup inbox_level] will look in the
+    storage [Commitment_first_publication_level] for the level of the oldest commit for
+    [inbox_level] and if it is more than [sc_rollup_challenge_window_in_blocks]
+    ago it fails with [Sc_rollup_commitment_past_curfew]. Otherwise it adds the
+    respective storage (if it is not set) and returns the context. *)
+let assert_commitment_is_not_past_curfew ctxt rollup inbox_level =
+  let open Lwt_result_syntax in
+  let refutation_deadline_blocks =
+    Int32.of_int @@ Constants_storage.sc_rollup_challenge_window_in_blocks ctxt
+  in
+  let current_level = (Raw_context.current_level ctxt).level in
+  let* ctxt, oldest_commit =
+    Store.Commitment_first_publication_level.find (ctxt, rollup) inbox_level
+  in
+  match oldest_commit with
+  | Some oldest_commit ->
+      if
+        Compare.Int32.(
+          Raw_level_repr.diff current_level oldest_commit
+          > refutation_deadline_blocks)
+      then tzfail Sc_rollup_commitment_past_curfew
+      else return ctxt
+  | None ->
+      (* The storage cost is covered by the stake. *)
+      let* ctxt, _diff, _existed =
+        Store.Commitment_first_publication_level.add
+          (ctxt, rollup)
+          inbox_level
+          current_level
+      in
+      return ctxt
+
+(** Check invariants on [inbox_level], enforcing overallocation of storage,
+    regularity of block production and curfew.
 
     The constants used by [assert_refine_conditions_met] must be chosen such
     that the maximum cost of storage allocated by each staker is at most the size
@@ -180,7 +212,10 @@ let assert_refine_conditions_met ctxt rollup lcc commitment =
   let open Lwt_result_syntax in
   let* ctxt = assert_commitment_not_too_far_ahead ctxt rollup lcc commitment in
   let* ctxt = assert_commitment_period ctxt rollup commitment in
-  return ctxt
+  assert_commitment_is_not_past_curfew
+    ctxt
+    rollup
+    Commitment.(commitment.inbox_level)
 
 let get_commitment_stake_count ctxt rollup node =
   let open Lwt_result_syntax in
@@ -398,6 +433,11 @@ let cement_commitment ctxt rollup new_lcc =
      [max_number_of_cemented_commitments], if such exist.
   *)
   let* ctxt = deallocate_commitment_metadata ctxt rollup old_lcc in
+  let* ctxt, _freed_size =
+    Store.Commitment_first_publication_level.remove_existing
+      (ctxt, rollup)
+      new_lcc_commitment.inbox_level
+  in
   (* Decrease max_number_of_stored_cemented_commitments by one because
      we start counting commitments from old_lcc, rather than from new_lcc. *)
   let num_commitments_to_keep =
diff --git a/src/proto_alpha/lib_protocol/storage.ml b/src/proto_alpha/lib_protocol/storage.ml
index fed23a171b4b1bbae20c271e7f3daf9aec09f62b..ab1eff9872cde7ea4c17bdbd89b371a650ac6cba 100644
--- a/src/proto_alpha/lib_protocol/storage.ml
+++ b/src/proto_alpha/lib_protocol/storage.ml
@@ -1795,6 +1795,15 @@ module Sc_rollup = struct
         let encoding = Data_encoding.int32
       end)
 
+  module Commitment_first_publication_level =
+    Make_indexed_carbonated_data_storage
+      (Make_subcontext (Registered) (Indexed_context.Raw_context)
+         (struct
+           let name = ["commitment_first_publication_level"]
+         end))
+         (Make_index (Raw_level_repr.Index))
+      (Raw_level_repr)
+
   module Commitment_added =
     Make_indexed_carbonated_data_storage
       (Make_subcontext (Registered) (Indexed_context.Raw_context)
diff --git a/src/proto_alpha/lib_protocol/storage.mli b/src/proto_alpha/lib_protocol/storage.mli
index 7e6bc25c3acdda05612cd28d4ed7335b6f96ca10..19930309cd5420be3651cbb4616d1556349f12df 100644
--- a/src/proto_alpha/lib_protocol/storage.mli
+++ b/src/proto_alpha/lib_protocol/storage.mli
@@ -824,6 +824,23 @@ module Sc_rollup : sig
        and type value = int32
        and type t = Raw_context.t * Sc_rollup_repr.t
 
+  (** This storage contains for each rollup and inbox level not yet cemented the
+      level of publication of the first commitment. This is used to compute the
+      curfew for a given rollup and inbox level.
+
+      The storage size is bounded for each rollup by 
+  
+                          [max_lookahead / commitment_period]
+
+      Since the storage is cleaned when commitments are cemented, this storage 
+      space is only temporarily bought by stakers with their deposits.
+  *)
+  module Commitment_first_publication_level :
+    Non_iterable_indexed_carbonated_data_storage
+      with type key = Raw_level_repr.t
+       and type value = Raw_level_repr.t
+       and type t = Raw_context.t * Sc_rollup_repr.t
+
   module Commitment_added :
     Non_iterable_indexed_carbonated_data_storage
       with type key = Sc_rollup_commitment_repr.Hash.t
diff --git a/src/proto_alpha/lib_protocol/test/integration/operations/test_sc_rollup.ml b/src/proto_alpha/lib_protocol/test/integration/operations/test_sc_rollup.ml
index df975ae634ab4da92a9a3c3446b7793ae72edb08..229263ab0153e3d5f31e3e6243c9d0fa2427e0f7 100644
--- a/src/proto_alpha/lib_protocol/test/integration/operations/test_sc_rollup.ml
+++ b/src/proto_alpha/lib_protocol/test/integration/operations/test_sc_rollup.ml
@@ -223,9 +223,15 @@ let number_of_ticks_exn n =
   | Some x -> x
   | None -> Stdlib.failwith "Bad Number_of_ticks"
 
-let dummy_commitment ?compressed_state ?(number_of_ticks = 3000L) ctxt rollup =
+let dummy_commitment ?predecessor ?compressed_state ?(number_of_ticks = 3000L)
+    ctxt rollup =
   let* genesis_info = Context.Sc_rollup.genesis_info ctxt rollup in
-  let predecessor = genesis_info.commitment_hash in
+  let predecessor, pred_level =
+    match predecessor with
+    | Some pred ->
+        (Sc_rollup.Commitment.hash_uncarbonated pred, pred.inbox_level)
+    | None -> (genesis_info.commitment_hash, genesis_info.level)
+  in
   let* compressed_state =
     match compressed_state with
     | None ->
@@ -235,7 +241,6 @@ let dummy_commitment ?compressed_state ?(number_of_ticks = 3000L) ctxt rollup =
         return compressed_state
     | Some compressed_state -> return compressed_state
   in
-  let root_level = genesis_info.level in
   let* inbox_level =
     let+ constants = Context.get_constants ctxt in
     let Constants.Parametric.{commitment_period_in_blocks = commitment_freq; _}
@@ -243,7 +248,7 @@ let dummy_commitment ?compressed_state ?(number_of_ticks = 3000L) ctxt rollup =
       constants.parametric.sc_rollup
     in
     Raw_level.of_int32_exn
-      (Int32.add (Raw_level.to_int32 root_level) (Int32.of_int commitment_freq))
+      (Int32.add (Raw_level.to_int32 pred_level) (Int32.of_int commitment_freq))
   in
   return
     Sc_rollup.Commitment.
@@ -254,6 +259,21 @@ let dummy_commitment ?compressed_state ?(number_of_ticks = 3000L) ctxt rollup =
         compressed_state;
       }
 
+let publish_op_and_dummy_commitment ~src ?compressed_state ?predecessor rollup
+    block =
+  let compressed_state =
+    Option.map
+      (fun s ->
+        Sc_rollup.State_hash.context_hash_to_state_hash
+          (Tezos_crypto.Context_hash.hash_string [s]))
+      compressed_state
+  in
+  let* commitment =
+    dummy_commitment ?compressed_state ?predecessor (B block) rollup
+  in
+  let* publish = Op.sc_rollup_publish (B block) src rollup commitment in
+  return (publish, commitment)
+
 (* Verify that parameters and unparsed parameters match. *)
 let verify_params ctxt ~parameters_ty ~parameters ~unparsed_parameters =
   let show exp = Expr.to_string @@ exp in
@@ -2178,6 +2198,191 @@ let test_zero_tick_commitment_fails () =
   in
   return_unit
 
+(** [test_curfew] creates a rollup, publishes two conflicting
+    commitments. Branches are expected to continue (commitment are able to be
+    published). Tries to publish another commitment at the same initial
+    `inbox_level` after [challenge_window_in_blocks - 1] and after
+    [challenge_window_in_blocks] blocks. Only the first attempt is expected to
+    succeed. *)
+let test_curfew () =
+  let open Lwt_result_syntax in
+  let* block, (account1, account2, account3), rollup =
+    init_and_originate Context.T3 "unit"
+  in
+  let* constants = Context.get_constants (B block) in
+  let challenge_window =
+    constants.parametric.sc_rollup.challenge_window_in_blocks
+  in
+  let commitment_period =
+    constants.parametric.sc_rollup.commitment_period_in_blocks
+  in
+  let* block = Block.bake_n commitment_period block in
+  let* publish1, commitment1 =
+    publish_op_and_dummy_commitment
+      ~src:account1
+      ~compressed_state:"first"
+      rollup
+      block
+  in
+  let* publish2, commitment2 =
+    publish_op_and_dummy_commitment
+      ~src:account2
+      ~compressed_state:"second"
+      rollup
+      block
+  in
+  let* block = Block.bake ~operations:[publish1; publish2] block in
+  let* block = Block.bake_n (challenge_window - 1) block in
+  let* publish11, commitment11 =
+    publish_op_and_dummy_commitment
+      ~src:account1
+      ~predecessor:commitment1
+      rollup
+      block
+  in
+  let* publish21, commitment21 =
+    publish_op_and_dummy_commitment
+      ~src:account2
+      ~predecessor:commitment2
+      rollup
+      block
+  in
+  let* publish3, _commitment3 =
+    publish_op_and_dummy_commitment
+      ~src:account3
+      ~compressed_state:"third"
+      rollup
+      block
+  in
+  let* block = Block.bake ~operations:[publish11; publish21; publish3] block in
+  let* publish111, _commitment111 =
+    publish_op_and_dummy_commitment
+      ~src:account1
+      ~predecessor:commitment11
+      rollup
+      block
+  in
+  let* publish211, _commitment211 =
+    publish_op_and_dummy_commitment
+      ~src:account2
+      ~predecessor:commitment21
+      rollup
+      block
+  in
+  let* publish4, _commitment4 =
+    publish_op_and_dummy_commitment
+      ~src:account3
+      ~compressed_state:"fourth"
+      rollup
+      block
+  in
+  let* incr = Incremental.begin_construction block in
+  let* incr = Incremental.add_operation incr publish111 in
+  let* incr = Incremental.add_operation incr publish211 in
+  let expect_apply_failure = function
+    | Environment.Ecoproto_error
+        (Sc_rollup_errors.Sc_rollup_commitment_past_curfew as e)
+      :: _ ->
+        Assert.test_error_encodings e ;
+        return_unit
+    | _ ->
+        failwith "It should have failed with [Sc_rollup_commitment_past_curfew]"
+  in
+  let* _incr = Incremental.add_operation ~expect_apply_failure incr publish4 in
+  return_unit
+
+(** [test_curfew_is_clean] makes sure that the curfew-related storage is cleaned
+    when a commitment is cemented. *)
+let test_curfew_is_clean () =
+  let open Lwt_result_syntax in
+  let* block, account1, rollup = init_and_originate Context.T1 "unit" in
+  let find_first_publication_level block inbox_level =
+    let* alpha_ctxt = Block.to_alpha_ctxt block in
+    let raw_ctxt = Alpha_context.Internal_for_tests.to_raw alpha_ctxt in
+    let rollup =
+      Data_encoding.Binary.(
+        to_bytes_exn Alpha_context.Sc_rollup.Address.encoding rollup
+        |> of_bytes_exn Protocol.Sc_rollup_repr.Address.encoding)
+    in
+    let inbox_level =
+      Data_encoding.Binary.(
+        to_bytes_exn Raw_level.encoding inbox_level
+        |> of_bytes_exn Raw_level_repr.encoding)
+    in
+    let* _raw_ctxt, first_publication_level =
+      Storage.Sc_rollup.Commitment_first_publication_level.find
+        (raw_ctxt, rollup)
+        inbox_level
+      >|= Environment.wrap_tzresult
+    in
+    return first_publication_level
+  in
+  let* constants = Context.get_constants (B block) in
+  let challenge_window =
+    constants.parametric.sc_rollup.challenge_window_in_blocks
+  in
+  let commitment_period =
+    constants.parametric.sc_rollup.commitment_period_in_blocks
+  in
+  let* block = Block.bake_n commitment_period block in
+  let* commitment = dummy_commitment (B block) rollup in
+  let* operation = Op.sc_rollup_publish (B block) account1 rollup commitment in
+  let* first_publication_level =
+    find_first_publication_level block commitment.inbox_level
+  in
+  let* () =
+    match first_publication_level with
+    | Some _x ->
+        failwith "The storage should be empty before the first publication."
+    | None -> return_unit
+  in
+  let* block = Block.bake ~operation block in
+  let* () =
+    let* first_publication_level =
+      find_first_publication_level block commitment.inbox_level
+    in
+    match first_publication_level with
+    | Some x ->
+        assert (
+          Int32.equal block.header.shell.level @@ Raw_level_repr.to_int32 x) ;
+        return_unit
+    | None -> failwith "The level of publication is expected to exist"
+  in
+  let* block = Block.bake_n challenge_window block in
+  let* cement_op =
+    let hash = Sc_rollup.Commitment.hash_uncarbonated commitment in
+    Op.sc_rollup_cement (B block) account1 rollup hash
+  in
+  let* block = Block.bake block ~operation:cement_op in
+  let* first_publication_level =
+    find_first_publication_level block commitment.inbox_level
+  in
+  match first_publication_level with
+  | Some _x ->
+      failwith
+        "The storage should have been cleaned when commitment is cemented"
+  | None -> return_unit
+
+(** [test_curfew_period_is_started_only_after_first_publication checks that
+    publishing the first commitment of a given [inbox_level] after 
+    [inbox_level + challenge_window] is still possible. *)
+let test_curfew_period_is_started_only_after_first_publication () =
+  let open Lwt_result_syntax in
+  let* block, account1, rollup = init_and_originate Context.T1 "unit" in
+  let* constants = Context.get_constants (B block) in
+  let challenge_window =
+    constants.parametric.sc_rollup.challenge_window_in_blocks
+  in
+  let commitment_period =
+    constants.parametric.sc_rollup.commitment_period_in_blocks
+  in
+  let* block = Block.bake_n commitment_period block in
+  let* block = Block.bake_n challenge_window block in
+  let* commitment = dummy_commitment (B block) rollup in
+  let* operation = Op.sc_rollup_publish (B block) account1 rollup commitment in
+  let* _block = Block.bake ~operation block in
+  return_unit
+
 let tests =
   [
     Tztest.tztest
@@ -2295,4 +2500,14 @@ let tests =
       "0-tick commitments are forbidden"
       `Quick
       test_zero_tick_commitment_fails;
+    Tztest.tztest "check the curfew functionality" `Quick test_curfew;
+    Tztest.tztest
+      "check the curfew storage is cleaned after cement"
+      `Quick
+      test_curfew_is_clean;
+    Tztest.tztest
+      "check that a commitment can be published after the inbox_level + \
+       challenge window is passed."
+      `Quick
+      test_curfew_period_is_started_only_after_first_publication;
   ]
diff --git a/tezt/tests/expected/sc_rollup.ml/Alpha- arith - participant of a refutation game are slashed-rewarded.out b/tezt/tests/expected/sc_rollup.ml/Alpha- arith - participant of a refutation game are slashed-rewarded.out
index 9d01f02ecc10a9135cee19c1b816373a8d7cb16f..d2a801bd2daf9836eff7a60d378f659d44ff4b1b 100644
--- a/tezt/tests/expected/sc_rollup.ml/Alpha- arith - participant of a refutation game are slashed-rewarded.out	
+++ b/tezt/tests/expected/sc_rollup.ml/Alpha- arith - participant of a refutation game are slashed-rewarded.out	
@@ -35,7 +35,7 @@ This sequence of operations was run:
 
 ./octez-client --wait none publish commitment from '[PUBLIC_KEY_HASH]' for sc rollup '[SC_ROLLUP_HASH]' with compressed state '[SC_ROLLUP_PVM_STATE_HASH]' at inbox level 4 and predecessor '[SC_ROLLUP_COMMITMENT_HASH]' and number of ticks 1
 Node is bootstrapped.
-Estimated gas: 5781.719 units (will add 100 for safety)
+Estimated gas: 6241.735 units (will add 100 for safety)
 Estimated storage: no bytes added
 Operation successfully injected in the node.
 Operation hash is '[OPERATION_HASH]'
@@ -46,13 +46,13 @@ and/or an external block explorer to make sure that it has been included.
 This sequence of operations was run:
   Manager signed operations:
     From: [PUBLIC_KEY_HASH]
-    Fee to the baker: ꜩ0.00093
+    Fee to the baker: ꜩ0.000976
     Expected counter: 1
-    Gas limit: 5882
+    Gas limit: 6342
     Storage limit: 0 bytes
     Balance updates:
-      [PUBLIC_KEY_HASH] ... -ꜩ0.00093
-      payload fees(the block proposer) ....... +ꜩ0.00093
+      [PUBLIC_KEY_HASH] ... -ꜩ0.000976
+      payload fees(the block proposer) ....... +ꜩ0.000976
     Smart contract rollup commitment publishing:
       Address: [SC_ROLLUP_HASH]
       Commitment:
@@ -61,7 +61,7 @@ This sequence of operations was run:
         predecessor: [SC_ROLLUP_COMMITMENT_HASH]
         number_of_ticks: 1
       This smart contract rollup commitment publishing was successfully applied
-      Consumed gas: 5781.719
+      Consumed gas: 6241.735
       Hash of commit: [SC_ROLLUP_COMMITMENT_HASH]
       Commitment published at level: 5
       Balance updates:
@@ -71,7 +71,7 @@ This sequence of operations was run:
 
 ./octez-client --wait none publish commitment from '[PUBLIC_KEY_HASH]' for sc rollup '[SC_ROLLUP_HASH]' with compressed state '[SC_ROLLUP_PVM_STATE_HASH]' at inbox level 4 and predecessor '[SC_ROLLUP_COMMITMENT_HASH]' and number of ticks 2
 Node is bootstrapped.
-Estimated gas: 5781.719 units (will add 100 for safety)
+Estimated gas: 6241.727 units (will add 100 for safety)
 Estimated storage: no bytes added
 Operation successfully injected in the node.
 Operation hash is '[OPERATION_HASH]'
@@ -82,13 +82,13 @@ and/or an external block explorer to make sure that it has been included.
 This sequence of operations was run:
   Manager signed operations:
     From: [PUBLIC_KEY_HASH]
-    Fee to the baker: ꜩ0.00093
+    Fee to the baker: ꜩ0.000976
     Expected counter: 1
-    Gas limit: 5882
+    Gas limit: 6342
     Storage limit: 0 bytes
     Balance updates:
-      [PUBLIC_KEY_HASH] ... -ꜩ0.00093
-      payload fees(the block proposer) ....... +ꜩ0.00093
+      [PUBLIC_KEY_HASH] ... -ꜩ0.000976
+      payload fees(the block proposer) ....... +ꜩ0.000976
     Smart contract rollup commitment publishing:
       Address: [SC_ROLLUP_HASH]
       Commitment:
@@ -97,7 +97,7 @@ This sequence of operations was run:
         predecessor: [SC_ROLLUP_COMMITMENT_HASH]
         number_of_ticks: 2
       This smart contract rollup commitment publishing was successfully applied
-      Consumed gas: 5781.719
+      Consumed gas: 6241.727
       Hash of commit: [SC_ROLLUP_COMMITMENT_HASH]
       Commitment published at level: 6
       Balance updates: