diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index 9399bc255..4cecb4ddd 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -244,6 +244,7 @@ Code snippets appearing in `this style` are to be interpreted as Python code. Be
 | `DOMAIN_ATTESTATION` | `1` |
 | `DOMAIN_PROPOSAL` | `2` |
 | `DOMAIN_EXIT` | `3` |
+| `DOMAIN_RANDAO` | `4` |
 
 ## Data structures
 
@@ -383,10 +384,6 @@ Code snippets appearing in `this style` are to be interpreted as Python code. Be
     'pubkey': 'bytes48',
     # Withdrawal credentials
     'withdrawal_credentials': 'bytes32',
-    # Initial RANDAO commitment
-    'randao_commitment': 'bytes32',
-    # Initial custody commitment
-    'custody_commitment': 'bytes32',
     # A BLS signature of this `DepositInput`
     'proof_of_possession': 'bytes96',
 }
@@ -417,7 +414,7 @@ Code snippets appearing in `this style` are to be interpreted as Python code. Be
     'slot': 'uint64',
     'parent_root': 'bytes32',
     'state_root': 'bytes32',
-    'randao_reveal': 'bytes32',
+    'randao_reveal': 'bytes96',
     'eth1_data': Eth1Data,
     'signature': 'bytes96',
 
@@ -514,10 +511,8 @@ Code snippets appearing in `this style` are to be interpreted as Python code. Be
     'pubkey': 'bytes48',
     # Withdrawal credentials
     'withdrawal_credentials': 'bytes32',
-    # RANDAO commitment
-    'randao_commitment': 'bytes32',
-    # Slots the proposer has skipped (i.e. layers of RANDAO expected)
-    'randao_layers': 'uint64',
+    # Number of proposer slots since genesis
+    'proposer_slots': 'uint64',
     # Slot when validator activated
     'activation_slot': 'uint64',
     # Slot when validator exited
@@ -530,8 +525,6 @@ Code snippets appearing in `this style` are to be interpreted as Python code. Be
     'exit_count': 'uint64',
     # Status flags
     'status_flags': 'uint64',
-    # Custody commitment
-    'custody_commitment': 'bytes32',
     # Slot of latest custody reseed
     'latest_custody_reseed_slot': 'uint64',
     # Slot of second-latest custody reseed
@@ -928,7 +921,7 @@ def get_crosslink_committees_at_slot(state: BeaconState,
     """
     Returns the list of ``(committee, shard)`` tuples for the ``slot``.
     """
-    state_epoch_slot = state.slot - (state.slot % EPOCH_LENGTH) 
+    state_epoch_slot = state.slot - (state.slot % EPOCH_LENGTH)
     assert state_epoch_slot <= slot + EPOCH_LENGTH
     assert slot < state_epoch_slot + EPOCH_LENGTH
     offset = slot % EPOCH_LENGTH
@@ -1044,7 +1037,7 @@ def get_attestation_participants(state: BeaconState,
 
     assert attestation_data.shard in [shard for _, shard in crosslink_committees]
     crosslink_committee = [committee for committee, shard in crosslink_committees if shard == attestation_data.shard][0]
-    assert len(aggregation_bitfield) == (len(committee) + 7) // 8
+    assert len(aggregation_bitfield) == (len(crosslink_committee) + 7) // 8
 
     # Find the participating attesters in the committee
     participants = []
@@ -1203,7 +1196,7 @@ A valid block with slot `GENESIS_SLOT` (a "genesis block") has the following val
     slot=GENESIS_SLOT,
     parent_root=ZERO_HASH,
     state_root=STARTUP_STATE_ROOT,
-    randao_reveal=ZERO_HASH,
+    randao_reveal=EMPTY_SIGNATURE,
     eth1_data=Eth1Data(
         deposit_root=ZERO_HASH,
         block_hash=ZERO_HASH
@@ -1284,8 +1277,6 @@ def get_initial_beacon_state(initial_validator_deposits: List[Deposit],
             amount=deposit.deposit_data.amount,
             proof_of_possession=deposit.deposit_data.deposit_input.proof_of_possession,
             withdrawal_credentials=deposit.deposit_data.deposit_input.withdrawal_credentials,
-            randao_commitment=deposit.deposit_data.deposit_input.randao_commitment,
-            custody_commitment=deposit.deposit_data.deposit_input.custody_commitment,
         )
 
     # Process initial activations
@@ -1304,14 +1295,10 @@ First, a helper function:
 def validate_proof_of_possession(state: BeaconState,
                                  pubkey: Bytes48,
                                  proof_of_possession: Bytes96,
-                                 withdrawal_credentials: Bytes32,
-                                 randao_commitment: Bytes32,
-                                 custody_commitment: Bytes32) -> bool:
+                                 withdrawal_credentials: Bytes32) -> bool:
     proof_of_possession_data = DepositInput(
         pubkey=pubkey,
         withdrawal_credentials=withdrawal_credentials,
-        randao_commitment=randao_commitment,
-        custody_commitment=custody_commitment,
         proof_of_possession=EMPTY_SIGNATURE,
     )
 
@@ -1334,9 +1321,7 @@ def process_deposit(state: BeaconState,
                     pubkey: Bytes48,
                     amount: int,
                     proof_of_possession: Bytes96,
-                    withdrawal_credentials: Bytes32,
-                    randao_commitment: Bytes32,
-                    custody_commitment: Bytes32) -> None:
+                    withdrawal_credentials: Bytes32) -> None:
     """
     Process a deposit from Ethereum 1.0.
     Note that this function mutates ``state``.
@@ -1347,8 +1332,6 @@ def process_deposit(state: BeaconState,
         pubkey,
         proof_of_possession,
         withdrawal_credentials,
-        randao_commitment,
-        custody_commitment,
     )
 
     validator_pubkeys = [v.pubkey for v in state.validator_registry]
@@ -1358,15 +1341,13 @@ def process_deposit(state: BeaconState,
         validator = Validator(
             pubkey=pubkey,
             withdrawal_credentials=withdrawal_credentials,
-            randao_commitment=randao_commitment,
-            randao_layers=0,
+            proposer_slots=0,
             activation_slot=FAR_FUTURE_SLOT,
             exit_slot=FAR_FUTURE_SLOT,
             withdrawal_slot=FAR_FUTURE_SLOT,
             penalized_slot=FAR_FUTURE_SLOT,
             exit_count=0,
             status_flags=0,
-            custody_commitment=custody_commitment,
             latest_custody_reseed_slot=GENESIS_SLOT,
             penultimate_custody_reseed_slot=GENESIS_SLOT,
         )
@@ -1439,7 +1420,7 @@ Below are the processing steps that happen at every slot.
 ### Misc counters
 
 * Set `state.slot += 1`.
-* Set `state.validator_registry[get_beacon_proposer_index(state, state.slot)].randao_layers += 1`.
+* Set `state.validator_registry[get_beacon_proposer_index(state, state.slot)].proposer_slots += 1`.
 * Set `state.latest_randao_mixes[state.slot % LATEST_RANDAO_MIXES_LENGTH] = state.latest_randao_mixes[(state.slot - 1) % LATEST_RANDAO_MIXES_LENGTH]`
 
 ### Block roots
@@ -1464,12 +1445,9 @@ Below are the processing steps that happen at every `block`.
 
 ### RANDAO
 
-* Let `repeat_hash(x, n) = x if n == 0 else repeat_hash(hash(x), n-1)`.
 * Let `proposer = state.validator_registry[get_beacon_proposer_index(state, state.slot)]`.
-* Verify that `repeat_hash(block.randao_reveal, proposer.randao_layers) == proposer.randao_commitment`.
-* Set `state.latest_randao_mixes[state.slot % LATEST_RANDAO_MIXES_LENGTH] = hash(xor(state.latest_randao_mixes[state.slot % LATEST_RANDAO_MIXES_LENGTH], block.randao_reveal))`
-* Set `proposer.randao_commitment = block.randao_reveal`.
-* Set `proposer.randao_layers = 0`.
+* Verify that `bls_verify(pubkey=proposer.pubkey, message=int_to_bytes32(proposer.proposer_slots), signature=block.randao_reveal, domain=get_domain(state.fork, state.slot, DOMAIN_RANDAO))`.
+* Set `state.latest_randao_mixes[state.slot % LATEST_RANDAO_MIXES_LENGTH] = hash(state.latest_randao_mixes[state.slot % LATEST_RANDAO_MIXES_LENGTH] + block.randao_reveal)`.
 
 ### Eth1 data
 
@@ -1560,8 +1538,6 @@ process_deposit(
     amount=deposit.deposit_data.amount,
     proof_of_possession=deposit.deposit_data.deposit_input.proof_of_possession,
     withdrawal_credentials=deposit.deposit_data.deposit_input.withdrawal_credentials,
-    randao_commitment=deposit.deposit_data.deposit_input.randao_commitment,
-    custody_commitment=deposit.deposit_data.deposit_input.custody_commitment,
 )
 ```
 
@@ -1730,6 +1706,7 @@ First, update `previous_epoch_calculation_slot`, `previous_epoch_start_shard` an
 * Set `state.previous_epoch_calculation_slot = state.current_epoch_calculation_slot`
 * Set `state.previous_epoch_start_shard = state.current_epoch_start_shard`
 * Set `state.latest_index_roots[epoch % LATEST_INDEX_ROOTS_LENGTH] = hash_tree_root(get_active_validator_indices(state, state.slot))`
+* Set `state.previous_epoch_seed = state.current_epoch_seed`
 
 If the following are satisfied:
 
@@ -1784,7 +1761,6 @@ def update_validator_registry(state: BeaconState) -> None:
 
 and perform the following updates:
 
-* Set `state.previous_epoch_seed = state.current_epoch_seed`
 * Set `state.current_epoch_calculation_slot = state.slot`
 * Set `state.current_epoch_start_shard = (state.current_epoch_start_shard + get_current_epoch_committee_count_per_slot(state) * EPOCH_LENGTH) % SHARD_COUNT`
 * Set `state.current_epoch_seed = hash(get_randao_mix(state, state.current_epoch_calculation_slot - SEED_LOOKAHEAD) + get_active_index_root(state, state.current_epoch_calculation_slot))`
@@ -1850,11 +1826,9 @@ This section is divided into Normative and Informative references.  Normative re
 ## Normative
 
 ## Informative
-<a id="ref-casper-ffg"></a> _**casper-ffg**_  
- &nbsp; _Casper the Friendly Finality Gadget_. V. Buterin and V. Griffith. URL: https://arxiv.org/abs/1710.09437
+<a id="ref-casper-ffg"></a> _**casper-ffg**_ </br> &nbsp; _Casper the Friendly Finality Gadget_. V. Buterin and V. Griffith. URL: https://arxiv.org/abs/1710.09437
 
-<a id="ref-python-poc"></a> _**python-poc**_  
- &nbsp; _Python proof-of-concept implementation_. Ethereum Foundation. URL: https://github.com/ethereum/beacon_chain
+<a id="ref-python-poc"></a> _**python-poc**_ </br> &nbsp; _Python proof-of-concept implementation_. Ethereum Foundation. URL: https://github.com/ethereum/beacon_chain
 
 # Copyright
 Copyright and related rights waived via [CC0](https://creativecommons.org/publicdomain/zero/1.0/).