diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index c11fd6936..198c4872a 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -34,6 +34,7 @@
                 - [`Deposit`](#deposit)
                 - [`DepositData`](#depositdata)
                 - [`DepositInput`](#depositinput)
+                - [`ProofOfPossessionData`](#proofofpossessiondata)
             - [Exits](#exits)
                 - [`Exit`](#exit)
         - [Beacon chain blocks](#beacon-chain-blocks)
@@ -49,6 +50,7 @@
             - [`CandidatePoWReceiptRootRecord`](#candidatepowreceiptrootrecord)
             - [`PendingAttestationRecord`](#pendingattestationrecord)
             - [`ForkData`](#forkdata)
+            - [`ValidatorRegistryDeltaBlock`](#validatorregistrydeltablock)
     - [Ethereum 1.0 deposit contract](#ethereum-10-deposit-contract)
         - [Deposit arguments](#deposit-arguments)
         - [`Eth1Deposit` logs](#eth1deposit-logs)
@@ -59,6 +61,7 @@
     - [Beacon chain state transition function](#beacon-chain-state-transition-function)
         - [Helper functions](#helper-functions)
             - [`hash`](#hash)
+            - [`hash_tree_root`](#hash_tree_root)
             - [`is_active_validator`](#is_active_validator)
             - [`get_active_validator_indices`](#get_active_validator_indices)
             - [`shuffle`](#shuffle)
@@ -75,7 +78,6 @@
             - [`get_new_validator_registry_delta_chain_tip`](#get_new_validator_registry_delta_chain_tip)
             - [`get_fork_version`](#get_fork_version)
             - [`get_domain`](#get_domain)
-            - [`hash_tree_root`](#hash_tree_root)
             - [`verify_slashable_vote_data`](#verify_slashable_vote_data)
             - [`is_double_vote`](#is_double_vote)
             - [`is_surround_vote`](#is_surround_vote)
@@ -165,6 +167,7 @@ Unless otherwise indicated, code appearing in `this style` is to be interpreted
 | `BLS_WITHDRAWAL_PREFIX_BYTE` | `0x00` | - |
 | `MAX_CASPER_VOTES` | `2**10` (= 1,024) | votes |
 | `LATEST_BLOCK_ROOTS_LENGTH` | `2**13` (= 8,192) | block roots |
+| `EMPTY_SIGNATURE` | `[bytes48(0), bytes48(0)]` | - |
 
 * For the safety of crosslinks a minimum committee size of 111 is [recommended](https://vitalik.ca/files/Ithaca201807_Sharding.pdf). (Unbiasable randomness with a Verifiable Delay Function (VDF) will improve committee robustness and lower the safe minimum committee size.) The shuffling algorithm generally ensures (assuming sufficient validators) committee sizes at least `TARGET_COMMITTEE_SIZE // 2`.
 
@@ -371,12 +374,12 @@ Unless otherwise indicated, code appearing in `this style` is to be interpreted
 {
     # BLS pubkey
     'pubkey': 'uint384',
-    # BLS proof of possession (a BLS signature)
-    'proof_of_possession': ['uint384'],
     # Withdrawal credentials
     'withdrawal_credentials': 'hash32',
     # Initial RANDAO commitment
     'randao_commitment': 'hash32',
+    # a BLS signature of this ``DepositInput``
+    'proof_of_possession': ['uint384'],
 }
 ```
 
@@ -581,6 +584,17 @@ Unless otherwise indicated, code appearing in `this style` is to be interpreted
 }
 ```
 
+#### `ValidatorRegistryDeltaBlock`
+
+```python
+{
+    latest_registry_delta_root: 'hash32',
+    validator_index: 'uint24',
+    pubkey: 'uint384',
+    flag: 'uint64',
+}
+```
+
 ## Ethereum 1.0 deposit contract
 
 The initial deployment phases of Ethereum 2.0 are implemented without consensus changes to Ethereum 1.0. A deposit contract at address `DEPOSIT_CONTRACT_ADDRESS` is added to Ethereum 1.0 for deposits of ETH to the beacon chain. Validator balances will be withdrawable to the shards when the EVM2.0 is deployed and the shards have state.
@@ -730,6 +744,10 @@ The hash function is denoted by `hash`. In Phase 0 the beacon chain is deployed
 
 Note: We aim to migrate to a S[T/N]ARK-friendly hash function in a future Ethereum 2.0 deployment phase.
 
+#### `hash_tree_root`
+
+`hash_tree_root` is a function for hashing objects into a single root utilizing a hash tree structure. `hash_tree_root` is defined in the [SimpleSerialize spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/simple-serialize.md#tree-hash).
+
 #### `is_active_validator`
 ```python
 def is_active_validator(validator: ValidatorRecord) -> bool:
@@ -970,17 +988,19 @@ def get_effective_balance(validator: ValidatorRecord) -> int:
 
 ```python
 def get_new_validator_registry_delta_chain_tip(current_validator_registry_delta_chain_tip: Hash32,
-                                               index: int,
+                                               validator_index: int,
                                                pubkey: int,
                                                flag: int) -> Hash32:
     """
-    Compute the next hash in the validator registry delta hash chain.
+    Compute the next root in the validator registry delta chain.
     """
-    return hash(
-        current_validator_registry_delta_chain_tip +
-        bytes1(flag) +
-        bytes3(index) +
-        bytes48(pubkey)
+    return hash_tree_root(
+        ValidatorRegistryDeltaBlock(
+            validator_registry_delta_chain_tip=current_validator_registry_delta_chain_tip,
+            validator_index=validator_index,
+            pubkey=pubkey,
+            flag=flag,
+        )
     )
 ```
 
@@ -1007,10 +1027,6 @@ def get_domain(fork_data: ForkData,
     ) * 2**32 + domain_type
 ```
 
-#### `hash_tree_root`
-
-`hash_tree_root` is a function for hashing objects into a single root utilizing a hash tree structure. `hash_tree_root` is defined in the [SimpleSerialize spec](https://github.com/ethereum/eth2.0-specs/blob/master/specs/simple-serialize.md#tree-hash).
-
 #### `verify_slashable_vote_data`
 
 ```python
@@ -1105,7 +1121,7 @@ A valid block with slot `INITIAL_SLOT_NUMBER` (a "genesis block") has the follow
     state_root=STARTUP_STATE_ROOT,
     randao_reveal=ZERO_HASH,
     candidate_pow_receipt_root=ZERO_HASH,
-    proposer_signature=[0, 0],
+    proposer_signature=EMPTY_SIGNATURE,
     'body': BeaconBlockBody(
         proposer_slashings=[],
         casper_slashings=[],
@@ -1116,7 +1132,7 @@ A valid block with slot `INITIAL_SLOT_NUMBER` (a "genesis block") has the follow
 }
 ```
 
-`STARTUP_STATE_ROOT` (in the above "genesis block") is generated from the `get_initial_beacon_state` function below. When enough full deposits have been made to the deposit contract and the `ChainStart` log has been emitted, `get_initial_beacon_state` will execute to compute the `ssz_tree_hash` of `BeaconState`.
+`STARTUP_STATE_ROOT` (in the above "genesis block") is generated from the `get_initial_beacon_state` function below. When enough full deposits have been made to the deposit contract and the `ChainStart` log has been emitted, `get_initial_beacon_state` will execute to compute the `hash_tree_root` of `BeaconState`.
 
 ```python
 def get_initial_beacon_state(initial_validator_deposits: List[Deposit],
@@ -1213,9 +1229,16 @@ def process_deposit(state: BeaconState,
     Process a deposit from Ethereum 1.0.
     Note that this function mutates ``state``.
     """
+    proof_of_possession_data = DepositInput(
+        pubkey=pubkey,
+        withdrawal_credentials=withdrawal_credentials,
+        randao_commitment=randao_commitment,
+        proof_of_possession=EMPTY_SIGNATURE,
+    )
+
     assert bls_verify(
         pubkey=pubkey,
-        message=hash(bytes32(pubkey) + withdrawal_credentials + randao_commitment),
+        message=hash_tree_root(proof_of_possession_data),
         signature=proof_of_possession,
         domain=get_domain(
             state.fork_data,
@@ -1292,7 +1315,7 @@ def activate_validator(state: BeaconState,
     validator.latest_status_change_slot = state.slot
     state.validator_registry_delta_chain_tip = get_new_validator_registry_delta_chain_tip(
         validator_registry_delta_chain_tip=state.validator_registry_delta_chain_tip,
-        index=index,
+        validator_index=index,
         pubkey=validator.pubkey,
         flag=ACTIVATION,
     )
@@ -1347,7 +1370,7 @@ def exit_validator(state: BeaconState,
     validator.exit_count = state.validator_registry_exit_count
     state.validator_registry_delta_chain_tip = get_new_validator_registry_delta_chain_tip(
         validator_registry_delta_chain_tip=state.validator_registry_delta_chain_tip,
-        index=index,
+        validator_index=index,
         pubkey=validator.pubkey,
         flag=EXIT
     )
@@ -1371,7 +1394,7 @@ Below are the processing steps that happen at every slot.
 
 ### Block roots
 
-* Let `previous_block_root` be the `tree_hash_root` of the previous beacon block processed in the chain.
+* Let `previous_block_root` be the `hash_tree_root` of the previous beacon block processed in the chain.
 * Set `state.latest_block_roots = state.latest_block_roots[1:] + [previous_block_root]`.
 * If `state.slot % LATEST_BLOCK_ROOTS_LENGTH == 0` append `merkle_root(state.latest_block_roots)` to `state.batched_block_roots`.
 
@@ -1385,7 +1408,7 @@ Below are the processing steps that happen at every `block`.
 
 ### Proposer signature
 
-* Let `block_without_signature_root` be the `hash_tree_root` of `block` where `block.signature` is set to `[0, 0]`.
+* Let `block_without_signature_root` be the `hash_tree_root` of `block` where `block.signature` is set to `EMPTY_SIGNATURE`.
 * Let `proposal_root = hash_tree_root(ProposalSignedData(state.slot, BEACON_CHAIN_SHARD_NUMBER, block_without_signature_root))`.
 * Verify that `bls_verify(pubkey=state.validator_registry[get_beacon_proposer_index(state, state.slot)].pubkey, data=proposal_root, signature=block.signature, domain=get_domain(state.fork_data, state.slot, DOMAIN_PROPOSAL))`.