diff --git a/README.md b/README.md
index c5c88daf9..ce0ae8738 100644
--- a/README.md
+++ b/README.md
@@ -10,6 +10,7 @@ This repo hosts the current eth2.0 specifications. Discussions about design rati
 
 Core specifications for eth2.0 client validation can be found in [specs/core](specs/core). These are divided into phases. Each subsequent phase depends upon the prior. The current phases specified are:
 * [Phase 0 -- The Beacon Chain](specs/core/0_beacon-chain.md)
+* [Phase 1 -- Custody game](specs/core/1_custody-game.md)
 * [Phase 1 -- Shard Data Chains](specs/core/1_shard-data-chains.md)
 
 Accompanying documents can be found in [specs](specs) and include
diff --git a/specs/core/0_beacon-chain.md b/specs/core/0_beacon-chain.md
index fa0c97acb..f95cb29e8 100644
--- a/specs/core/0_beacon-chain.md
+++ b/specs/core/0_beacon-chain.md
@@ -18,7 +18,7 @@
         - [Time parameters](#time-parameters)
         - [State list lengths](#state-list-lengths)
         - [Reward and penalty quotients](#reward-and-penalty-quotients)
-        - [Max transactions per block](#max-transactions-per-block)
+        - [Max operations per block](#max-operations-per-block)
         - [Signature domains](#signature-domains)
     - [Data structures](#data-structures)
         - [Misc dependencies](#misc-dependencies)
@@ -34,7 +34,7 @@
             - [`Validator`](#validator)
             - [`PendingAttestation`](#pendingattestation)
             - [`HistoricalBatch`](#historicalbatch)
-        - [Beacon transactions](#beacon-transactions)
+        - [Beacon operations](#beacon-operations)
             - [`ProposerSlashing`](#proposerslashing)
             - [`AttesterSlashing`](#attesterslashing)
             - [`Attestation`](#attestation)
@@ -132,7 +132,7 @@
             - [Block header](#block-header)
             - [RANDAO](#randao)
             - [Eth1 data](#eth1-data-1)
-            - [Transactions](#transactions)
+            - [Operations](#operations)
                 - [Proposer slashings](#proposer-slashings)
                 - [Attester slashings](#attester-slashings)
                 - [Attestations](#attestations)
@@ -261,8 +261,7 @@ Code snippets appearing in `this style` are to be interpreted as Python code.
 * The `BASE_REWARD_QUOTIENT` parameter dictates the per-epoch reward. It corresponds to ~2.54% annual interest assuming 10 million participating ETH in every epoch.
 * The `INACTIVITY_PENALTY_QUOTIENT` equals `INVERSE_SQRT_E_DROP_TIME**2` where `INVERSE_SQRT_E_DROP_TIME := 2**12 epochs` (~18 days) is the time it takes the inactivity penalty to reduce the balance of non-participating [validators](#dfn-validator) to about `1/sqrt(e) ~= 60.6%`. Indeed, the balance retained by offline [validators](#dfn-validator) after `n` epochs is about `(1 - 1/INACTIVITY_PENALTY_QUOTIENT)**(n**2/2)` so after `INVERSE_SQRT_E_DROP_TIME` epochs it is roughly `(1 - 1/INACTIVITY_PENALTY_QUOTIENT)**(INACTIVITY_PENALTY_QUOTIENT/2) ~= 1/sqrt(e)`.
 
-
-### Max transactions per block
+### Max operations per block
 
 | Name | Value |
 | - | - |
@@ -460,7 +459,7 @@ The types are defined topologically to aid in facilitating an executable version
 }
 ```
 
-### Beacon transactions
+### Beacon operations
 
 #### `ProposerSlashing`
 
@@ -1188,6 +1187,9 @@ def verify_indexed_attestation(state: BeaconState, indexed_attestation: IndexedA
     custody_bit_0_indices = indexed_attestation.custody_bit_0_indices
     custody_bit_1_indices = indexed_attestation.custody_bit_1_indices
 
+    # ensure no duplicate indices across custody bits
+    assert len(set(custody_bit_0_indices).intersection(set(custody_bit_1_indices))) == 0
+
     if len(custody_bit_1_indices) > 0:  # [TO BE REMOVED IN PHASE 1]
         return False
 
@@ -2243,7 +2245,7 @@ def process_eth1_data(state: BeaconState, block: BeaconBlock) -> None:
     state.eth1_data_votes.append(Eth1DataVote(eth1_data=block.body.eth1_data, vote_count=1))
 ```
 
-#### Transactions
+#### Operations
 
 ##### Proposer slashings
 
@@ -2255,7 +2257,7 @@ For each `proposer_slashing` in `block.body.proposer_slashings`, run the followi
 def process_proposer_slashing(state: BeaconState,
                               proposer_slashing: ProposerSlashing) -> None:
     """
-    Process ``ProposerSlashing`` transaction.
+    Process ``ProposerSlashing`` operation.
     Note that this function mutates ``state``.
     """
     proposer = state.validator_registry[proposer_slashing.proposer_index]
@@ -2286,7 +2288,7 @@ For each `attester_slashing` in `block.body.attester_slashings`, run the followi
 def process_attester_slashing(state: BeaconState,
                               attester_slashing: AttesterSlashing) -> None:
     """
-    Process ``AttesterSlashing`` transaction.
+    Process ``AttesterSlashing`` operation.
     Note that this function mutates ``state``.
     """
     attestation1 = attester_slashing.attestation_1
@@ -2300,10 +2302,12 @@ def process_attester_slashing(state: BeaconState,
 
     assert verify_indexed_attestation(state, attestation1)
     assert verify_indexed_attestation(state, attestation2)
+    attesting_indices_1 = attestation1.custody_bit_0_indices + attestation1.custody_bit_1_indices
+    attesting_indices_2 = attestation2.custody_bit_0_indices + attestation2.custody_bit_1_indices
     slashable_indices = [
-        index for index in attestation1.validator_indices
+        index for index in attesting_indices_1
         if (
-            index in attestation2.validator_indices and
+            index in attesting_indices_2 and
             is_slashable_validator(state.validator_registry[index], get_current_epoch(state))
         )
     ]
@@ -2321,7 +2325,7 @@ For each `attestation` in `block.body.attestations`, run the following function:
 ```python
 def process_attestation(state: BeaconState, attestation: Attestation) -> None:
     """
-    Process ``Attestation`` transaction.
+    Process ``Attestation`` operation.
     Note that this function mutates ``state``.
     """
     assert max(GENESIS_SLOT, state.slot - SLOTS_PER_EPOCH) <= attestation.data.slot
@@ -2370,7 +2374,7 @@ For each `exit` in `block.body.voluntary_exits`, run the following function:
 ```python
 def process_voluntary_exit(state: BeaconState, exit: VoluntaryExit) -> None:
     """
-    Process ``VoluntaryExit`` transaction.
+    Process ``VoluntaryExit`` operation.
     Note that this function mutates ``state``.
     """
     validator = state.validator_registry[exit.validator_index]
@@ -2406,7 +2410,7 @@ For each `transfer` in `block.body.transfers`, run the following function:
 ```python
 def process_transfer(state: BeaconState, transfer: Transfer) -> None:
     """
-    Process ``Transfer`` transaction.
+    Process ``Transfer`` operation.
     Note that this function mutates ``state``.
     """
     # Verify the amount and fee aren't individually too big (for anti-overflow purposes)
diff --git a/specs/core/1_custody-game.md b/specs/core/1_custody-game.md
index fd754634e..e28536d34 100644
--- a/specs/core/1_custody-game.md
+++ b/specs/core/1_custody-game.md
@@ -13,7 +13,7 @@
     - [Constants](#constants)
         - [Misc](#misc)
         - [Time parameters](#time-parameters)
-        - [Max transactions per block](#max-transactions-per-block)
+        - [Max operations per block](#max-operations-per-block)
         - [Signature domains](#signature-domains)
     - [Data structures](#data-structures)
         - [Custody objects](#custody-objects)
@@ -33,7 +33,7 @@
         - [`epoch_to_custody_period`](#epoch_to_custody_period)
         - [`verify_custody_key`](#verify_custody_key)
     - [Per-block processing](#per-block-processing)
-        - [Transactions](#transactions)
+        - [Operations](#operations)
             - [Custody reveals](#custody-reveals)
             - [Chunk challenges](#chunk-challenges)
             - [Bit challenges](#bit-challenges)
@@ -79,7 +79,7 @@ This document details the beacon chain additions and changes in Phase 1 of Ether
 | `EPOCHS_PER_CUSTODY_PERIOD` | `2**11` (= 2,048) | epochs | ~9 days |
 | `CUSTODY_RESPONSE_DEADLINE` | `2**14` (= 16,384) | epochs | ~73 days |
 
-### Max transactions per block
+### Max operations per block
 
 | Name | Value |
 | - | - |
@@ -259,9 +259,9 @@ def verify_custody_key(state: BeaconState, reveal: CustodyKeyReveal) -> bool:
 
 ## Per-block processing
 
-### Transactions
+### Operations
 
-Add the following transactions to the per-block processing, in order the given below and after all other transactions in phase 0.
+Add the following operations to the per-block processing, in order the given below and after all other operations in phase 0.
 
 #### Custody reveals
 
diff --git a/tests/phase0/block_processing/test_process_attester_slashing.py b/tests/phase0/block_processing/test_process_attester_slashing.py
new file mode 100644
index 000000000..06f214c4b
--- /dev/null
+++ b/tests/phase0/block_processing/test_process_attester_slashing.py
@@ -0,0 +1,115 @@
+from copy import deepcopy
+import pytest
+
+import build.phase0.spec as spec
+from build.phase0.spec import (
+    get_balance,
+    get_beacon_proposer_index,
+    process_attester_slashing,
+)
+from tests.phase0.helpers import (
+    get_valid_attester_slashing,
+)
+
+# mark entire file as 'attester_slashing'
+pytestmark = pytest.mark.attester_slashings
+
+
+def run_attester_slashing_processing(state, attester_slashing, valid=True):
+    """
+    Run ``process_attester_slashing`` returning the pre and post state.
+    If ``valid == False``, run expecting ``AssertionError``
+    """
+    post_state = deepcopy(state)
+
+    if not valid:
+        with pytest.raises(AssertionError):
+            process_attester_slashing(post_state, attester_slashing)
+        return state, None
+
+    process_attester_slashing(post_state, attester_slashing)
+
+    slashed_index = attester_slashing.attestation_1.custody_bit_0_indices[0]
+    slashed_validator = post_state.validator_registry[slashed_index]
+    assert not slashed_validator.initiated_exit
+    assert slashed_validator.slashed
+    assert slashed_validator.exit_epoch < spec.FAR_FUTURE_EPOCH
+    assert slashed_validator.withdrawable_epoch < spec.FAR_FUTURE_EPOCH
+    # lost whistleblower reward
+    assert (
+        get_balance(post_state, slashed_index) <
+        get_balance(state, slashed_index)
+    )
+    proposer_index = get_beacon_proposer_index(state, state.slot)
+    # gained whistleblower reward
+    assert (
+        get_balance(post_state, proposer_index) >
+        get_balance(state, proposer_index)
+    )
+
+    return state, post_state
+
+
+def test_success_double(state):
+    attester_slashing = get_valid_attester_slashing(state)
+
+    pre_state, post_state = run_attester_slashing_processing(state, attester_slashing)
+
+    return pre_state, attester_slashing, post_state
+
+
+def test_success_surround(state):
+    attester_slashing = get_valid_attester_slashing(state)
+
+    # set attestion1 to surround attestation 2
+    attester_slashing.attestation_1.data.source_epoch = attester_slashing.attestation_2.data.source_epoch - 1
+    attester_slashing.attestation_1.data.slot = attester_slashing.attestation_2.data.slot + spec.SLOTS_PER_EPOCH
+
+    pre_state, post_state = run_attester_slashing_processing(state, attester_slashing)
+
+    return pre_state, attester_slashing, post_state
+
+
+def test_same_data(state):
+    attester_slashing = get_valid_attester_slashing(state)
+
+    attester_slashing.attestation_1.data = attester_slashing.attestation_2.data
+
+    pre_state, post_state = run_attester_slashing_processing(state, attester_slashing, False)
+
+    return pre_state, attester_slashing, post_state
+
+
+def test_no_double_or_surround(state):
+    attester_slashing = get_valid_attester_slashing(state)
+
+    attester_slashing.attestation_1.data.slot += spec.SLOTS_PER_EPOCH
+
+    pre_state, post_state = run_attester_slashing_processing(state, attester_slashing, False)
+
+    return pre_state, attester_slashing, post_state
+
+
+def test_participants_already_slashed(state):
+    attester_slashing = get_valid_attester_slashing(state)
+
+    # set all indices to slashed
+    attestation_1 = attester_slashing.attestation_1
+    validator_indices = attestation_1.custody_bit_0_indices + attestation_1.custody_bit_1_indices
+    for index in validator_indices:
+        state.validator_registry[index].slashed = True
+
+    pre_state, post_state = run_attester_slashing_processing(state, attester_slashing, False)
+
+    return pre_state, attester_slashing, post_state
+
+
+def test_custody_bit_0_and_1(state):
+    attester_slashing = get_valid_attester_slashing(state)
+
+    attester_slashing.attestation_1.custody_bit_1_indices = (
+        attester_slashing.attestation_1.custody_bit_0_indices
+    )
+    pre_state, post_state = run_attester_slashing_processing(state, attester_slashing, False)
+
+    return pre_state, attester_slashing, post_state
diff --git a/tests/phase0/helpers.py b/tests/phase0/helpers.py
index 083d31b80..0fd7bab73 100644
--- a/tests/phase0/helpers.py
+++ b/tests/phase0/helpers.py
@@ -12,6 +12,7 @@ from build.phase0.spec import (
     Attestation,
     AttestationData,
     AttestationDataAndCustodyBit,
+    AttesterSlashing,
     BeaconBlockHeader,
     Deposit,
     DepositData,
@@ -19,6 +20,7 @@ from build.phase0.spec import (
     ProposerSlashing,
     VoluntaryExit,
     # functions
+    convert_to_indexed,
     get_active_validator_indices,
     get_attestation_participants,
     get_block_root,
@@ -241,6 +243,17 @@ def get_valid_proposer_slashing(state):
     )
 
 
+def get_valid_attester_slashing(state):
+    attestation_1 = get_valid_attestation(state)
+    attestation_2 = deepcopy(attestation_1)
+    attestation_2.data.target_root = b'\x01'*32
+
+    return AttesterSlashing(
+        attestation_1=convert_to_indexed(state, attestation_1),
+        attestation_2=convert_to_indexed(state, attestation_2),
+    )
+
+
 def get_valid_attestation(state, slot=None):
     if slot is None:
         slot = state.slot
diff --git a/tests/phase0/test_sanity.py b/tests/phase0/test_sanity.py
index a7a6b9961..e1308aebe 100644
--- a/tests/phase0/test_sanity.py
+++ b/tests/phase0/test_sanity.py
@@ -17,6 +17,7 @@ from build.phase0.spec import (
     # functions
     get_active_validator_indices,
     get_balance,
+    get_beacon_proposer_index,
     get_block_root,
     get_current_epoch,
     get_domain,
@@ -41,6 +42,7 @@ from tests.phase0.helpers import (
     build_empty_block_for_next_slot,
     force_registry_change_at_next_epoch,
     get_valid_attestation,
+    get_valid_attester_slashing,
     get_valid_proposer_slashing,
     privkeys,
     pubkeys,
@@ -141,6 +143,39 @@ def test_proposer_slashing(state):
     return state, [block], test_state
 
 
+def test_attester_slashing(state):
+    test_state = deepcopy(state)
+    attester_slashing = get_valid_attester_slashing(state)
+    validator_index = attester_slashing.attestation_1.custody_bit_0_indices[0]
+
+    #
+    # Add to state via block transition
+    #
+    block = build_empty_block_for_next_slot(test_state)
+    block.body.attester_slashings.append(attester_slashing)
+    state_transition(test_state, block)
+
+    assert not state.validator_registry[validator_index].initiated_exit
+    assert not state.validator_registry[validator_index].slashed
+
+    slashed_validator = test_state.validator_registry[validator_index]
+    assert not slashed_validator.initiated_exit
+    assert slashed_validator.slashed
+    assert slashed_validator.exit_epoch < spec.FAR_FUTURE_EPOCH
+    assert slashed_validator.withdrawable_epoch < spec.FAR_FUTURE_EPOCH
+    # lost whistleblower reward
+    assert get_balance(test_state, validator_index) < get_balance(state, validator_index)
+
+    proposer_index = get_beacon_proposer_index(test_state, test_state.slot)
+    # gained whistleblower reward
+    assert (
+        get_balance(test_state, proposer_index) >
+        get_balance(state, proposer_index)
+    )
+
+    return state, [block], test_state
+
+
 def test_deposit_in_block(state):
     pre_state = deepcopy(state)
     test_deposit_data_leaves = [ZERO_HASH] * len(pre_state.validator_registry)
diff --git a/utils/phase0/state_transition.py b/utils/phase0/state_transition.py
index cfd941c42..2c420014f 100644
--- a/utils/phase0/state_transition.py
+++ b/utils/phase0/state_transition.py
@@ -22,31 +22,31 @@ def expected_deposit_count(state: BeaconState) -> int:
     )
 
 
-def process_transaction_type(state: BeaconState,
-                             transactions: List[Any],
-                             max_transactions: int,
-                             tx_fn: Callable[[BeaconState, Any], None]) -> None:
-    assert len(transactions) <= max_transactions
-    for transaction in transactions:
-        tx_fn(state, transaction)
+def process_operation_type(state: BeaconState,
+                           operations: List[Any],
+                           max_operations: int,
+                           tx_fn: Callable[[BeaconState, Any], None]) -> None:
+    assert len(operations) <= max_operations
+    for operation in operations:
+        tx_fn(state, operation)
 
 
-def process_transactions(state: BeaconState, block: BeaconBlock) -> None:
-    process_transaction_type(
+def process_operations(state: BeaconState, block: BeaconBlock) -> None:
+    process_operation_type(
         state,
         block.body.proposer_slashings,
         spec.MAX_PROPOSER_SLASHINGS,
         spec.process_proposer_slashing,
     )
 
-    process_transaction_type(
+    process_operation_type(
         state,
         block.body.attester_slashings,
         spec.MAX_ATTESTER_SLASHINGS,
         spec.process_attester_slashing,
     )
 
-    process_transaction_type(
+    process_operation_type(
         state,
         block.body.attestations,
         spec.MAX_ATTESTATIONS,
@@ -54,14 +54,14 @@ def process_transactions(state: BeaconState, block: BeaconBlock) -> None:
     )
 
     assert len(block.body.deposits) == expected_deposit_count(state)
-    process_transaction_type(
+    process_operation_type(
         state,
         block.body.deposits,
         spec.MAX_DEPOSITS,
         spec.process_deposit,
     )
 
-    process_transaction_type(
+    process_operation_type(
         state,
         block.body.voluntary_exits,
         spec.MAX_VOLUNTARY_EXITS,
@@ -69,7 +69,7 @@ def process_transactions(state: BeaconState, block: BeaconBlock) -> None:
     )
 
     assert len(block.body.transfers) == len(set(block.body.transfers))
-    process_transaction_type(
+    process_operation_type(
         state,
         block.body.transfers,
         spec.MAX_TRANSFERS,
@@ -84,7 +84,7 @@ def process_block(state: BeaconState,
     spec.process_randao(state, block)
     spec.process_eth1_data(state, block)
 
-    process_transactions(state, block)
+    process_operations(state, block)
     if verify_state_root:
         spec.verify_block_state_root(state, block)