diff --git a/configs/mainnet/altair.yaml b/configs/mainnet/altair.yaml
index 13b62bd7a..2e4839c16 100644
--- a/configs/mainnet/altair.yaml
+++ b/configs/mainnet/altair.yaml
@@ -31,3 +31,9 @@ EPOCHS_PER_SYNC_COMMITTEE_PERIOD: 256
 # Signature domains
 # ---------------------------------------------------------------
 DOMAIN_SYNC_COMMITTEE: 0x07000000
+
+
+# Sync protocol
+# ---------------------------------------------------------------
+# 2**13 (=8192)
+LIGHT_CLIENT_UPDATE_TIMEOUT: 8192
diff --git a/configs/minimal/altair.yaml b/configs/minimal/altair.yaml
index e98fee699..80233404d 100644
--- a/configs/minimal/altair.yaml
+++ b/configs/minimal/altair.yaml
@@ -31,3 +31,9 @@ EPOCHS_PER_SYNC_COMMITTEE_PERIOD: 8
 # Signature domains
 # ---------------------------------------------------------------
 DOMAIN_SYNC_COMMITTEE: 0x07000000
+
+
+# Sync protocol
+# ---------------------------------------------------------------
+# [customized]
+LIGHT_CLIENT_UPDATE_TIMEOUT: 32
diff --git a/setup.py b/setup.py
index d0a2371e8..3bd64869f 100644
--- a/setup.py
+++ b/setup.py
@@ -10,10 +10,17 @@ from typing import Dict, NamedTuple, List
 FUNCTION_REGEX = r'^def [\w_]*'
 
 
+# Definitions in context.py
+PHASE0 = 'phase0'
+ALTAIR = 'altair'
+PHASE1 = 'phase1'
+
+
 class SpecObject(NamedTuple):
     functions: Dict[str, str]
     custom_types: Dict[str, str]
     constants: Dict[str, str]
+    ssz_dep_constants: Dict[str, str]  # the constants that depend on ssz_objects
     ssz_objects: Dict[str, str]
     dataclasses: Dict[str, str]
 
@@ -35,6 +42,7 @@ def get_spec(file_name: str) -> SpecObject:
     current_name = None  # most recent section title
     functions: Dict[str, str] = {}
     constants: Dict[str, str] = {}
+    ssz_dep_constants: Dict[str, str] = {}
     ssz_objects: Dict[str, str] = {}
     dataclasses: Dict[str, str] = {}
     function_matcher = re.compile(FUNCTION_REGEX)
@@ -88,10 +96,20 @@ def get_spec(file_name: str) -> SpecObject:
                         if c not in 'ABCDEFGHIJKLMNOPQRSTUVWXYZ_0123456789':
                             is_constant_def = False
                     if is_constant_def:
-                        constants[row[0]] = row[1].replace('**TBD**', '2**32')
+                        if row[1].startswith('get_generalized_index'):
+                            ssz_dep_constants[row[0]] = row[1]
+                        else:
+                            constants[row[0]] = row[1].replace('**TBD**', '2**32')
                     elif row[1].startswith('uint') or row[1].startswith('Bytes'):
                         custom_types[row[0]] = row[1]
-    return SpecObject(functions, custom_types, constants, ssz_objects, dataclasses)
+    return SpecObject(
+        functions=functions,
+        custom_types=custom_types,
+        constants=constants,
+        ssz_dep_constants=ssz_dep_constants,
+        ssz_objects=ssz_objects,
+        dataclasses=dataclasses,
+    )
 
 
 CONFIG_LOADER = '''
@@ -157,10 +175,10 @@ SSZObject = TypeVar('SSZObject', bound=View)
 
 CONFIG_NAME = 'mainnet'
 '''
-LIGHTCLIENT_IMPORT = '''from eth2spec.phase0 import spec as phase0
+ALTAIR_IMPORTS = '''from eth2spec.phase0 import spec as phase0
 from eth2spec.config.config_util import apply_constants_config
 from typing import (
-    Any, Dict, Set, Sequence, NewType, Tuple, TypeVar, Callable, Optional
+    Any, Dict, Set, Sequence, NewType, Tuple, TypeVar, Callable, Optional, Union
 )
 
 from dataclasses import (
@@ -174,6 +192,7 @@ from eth2spec.utils.ssz.ssz_impl import hash_tree_root, copy, uint_to_bytes
 from eth2spec.utils.ssz.ssz_typing import (
     View, boolean, Container, List, Vector, uint8, uint32, uint64,
     Bytes1, Bytes4, Bytes32, Bytes48, Bytes96, Bitlist, Bitvector,
+    Path,
 )
 from eth2spec.utils import bls
 
@@ -196,6 +215,12 @@ def ceillog2(x: int) -> uint64:
     if x < 1:
         raise ValueError(f"ceillog2 accepts only positive values, x={x}")
     return uint64((x - 1).bit_length())
+
+
+def floorlog2(x: int) -> uint64:
+    if x < 1:
+        raise ValueError(f"floorlog2 accepts only positive values, x={x}")
+    return uint64(x.bit_length() - 1)
 '''
 PHASE0_SUNDRY_FUNCTIONS = '''
 def get_eth1_data(block: Eth1Block) -> Eth1Data:
@@ -277,6 +302,35 @@ get_start_shard = cache_this(
     _get_start_shard, lru_size=SLOTS_PER_EPOCH * 3)'''
 
 
+ALTAIR_SUNDRY_FUNCTIONS = '''
+
+def get_generalized_index(ssz_class: Any, *path: Sequence[Union[int, SSZVariableName]]) -> GeneralizedIndex:
+    ssz_path = Path(ssz_class)
+    for item in path:
+        ssz_path = ssz_path / item
+    return GeneralizedIndex(ssz_path.gindex())'''
+
+
+# The constants that depend on SSZ objects
+# Will verify the value at the end of the spec
+ALTAIR_HARDCODED_SSZ_DEP_CONSTANTS = {
+    'FINALIZED_ROOT_INDEX': 'GeneralizedIndex(105)',
+    'NEXT_SYNC_COMMITTEE_INDEX': 'GeneralizedIndex(54)',
+}
+
+
+def is_phase0(fork):
+    return fork == PHASE0
+
+
+def is_altair(fork):
+    return fork == ALTAIR
+
+
+def is_phase1(fork):
+    return fork == PHASE1
+
+
 def objects_to_spec(spec_object: SpecObject, imports: str, fork: str, ordered_class_objects: Dict[str, str]) -> str:
     """
     Given all the objects that constitute a spec, combine them into a single pyfile.
@@ -290,7 +344,7 @@ def objects_to_spec(spec_object: SpecObject, imports: str, fork: str, ordered_cl
         )
     )
     for k in list(spec_object.functions):
-        if "ceillog2" in k:
+        if "ceillog2" in k or "floorlog2" in k:
             del spec_object.functions[k]
     functions_spec = '\n\n'.join(spec_object.functions.values())
     for k in list(spec_object.constants.keys()):
@@ -298,19 +352,33 @@ def objects_to_spec(spec_object: SpecObject, imports: str, fork: str, ordered_cl
             spec_object.constants[k] += "  # noqa: E501"
     constants_spec = '\n'.join(map(lambda x: '%s = %s' % (x, spec_object.constants[x]), spec_object.constants))
     ordered_class_objects_spec = '\n\n'.join(ordered_class_objects.values())
+
+    if is_altair(fork):
+        altair_ssz_dep_constants = '\n'.join(map(lambda x: '%s = %s' % (x, ALTAIR_HARDCODED_SSZ_DEP_CONSTANTS[x]), ALTAIR_HARDCODED_SSZ_DEP_CONSTANTS))
+
     spec = (
             imports
             + '\n\n' + f"fork = \'{fork}\'\n"
             + '\n\n' + new_type_definitions
             + '\n' + SUNDRY_CONSTANTS_FUNCTIONS
+            # The constants that some SSZ containers require. Need to be defined before `constants_spec`
+            + ('\n\n' + altair_ssz_dep_constants if is_altair(fork) else '')
             + '\n\n' + constants_spec
             + '\n\n' + CONFIG_LOADER
             + '\n\n' + ordered_class_objects_spec
             + '\n\n' + functions_spec
+            # Functions to make pyspec work
             + '\n' + PHASE0_SUNDRY_FUNCTIONS
+            + ('\n' + ALTAIR_SUNDRY_FUNCTIONS if is_altair(fork) else '')
+            + ('\n' + PHASE1_SUNDRY_FUNCTIONS if is_phase1(fork) else '')
     )
-    if fork == 'phase1':
-        spec += '\n' + PHASE1_SUNDRY_FUNCTIONS
+
+    # Since some constants are hardcoded in setup.py, the following assertions verify that the hardcoded constants are
+    # as same as the spec definition.
+    if is_altair(fork):
+        altair_ssz_dep_constants_verification = '\n'.join(map(lambda x: 'assert %s == %s' % (x, spec_object.ssz_dep_constants[x]), ALTAIR_HARDCODED_SSZ_DEP_CONSTANTS))
+        spec += '\n\n\n' + altair_ssz_dep_constants_verification
+
     spec += '\n'
     return spec
 
@@ -332,7 +400,7 @@ ignored_dependencies = [
     'Bytes1', 'Bytes4', 'Bytes32', 'Bytes48', 'Bytes96', 'Bitlist', 'Bitvector',
     'uint8', 'uint16', 'uint32', 'uint64', 'uint128', 'uint256',
     'bytes', 'byte', 'ByteList', 'ByteVector',
-    'Dict', 'dict', 'field',
+    'Dict', 'dict', 'field', 'ceillog2', 'floorlog2',
 ]
 
 
@@ -373,20 +441,28 @@ def combine_spec_objects(spec0: SpecObject, spec1: SpecObject) -> SpecObject:
     """
     Takes in two spec variants (as tuples of their objects) and combines them using the appropriate combiner function.
     """
-    functions0, custom_types0, constants0, ssz_objects0, dataclasses0 = spec0
-    functions1, custom_types1, constants1, ssz_objects1, dataclasses1 = spec1
+    functions0, custom_types0, constants0, ssz_dep_constants0, ssz_objects0, dataclasses0 = spec0
+    functions1, custom_types1, constants1, ssz_dep_constants1, ssz_objects1, dataclasses1 = spec1
     functions = combine_functions(functions0, functions1)
     custom_types = combine_constants(custom_types0, custom_types1)
     constants = combine_constants(constants0, constants1)
+    ssz_dep_constants = combine_constants(ssz_dep_constants0, ssz_dep_constants1)
     ssz_objects = combine_ssz_objects(ssz_objects0, ssz_objects1, custom_types)
     dataclasses = combine_functions(dataclasses0, dataclasses1)
-    return SpecObject(functions, custom_types, constants, ssz_objects, dataclasses)
+    return SpecObject(
+        functions=functions,
+        custom_types=custom_types,
+        constants=constants,
+        ssz_dep_constants=ssz_dep_constants,
+        ssz_objects=ssz_objects,
+        dataclasses=dataclasses,
+    )
 
 
 fork_imports = {
     'phase0': PHASE0_IMPORTS,
     'phase1': PHASE1_IMPORTS,
-    'altair': LIGHTCLIENT_IMPORT,
+    'altair': ALTAIR_IMPORTS,
 }
 
 
@@ -423,7 +499,7 @@ class PySpecCommand(Command):
     def initialize_options(self):
         """Set default values for options."""
         # Each user option must be listed here with their default value.
-        self.spec_fork = 'phase0'
+        self.spec_fork = PHASE0
         self.md_doc_paths = ''
         self.out_dir = 'pyspec_output'
 
@@ -432,14 +508,14 @@ class PySpecCommand(Command):
         if len(self.md_doc_paths) == 0:
             print("no paths were specified, using default markdown file paths for pyspec"
                   " build (spec fork: %s)" % self.spec_fork)
-            if self.spec_fork == "phase0":
+            if is_phase0(self.spec_fork):
                 self.md_doc_paths = """
                     specs/phase0/beacon-chain.md
                     specs/phase0/fork-choice.md
                     specs/phase0/validator.md
                     specs/phase0/weak-subjectivity.md
                 """
-            elif self.spec_fork == "phase1":
+            elif is_phase1(self.spec_fork):
                 self.md_doc_paths = """
                     specs/phase0/beacon-chain.md
                     specs/phase0/fork-choice.md
@@ -453,7 +529,7 @@ class PySpecCommand(Command):
                     specs/phase1/shard-fork-choice.md
                     specs/phase1/validator.md
                 """
-            elif self.spec_fork == "altair":
+            elif is_altair(self.spec_fork):
                 self.md_doc_paths = """
                     specs/phase0/beacon-chain.md
                     specs/phase0/fork-choice.md
@@ -461,6 +537,7 @@ class PySpecCommand(Command):
                     specs/phase0/weak-subjectivity.md
                     specs/altair/beacon-chain.md
                     specs/altair/fork.md
+                    specs/altair/sync-protocol.md
                 """
                 # TODO: add specs/altair/sync-protocol.md back when the GeneralizedIndex helpers are included.
             else:
diff --git a/specs/altair/sync-protocol.md b/specs/altair/sync-protocol.md
index 310aad2df..28705803b 100644
--- a/specs/altair/sync-protocol.md
+++ b/specs/altair/sync-protocol.md
@@ -14,11 +14,13 @@
   - [Misc](#misc)
   - [Time parameters](#time-parameters)
 - [Containers](#containers)
-    - [`LightClientSnapshot`](#lightclientsnapshot)
-    - [`LightClientUpdate`](#lightclientupdate)
-    - [`LightClientStore`](#lightclientstore)
+  - [`LightClientSnapshot`](#lightclientsnapshot)
+  - [`LightClientUpdate`](#lightclientupdate)
+  - [`LightClientStore`](#lightclientstore)
+- [Helper functions](#helper-functions)
+  - [`get_subtree_index`](#get_subtree_index)
 - [Light client state updates](#light-client-state-updates)
-    - [`is_valid_light_client_update`](#is_valid_light_client_update)
+    - [`validate_light_client_update`](#validate_light_client_update)
     - [`apply_light_client_update`](#apply_light_client_update)
     - [`process_light_client_update`](#process_light_client_update)
 
@@ -39,8 +41,8 @@ uses sync committees introduced in [this beacon chain extension](./beacon-chain.
 
 | Name | Value |
 | - | - |
-| `FINALIZED_ROOT_INDEX` | `Index(BeaconState, 'finalized_checkpoint', 'root')` |
-| `NEXT_SYNC_COMMITTEE_INDEX` | `Index(BeaconState, 'next_sync_committee')` |
+| `FINALIZED_ROOT_INDEX` | `get_generalized_index(BeaconState, 'finalized_checkpoint', 'root')` |
+| `NEXT_SYNC_COMMITTEE_INDEX` | `get_generalized_index(BeaconState, 'next_sync_committee')` |
 
 ## Configuration
 
@@ -59,7 +61,7 @@ uses sync committees introduced in [this beacon chain extension](./beacon-chain.
 
 ## Containers
 
-#### `LightClientSnapshot`
+### `LightClientSnapshot`
 
 ```python
 class LightClientSnapshot(Container):
@@ -70,7 +72,7 @@ class LightClientSnapshot(Container):
     next_sync_committee: SyncCommittee
 ```
 
-#### `LightClientUpdate`
+### `LightClientUpdate`
 
 ```python
 class LightClientUpdate(Container):
@@ -78,10 +80,10 @@ class LightClientUpdate(Container):
     header: BeaconBlockHeader
     # Next sync committee corresponding to the header
     next_sync_committee: SyncCommittee
-    next_sync_committee_branch: Vector[Bytes32, log2(NEXT_SYNC_COMMITTEE_INDEX)]
+    next_sync_committee_branch: Vector[Bytes32, floorlog2(NEXT_SYNC_COMMITTEE_INDEX)]
     # Finality proof for the update header
     finality_header: BeaconBlockHeader
-    finality_branch: Vector[Bytes32, log2(FINALIZED_ROOT_INDEX)]
+    finality_branch: Vector[Bytes32, floorlog2(FINALIZED_ROOT_INDEX)]
     # Sync committee aggregate signature
     sync_committee_bits: Bitvector[SYNC_COMMITTEE_SIZE]
     sync_committee_signature: BLSSignature
@@ -89,7 +91,7 @@ class LightClientUpdate(Container):
     fork_version: Version
 ```
 
-#### `LightClientStore`
+### `LightClientStore`
 
 ```python
 class LightClientStore(Container):
@@ -97,14 +99,24 @@ class LightClientStore(Container):
     valid_updates: List[LightClientUpdate, MAX_VALID_LIGHT_CLIENT_UPDATES]
 ```
 
+## Helper functions
+
+### `get_subtree_index`
+
+```python
+def get_subtree_index(generalized_index: GeneralizedIndex) -> uint64:
+    return uint64(generalized_index % 2**(floorlog2(generalized_index)))
+```
+
 ## Light client state updates
 
 A light client maintains its state in a `store` object of type `LightClientStore` and receives `update` objects of type `LightClientUpdate`. Every `update` triggers `process_light_client_update(store, update, current_slot)` where `current_slot` is the current slot based on some local clock.
 
-#### `is_valid_light_client_update`
+#### `validate_light_client_update`
 
 ```python
-def is_valid_light_client_update(snapshot: LightClientSnapshot, update: LightClientUpdate) -> bool:
+def validate_light_client_update(snapshot: LightClientSnapshot, update: LightClientUpdate,
+                                 genesis_validators_root: Root) -> None:
     # Verify update slot is larger than snapshot slot
     assert update.header.slot > snapshot.header.slot
 
@@ -116,28 +128,28 @@ def is_valid_light_client_update(snapshot: LightClientSnapshot, update: LightCli
     # Verify update header root is the finalized root of the finality header, if specified
     if update.finality_header == BeaconBlockHeader():
         signed_header = update.header
-        assert update.finality_branch == [ZERO_HASH for _ in range(log2(FINALIZED_ROOT_INDEX))]
+        assert update.finality_branch == [Bytes32() for _ in range(floorlog2(FINALIZED_ROOT_INDEX))]
     else:
         signed_header = update.finality_header
         assert is_valid_merkle_branch(
             leaf=hash_tree_root(update.header),
             branch=update.finality_branch,
-            depth=log2(FINALIZED_ROOT_INDEX),
-            index=FINALIZED_ROOT_INDEX % 2**log2(FINALIZED_ROOT_INDEX),
+            depth=floorlog2(FINALIZED_ROOT_INDEX),
+            index=get_subtree_index(FINALIZED_ROOT_INDEX),
             root=update.finality_header.state_root,
         )
 
     # Verify update next sync committee if the update period incremented
     if update_period == snapshot_period:
         sync_committee = snapshot.current_sync_committee
-        assert update.next_sync_committee_branch == [ZERO_HASH for _ in range(log2(NEXT_SYNC_COMMITTEE_INDEX))]
+        assert update.next_sync_committee_branch == [Bytes32() for _ in range(floorlog2(NEXT_SYNC_COMMITTEE_INDEX))]
     else:
         sync_committee = snapshot.next_sync_committee
         assert is_valid_merkle_branch(
             leaf=hash_tree_root(update.next_sync_committee),
             branch=update.next_sync_committee_branch,
-            depth=log2(NEXT_SYNC_COMMITTEE_INDEX),
-            index=NEXT_SYNC_COMMITTEE_INDEX % 2**log2(NEXT_SYNC_COMMITTEE_INDEX),
+            depth=floorlog2(NEXT_SYNC_COMMITTEE_INDEX),
+            index=get_subtree_index(NEXT_SYNC_COMMITTEE_INDEX),
             root=update.header.state_root,
         )
 
@@ -146,11 +158,9 @@ def is_valid_light_client_update(snapshot: LightClientSnapshot, update: LightCli
 
     # Verify sync committee aggregate signature
     participant_pubkeys = [pubkey for (bit, pubkey) in zip(update.sync_committee_bits, sync_committee.pubkeys) if bit]
-    domain = compute_domain(DOMAIN_SYNC_COMMITTEE, update.fork_version)
+    domain = compute_domain(DOMAIN_SYNC_COMMITTEE, update.fork_version, genesis_validators_root)
     signing_root = compute_signing_root(signed_header, domain)
     assert bls.FastAggregateVerify(participant_pubkeys, signing_root, update.sync_committee_signature)
-
-    return True
 ```
 
 #### `apply_light_client_update`
@@ -168,17 +178,23 @@ def apply_light_client_update(snapshot: LightClientSnapshot, update: LightClient
 #### `process_light_client_update`
 
 ```python
-def process_light_client_update(store: LightClientStore, update: LightClientUpdate, current_slot: Slot) -> None:
-    # Validate update
-    assert is_valid_light_client_update(store.snapshot, update)
+def process_light_client_update(store: LightClientStore, update: LightClientUpdate, current_slot: Slot,
+                                genesis_validators_root: Root) -> None:
+    validate_light_client_update(store.snapshot, update, genesis_validators_root)
     store.valid_updates.append(update)
 
-    if sum(update.sync_committee_bits) * 3 > len(update.sync_committee_bits) * 2 and update.header != update.finality_header:
-        # Apply update if 2/3 quorum is reached and we have a finality proof
-        apply_light_client_update(store, update)
+    if (
+        sum(update.sync_committee_bits) * 3 > len(update.sync_committee_bits) * 2
+        and update.finality_header != BeaconBlockHeader()
+    ):
+        # Apply update if (1) 2/3 quorum is reached and (2) we have a finality proof.
+        # Note that (2) means that the current light client design needs finality.
+        # It may be changed to re-organizable light client design. See the on-going issue eth2.0-specs#2182.
+        apply_light_client_update(store.snapshot, update)
         store.valid_updates = []
-    elif current_slot > snapshot.header.slot + LIGHT_CLIENT_UPDATE_TIMEOUT:
+    elif current_slot > store.snapshot.header.slot + LIGHT_CLIENT_UPDATE_TIMEOUT:
         # Forced best update when the update timeout has elapsed
-        apply_light_client_update(store, max(store.valid_updates, key=lambda update: sum(update.sync_committee_bits)))
+        apply_light_client_update(store.snapshot,
+                                  max(store.valid_updates, key=lambda update: sum(update.sync_committee_bits)))
         store.valid_updates = []
 ```
diff --git a/tests/core/pyspec/eth2spec/test/altair/unittests/test_helpers.py b/tests/core/pyspec/eth2spec/test/altair/unittests/test_helpers.py
new file mode 100644
index 000000000..d89ff6d84
--- /dev/null
+++ b/tests/core/pyspec/eth2spec/test/altair/unittests/test_helpers.py
@@ -0,0 +1,35 @@
+from eth2spec.test.context import (
+    spec_state_test,
+    with_phases,
+    ALTAIR,
+)
+from eth2spec.test.helpers.merkle import build_proof
+
+
+@with_phases([ALTAIR])
+@spec_state_test
+def test_next_sync_committee_tree(spec, state):
+    state.next_sync_committee: object = spec.SyncCommittee(
+        pubkeys=[state.validators[i]for i in range(spec.SYNC_COMMITTEE_SIZE)]
+    )
+    next_sync_committee_branch = build_proof(state.get_backing(), spec.NEXT_SYNC_COMMITTEE_INDEX)
+    assert spec.is_valid_merkle_branch(
+        leaf=state.next_sync_committee.hash_tree_root(),
+        branch=next_sync_committee_branch,
+        depth=spec.floorlog2(spec.NEXT_SYNC_COMMITTEE_INDEX),
+        index=spec.get_subtree_index(spec.NEXT_SYNC_COMMITTEE_INDEX),
+        root=state.hash_tree_root(),
+    )
+
+
+@with_phases([ALTAIR])
+@spec_state_test
+def test_finality_root_tree(spec, state):
+    finality_branch = build_proof(state.get_backing(), spec.FINALIZED_ROOT_INDEX)
+    assert spec.is_valid_merkle_branch(
+        leaf=state.finalized_checkpoint.root,
+        branch=finality_branch,
+        depth=spec.floorlog2(spec.FINALIZED_ROOT_INDEX),
+        index=spec.get_subtree_index(spec.FINALIZED_ROOT_INDEX),
+        root=state.hash_tree_root(),
+    )
diff --git a/tests/core/pyspec/eth2spec/test/altair/unittests/test_sync_protocol.py b/tests/core/pyspec/eth2spec/test/altair/unittests/test_sync_protocol.py
new file mode 100644
index 000000000..4c9b98e0a
--- /dev/null
+++ b/tests/core/pyspec/eth2spec/test/altair/unittests/test_sync_protocol.py
@@ -0,0 +1,216 @@
+from eth2spec.test.context import (
+    ALTAIR,
+    MINIMAL,
+    spec_state_test,
+    with_configs,
+    with_phases,
+)
+from eth2spec.test.helpers.attestations import next_epoch_with_attestations
+from eth2spec.test.helpers.block import (
+    build_empty_block,
+    build_empty_block_for_next_slot,
+)
+from eth2spec.test.helpers.state import (
+    next_slots,
+    state_transition_and_sign_block,
+)
+from eth2spec.test.helpers.sync_committee import (
+    compute_aggregate_sync_committee_signature,
+)
+from eth2spec.test.helpers.merkle import build_proof
+
+
+@with_phases([ALTAIR])
+@spec_state_test
+def test_process_light_client_update_not_updated(spec, state):
+    pre_snapshot = spec.LightClientSnapshot(
+        header=spec.BeaconBlockHeader(),
+        current_sync_committee=state.current_sync_committee,
+        next_sync_committee=state.next_sync_committee,
+    )
+    store = spec.LightClientStore(
+        snapshot=pre_snapshot,
+        valid_updates=[]
+    )
+
+    # Block at slot 1 doesn't increase sync committee period, so it won't update snapshot
+    block = build_empty_block_for_next_slot(spec, state)
+    signed_block = state_transition_and_sign_block(spec, state, block)
+    block_header = spec.BeaconBlockHeader(
+        slot=signed_block.message.slot,
+        proposer_index=signed_block.message.proposer_index,
+        parent_root=signed_block.message.parent_root,
+        state_root=signed_block.message.state_root,
+        body_root=signed_block.message.body.hash_tree_root(),
+    )
+    # Sync committee signing the header
+    committee = spec.get_sync_committee_indices(state, spec.get_current_epoch(state))
+    sync_committee_bits = [True] * len(committee)
+    sync_committee_signature = compute_aggregate_sync_committee_signature(
+        spec,
+        state,
+        block.slot,
+        committee,
+    )
+    next_sync_committee_branch = [spec.Bytes32() for _ in range(spec.floorlog2(spec.NEXT_SYNC_COMMITTEE_INDEX))]
+
+    # Ensure that finality checkpoint is genesis
+    assert state.finalized_checkpoint.epoch == 0
+    # Finality is unchanged
+    finality_header = spec.BeaconBlockHeader()
+    finality_branch = [spec.Bytes32() for _ in range(spec.floorlog2(spec.FINALIZED_ROOT_INDEX))]
+
+    update = spec.LightClientUpdate(
+        header=block_header,
+        next_sync_committee=state.next_sync_committee,
+        next_sync_committee_branch=next_sync_committee_branch,
+        finality_header=finality_header,
+        finality_branch=finality_branch,
+        sync_committee_bits=sync_committee_bits,
+        sync_committee_signature=sync_committee_signature,
+        fork_version=state.fork.current_version,
+    )
+
+    spec.process_light_client_update(store, update, state.slot, state.genesis_validators_root)
+
+    assert len(store.valid_updates) == 1
+    assert store.valid_updates[0] == update
+    assert store.snapshot == pre_snapshot
+
+
+@with_phases([ALTAIR])
+@spec_state_test
+@with_configs([MINIMAL], reason="too slow")
+def test_process_light_client_update_timeout(spec, state):
+    pre_snapshot = spec.LightClientSnapshot(
+        header=spec.BeaconBlockHeader(),
+        current_sync_committee=state.current_sync_committee,
+        next_sync_committee=state.next_sync_committee,
+    )
+    store = spec.LightClientStore(
+        snapshot=pre_snapshot,
+        valid_updates=[]
+    )
+
+    # Forward to next sync committee period
+    next_slots(spec, state, spec.SLOTS_PER_EPOCH * (spec.EPOCHS_PER_SYNC_COMMITTEE_PERIOD))
+    snapshot_period = spec.compute_epoch_at_slot(pre_snapshot.header.slot) // spec.EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+    update_period = spec.compute_epoch_at_slot(state.slot) // spec.EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+    assert snapshot_period + 1 == update_period
+
+    block = build_empty_block_for_next_slot(spec, state)
+    signed_block = state_transition_and_sign_block(spec, state, block)
+    block_header = spec.BeaconBlockHeader(
+        slot=signed_block.message.slot,
+        proposer_index=signed_block.message.proposer_index,
+        parent_root=signed_block.message.parent_root,
+        state_root=signed_block.message.state_root,
+        body_root=signed_block.message.body.hash_tree_root(),
+    )
+
+    # Sync committee signing the finalized_block_header
+    committee = spec.get_sync_committee_indices(state, spec.get_current_epoch(state))
+    sync_committee_bits = [True] * len(committee)
+    sync_committee_signature = compute_aggregate_sync_committee_signature(
+        spec,
+        state,
+        block_header.slot,
+        committee,
+        block_root=spec.Root(block_header.hash_tree_root()),
+    )
+
+    # Sync committee is updated
+    next_sync_committee_branch = build_proof(state.get_backing(), spec.NEXT_SYNC_COMMITTEE_INDEX)
+    # Finality is unchanged
+    finality_header = spec.BeaconBlockHeader()
+    finality_branch = [spec.Bytes32() for _ in range(spec.floorlog2(spec.FINALIZED_ROOT_INDEX))]
+
+    update = spec.LightClientUpdate(
+        header=block_header,
+        next_sync_committee=state.next_sync_committee,
+        next_sync_committee_branch=next_sync_committee_branch,
+        finality_header=finality_header,
+        finality_branch=finality_branch,
+        sync_committee_bits=sync_committee_bits,
+        sync_committee_signature=sync_committee_signature,
+        fork_version=state.fork.current_version,
+    )
+
+    spec.process_light_client_update(store, update, state.slot, state.genesis_validators_root)
+
+    # snapshot has been updated
+    assert len(store.valid_updates) == 0
+    assert store.snapshot.header == update.header
+
+
+@with_phases([ALTAIR])
+@spec_state_test
+@with_configs([MINIMAL], reason="too slow")
+def test_process_light_client_update_finality_updated(spec, state):
+    pre_snapshot = spec.LightClientSnapshot(
+        header=spec.BeaconBlockHeader(),
+        current_sync_committee=state.current_sync_committee,
+        next_sync_committee=state.next_sync_committee,
+    )
+    store = spec.LightClientStore(
+        snapshot=pre_snapshot,
+        valid_updates=[]
+    )
+
+    # Change finality
+    blocks = []
+    next_slots(spec, state, spec.SLOTS_PER_EPOCH * 2)
+    for epoch in range(3):
+        prev_state, new_blocks, state = next_epoch_with_attestations(spec, state, True, True)
+        blocks += new_blocks
+    # Ensure that finality checkpoint has changed
+    assert state.finalized_checkpoint.epoch == 3
+    # Ensure that it's same period
+    snapshot_period = spec.compute_epoch_at_slot(pre_snapshot.header.slot) // spec.EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+    update_period = spec.compute_epoch_at_slot(state.slot) // spec.EPOCHS_PER_SYNC_COMMITTEE_PERIOD
+    assert snapshot_period == update_period
+
+    # Updated sync_committee and finality
+    next_sync_committee_branch = [spec.Bytes32() for _ in range(spec.floorlog2(spec.NEXT_SYNC_COMMITTEE_INDEX))]
+    finalized_block_header = blocks[spec.SLOTS_PER_EPOCH - 1].message
+    assert finalized_block_header.slot == spec.compute_start_slot_at_epoch(state.finalized_checkpoint.epoch)
+    assert finalized_block_header.hash_tree_root() == state.finalized_checkpoint.root
+    finality_branch = build_proof(state.get_backing(), spec.FINALIZED_ROOT_INDEX)
+
+    # Build block header
+    block = build_empty_block(spec, state)
+    block_header = spec.BeaconBlockHeader(
+        slot=block.slot,
+        proposer_index=block.proposer_index,
+        parent_root=block.parent_root,
+        state_root=state.hash_tree_root(),
+        body_root=block.body.hash_tree_root(),
+    )
+
+    # Sync committee signing the finalized_block_header
+    committee = spec.get_sync_committee_indices(state, spec.get_current_epoch(state))
+    sync_committee_bits = [True] * len(committee)
+    sync_committee_signature = compute_aggregate_sync_committee_signature(
+        spec,
+        state,
+        block_header.slot,
+        committee,
+        block_root=spec.Root(block_header.hash_tree_root()),
+    )
+
+    update = spec.LightClientUpdate(
+        header=finalized_block_header,
+        next_sync_committee=state.next_sync_committee,
+        next_sync_committee_branch=next_sync_committee_branch,
+        finality_header=block_header,  # block_header is the signed header
+        finality_branch=finality_branch,
+        sync_committee_bits=sync_committee_bits,
+        sync_committee_signature=sync_committee_signature,
+        fork_version=state.fork.current_version,
+    )
+
+    spec.process_light_client_update(store, update, state.slot, state.genesis_validators_root)
+
+    # snapshot has been updated
+    assert len(store.valid_updates) == 0
+    assert store.snapshot.header == update.header
diff --git a/tests/core/pyspec/eth2spec/test/helpers/custody.py b/tests/core/pyspec/eth2spec/test/helpers/custody.py
index b3a8c0a95..8e9aafa66 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/custody.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/custody.py
@@ -1,7 +1,7 @@
 from eth2spec.test.helpers.keys import privkeys
+from eth2spec.test.helpers.merkle import build_proof
 from eth2spec.utils import bls
 from eth2spec.utils.ssz.ssz_typing import Bitlist, ByteVector, ByteList
-from remerkleable.tree import gindex_bit_iter
 
 BYTES_PER_CHUNK = 32
 
@@ -116,26 +116,6 @@ def custody_chunkify(spec, x):
     return [ByteVector[spec.BYTES_PER_CUSTODY_CHUNK](c) for c in chunks]
 
 
-def build_proof(anchor, leaf_index):
-    if leaf_index <= 1:
-        return []  # Nothing to prove / invalid index
-    node = anchor
-    proof = []
-    # Walk down, top to bottom to the leaf
-    bit_iter, _ = gindex_bit_iter(leaf_index)
-    for bit in bit_iter:
-        # Always take the opposite hand for the proof.
-        # 1 = right as leaf, thus get left
-        if bit:
-            proof.append(node.get_left().merkle_root())
-            node = node.get_right()
-        else:
-            proof.append(node.get_right().merkle_root())
-            node = node.get_left()
-
-    return list(reversed(proof))
-
-
 def get_valid_custody_chunk_response(spec, state, chunk_challenge, challenge_index,
                                      block_length_or_custody_data,
                                      invalid_chunk_data=False):
diff --git a/tests/core/pyspec/eth2spec/test/helpers/merkle.py b/tests/core/pyspec/eth2spec/test/helpers/merkle.py
new file mode 100644
index 000000000..d49827954
--- /dev/null
+++ b/tests/core/pyspec/eth2spec/test/helpers/merkle.py
@@ -0,0 +1,21 @@
+from remerkleable.tree import gindex_bit_iter
+
+
+def build_proof(anchor, leaf_index):
+    if leaf_index <= 1:
+        return []  # Nothing to prove / invalid index
+    node = anchor
+    proof = []
+    # Walk down, top to bottom to the leaf
+    bit_iter, _ = gindex_bit_iter(leaf_index)
+    for bit in bit_iter:
+        # Always take the opposite hand for the proof.
+        # 1 = right as leaf, thus get left
+        if bit:
+            proof.append(node.get_left().merkle_root())
+            node = node.get_right()
+        else:
+            proof.append(node.get_right().merkle_root())
+            node = node.get_left()
+
+    return list(reversed(proof))
diff --git a/tests/core/pyspec/eth2spec/test/helpers/sync_committee.py b/tests/core/pyspec/eth2spec/test/helpers/sync_committee.py
index b7b2381e3..da85fad60 100644
--- a/tests/core/pyspec/eth2spec/test/helpers/sync_committee.py
+++ b/tests/core/pyspec/eth2spec/test/helpers/sync_committee.py
@@ -5,17 +5,18 @@ from eth2spec.test.helpers.block import (
 from eth2spec.utils import bls
 
 
-def compute_sync_committee_signature(spec, state, slot, privkey):
+def compute_sync_committee_signature(spec, state, slot, privkey, block_root=None):
     domain = spec.get_domain(state, spec.DOMAIN_SYNC_COMMITTEE, spec.compute_epoch_at_slot(slot))
-    if slot == state.slot:
-        block_root = build_empty_block_for_next_slot(spec, state).parent_root
-    else:
-        block_root = spec.get_block_root_at_slot(state, slot)
+    if block_root is None:
+        if slot == state.slot:
+            block_root = build_empty_block_for_next_slot(spec, state).parent_root
+        else:
+            block_root = spec.get_block_root_at_slot(state, slot)
     signing_root = spec.compute_signing_root(block_root, domain)
     return bls.Sign(privkey, signing_root)
 
 
-def compute_aggregate_sync_committee_signature(spec, state, slot, participants):
+def compute_aggregate_sync_committee_signature(spec, state, slot, participants, block_root=None):
     if len(participants) == 0:
         return spec.G2_POINT_AT_INFINITY
 
@@ -28,6 +29,7 @@ def compute_aggregate_sync_committee_signature(spec, state, slot, participants):
                 state,
                 slot,
                 privkey,
+                block_root=block_root,
             )
         )
     return bls.Aggregate(signatures)
diff --git a/tests/core/pyspec/eth2spec/utils/ssz/ssz_typing.py b/tests/core/pyspec/eth2spec/utils/ssz/ssz_typing.py
index b3a0b9962..6626e26d6 100644
--- a/tests/core/pyspec/eth2spec/utils/ssz/ssz_typing.py
+++ b/tests/core/pyspec/eth2spec/utils/ssz/ssz_typing.py
@@ -5,4 +5,4 @@ from remerkleable.complex import Container, Vector, List
 from remerkleable.basic import boolean, bit, uint, byte, uint8, uint16, uint32, uint64, uint128, uint256
 from remerkleable.bitfields import Bitvector, Bitlist
 from remerkleable.byte_arrays import ByteVector, Bytes1, Bytes4, Bytes8, Bytes32, Bytes48, Bytes96, ByteList
-from remerkleable.core import BasicView, View
+from remerkleable.core import BasicView, View, Path