diff --git a/cryptarchia/cryptarchia.py b/cryptarchia/cryptarchia.py
index b510962..6f2f310 100644
--- a/cryptarchia/cryptarchia.py
+++ b/cryptarchia/cryptarchia.py
@@ -1,4 +1,4 @@
-from typing import TypeAlias, List, Dict
+from typing import TypeAlias, List, Dict, Generator
 from hashlib import sha256, blake2b
 from math import floor
 from copy import deepcopy
@@ -10,7 +10,6 @@ from collections import defaultdict
 
 import numpy as np
 
-
 logger = logging.getLogger(__name__)
 
 
@@ -124,6 +123,9 @@ class Slot:
     def __lt__(self, other):
         return self.absolute_slot < other.absolute_slot
 
+    def __hash__(self):
+        return hash(self.absolute_slot)
+
 
 @dataclass
 class Coin:
@@ -248,6 +250,9 @@ class BlockHeader:
         self.update_header_hash(h)
         return h.digest()
 
+    def __hash__(self):
+        return hash(self.id())
+
 
 @dataclass
 class LedgerState:
@@ -362,17 +367,16 @@ class EpochState:
 class Follower:
     def __init__(self, genesis_state: LedgerState, config: Config):
         self.config = config
-        self.forks = []
+        self.forks: list[Id] = []
         self.local_chain = genesis_state.block.id()
         self.genesis_state = genesis_state
         self.ledger_state = {genesis_state.block.id(): genesis_state.copy()}
         self.epoch_state = {}
 
-    def validate_header(self, block: BlockHeader) -> bool:
+    def validate_header(self, block: BlockHeader):
         # TODO: verify blocks are not in the 'future'
         if block.parent not in self.ledger_state:
-            logger.warning("We have not seen block parent")
-            return False
+            raise ParentNotFound
 
         current_state = self.ledger_state[block.parent].copy()
 
@@ -391,8 +395,7 @@ class Follower:
             # We take a shortcut for (1.) by restricting orphans to proofs we've
             # already processed in other branches.
             if orphan.id() not in self.ledger_state:
-                logger.warning("missing orphan proof")
-                return False
+                raise MissingOrphanProof
 
             # (2.) is satisfied by verifying the proof against current state ensuring:
             # - it is a valid proof
@@ -404,21 +407,21 @@ class Follower:
                 epoch_state,
                 current_state,
             ):
-                logger.warning("invalid orphan proof")
-                return False
+                raise InvalidOrphanProof
 
             # if an adopted leadership proof is valid we need to apply its
             # effects to the ledger state
             current_state.apply_leader_proof(orphan.leader_proof)
 
         # TODO: this is not the full block validation spec, only slot leader is verified
-        return self.verify_slot_leader(
+        if not self.verify_slot_leader(
             block.slot,
             block.parent,
             block.leader_proof,
             epoch_state,
             current_state,
-        )
+        ):
+            raise InvalidLeaderProof
 
     def verify_slot_leader(
         self,
@@ -441,19 +444,23 @@ class Follower:
             and current_state.verify_unspent(proof.nullifier)
         )
 
-    def on_block(self, block: BlockHeader):
+    def apply_block_to_ledger_state(self, block: BlockHeader) -> bool:
         if block.id() in self.ledger_state:
             logger.warning("dropping already processed block")
-            return
+            return False
 
-        if not self.validate_header(block):
-            logger.warning("invalid header")
-            return
+        self.validate_header(block)
 
         new_state = self.ledger_state[block.parent].copy()
         new_state.apply(block)
         self.ledger_state[block.id()] = new_state
 
+        return True
+
+    def on_block(self, block: BlockHeader):
+        if not self.apply_block_to_ledger_state(block):
+            return
+
         if block.parent == self.local_chain:
             # simply extending the local chain
             self.local_chain = block.id()
@@ -471,6 +478,15 @@ class Follower:
             self.forks.remove(new_tip)
             self.local_chain = new_tip
 
+    def apply_checkpoint(self, checkpoint: LedgerState):
+        checkpoint_block_id = checkpoint.block.id()
+        self.ledger_state[checkpoint_block_id] = checkpoint
+        if self.local_chain != self.genesis_state.block.id():
+            self.forks.append(self.local_chain)
+        if checkpoint_block_id in self.forks:
+            self.forks.remove(checkpoint_block_id)
+        self.local_chain = checkpoint_block_id
+
     def unimported_orphans(self) -> list[BlockHeader]:
         """
         Returns all unimported orphans w.r.t. the given tip's state.
@@ -482,9 +498,10 @@ class Follower:
         orphans = []
 
         for fork in self.forks:
-            _, fork_depth = common_prefix_depth(tip, fork, self.ledger_state)
-            for block_state in chain_suffix(fork, fork_depth, self.ledger_state):
-                b = block_state.block
+            _, _, fork_depth, fork_suffix = common_prefix_depth(
+                tip, fork, self.ledger_state
+            )
+            for b in fork_suffix:
                 if b.leader_proof.nullifier not in tip_state.nullifiers:
                     tip_state.nullifiers.add(b.leader_proof.nullifier)
                     orphans += [b]
@@ -592,6 +609,17 @@ class Follower:
         )
         return int(prev_epoch.inferred_total_active_stake - h * blocks_per_slot_err)
 
+    def blocks_by_slot(self, from_slot: Slot) -> Generator[BlockHeader, None, None]:
+        # Returns blocks in the given range of slots in order of slot
+        # NOTE: In real implementation, this should be done by optimized data structures.
+        blocks_by_slot: dict[Slot, list[BlockHeader]] = defaultdict(list)
+        for state in self.ledger_state.values():
+            if from_slot <= state.block.slot:
+                blocks_by_slot[state.block.slot].append(state.block)
+        for slot in sorted(blocks_by_slot.keys()):
+            for block in blocks_by_slot[slot]:
+                yield block
+
 
 def phi(f: float, alpha: float) -> float:
     """
@@ -646,39 +674,68 @@ class Leader:
         )
 
 
-def iter_chain(tip: Id, states: Dict[Id, LedgerState]):
+def iter_chain(
+    tip: Id, states: Dict[Id, LedgerState]
+) -> Generator[LedgerState, None, None]:
     while tip in states:
         yield states[tip]
         tip = states[tip].block.parent
 
 
-def chain_suffix(tip: Id, n: int, states: Dict[Id, LedgerState]) -> list[LedgerState]:
-    return list(reversed(list(itertools.islice(iter_chain(tip, states), n))))
+def iter_chain_blocks(
+    tip: Id, states: Dict[Id, LedgerState]
+) -> Generator[BlockHeader, None, None]:
+    for state in iter_chain(tip, states):
+        yield state.block
 
 
-def common_prefix_depth(a: Id, b: Id, states: Dict[Id, LedgerState]) -> (int, int):
-    a_blocks = iter_chain(a, states)
-    b_blocks = iter_chain(b, states)
+def common_prefix_depth(
+    a: Id, b: Id, states: Dict[Id, LedgerState]
+) -> tuple[int, list[BlockHeader], int, list[BlockHeader]]:
+    return common_prefix_depth_from_chains(
+        iter_chain_blocks(a, states), iter_chain_blocks(b, states)
+    )
 
+
+def common_prefix_depth_from_chains(
+    a_blocks: Generator[BlockHeader, None, None],
+    b_blocks: Generator[BlockHeader, None, None],
+) -> tuple[int, list[BlockHeader], int, list[BlockHeader]]:
     seen = {}
+    a_suffix: list[BlockHeader] = []
+    b_suffix: list[BlockHeader] = []
     depth = 0
     while True:
         try:
-            a_block = next(a_blocks).block.id()
-            if a_block in seen:
+            a_block = next(a_blocks)
+            a_suffix.append(a_block)
+            a_block_id = a_block.id()
+            if a_block_id in seen:
                 # we had seen this block from the fork chain
-                return depth, seen[a_block]
+                return (
+                    depth,
+                    list(reversed(a_suffix[: depth + 1])),
+                    seen[a_block_id],
+                    list(reversed(b_suffix[: seen[a_block_id] + 1])),
+                )
 
-            seen[a_block] = depth
+            seen[a_block_id] = depth
         except StopIteration:
             pass
 
         try:
-            b_block = next(b_blocks).block.id()
-            if b_block in seen:
+            b_block = next(b_blocks)
+            b_suffix.append(b_block)
+            b_block_id = b_block.id()
+            if b_block_id in seen:
                 # we had seen the fork in the local chain
-                return seen[b_block], depth
-            seen[b_block] = depth
+                return (
+                    seen[b_block_id],
+                    list(reversed(a_suffix[: seen[b_block_id] + 1])),
+                    depth,
+                    list(reversed(b_suffix[: depth + 1])),
+                )
+            seen[b_block_id] = depth
         except StopIteration:
             pass
 
@@ -687,13 +744,8 @@ def common_prefix_depth(a: Id, b: Id, states: Dict[Id, LedgerState]) -> (int, in
     assert False
 
 
-def chain_density(
-    head: Id, slot: Slot, reorg_depth: int, states: Dict[Id, LedgerState]
-) -> int:
-    assert type(head) == Id
-    chain = iter_chain(head, states)
-    segment = itertools.islice(chain, reorg_depth)
-    return sum(1 for b in segment if b.block.slot < slot)
+def chain_density(chain: list[BlockHeader], slot: Slot) -> int:
+    return sum(1 for b in chain if b.slot < slot)
 
 
 def block_children(states: Dict[Id, LedgerState]) -> Dict[Id, set[Id]]:
@@ -723,7 +775,9 @@ def maxvalid_bg(
 
     cmax = local_chain
     for fork in forks:
-        cmax_depth, fork_depth = common_prefix_depth(cmax, fork, states)
+        cmax_depth, cmax_suffix, fork_depth, fork_suffix = common_prefix_depth(
+            cmax, fork, states
+        )
         if cmax_depth <= k:
             # Longest chain fork choice rule
             if cmax_depth < fork_depth:
@@ -731,11 +785,11 @@ def maxvalid_bg(
         else:
             # The chain is forking too much, we need to pay a bit more attention
             # In particular, select the chain that is the densest after the fork
-            cmax_divergent_block = chain_suffix(cmax, cmax_depth, states)[0].block
+            cmax_divergent_block = cmax_suffix[0]
 
             forking_slot = Slot(cmax_divergent_block.slot.absolute_slot + s)
-            cmax_density = chain_density(cmax, forking_slot, cmax_depth, states)
-            fork_density = chain_density(fork, forking_slot, fork_depth, states)
+            cmax_density = chain_density(cmax_suffix, forking_slot)
+            fork_density = chain_density(fork_suffix, forking_slot)
 
             if cmax_density < fork_density:
                 cmax = fork
@@ -743,5 +797,25 @@ def maxvalid_bg(
     return cmax
 
 
+class ParentNotFound(Exception):
+    def __str__(self):
+        return "Parent not found"
+
+
+class MissingOrphanProof(Exception):
+    def __str__(self):
+        return "Missing orphan proof"
+
+
+class InvalidOrphanProof(Exception):
+    def __str__(self):
+        return "Invalid orphan proof"
+
+
+class InvalidLeaderProof(Exception):
+    def __str__(self):
+        return "Invalid leader proof"
+
+
 if __name__ == "__main__":
     pass
diff --git a/cryptarchia/sync.py b/cryptarchia/sync.py
new file mode 100644
index 0000000..6921c3b
--- /dev/null
+++ b/cryptarchia/sync.py
@@ -0,0 +1,181 @@
+from collections import defaultdict
+from typing import Generator
+
+from cryptarchia.cryptarchia import (
+    BlockHeader,
+    Follower,
+    Id,
+    ParentNotFound,
+    Slot,
+    common_prefix_depth_from_chains,
+    iter_chain_blocks,
+)
+
+
+def sync(local: Follower, peers: list[Follower]):
+    # Syncs the local block tree with the peers, starting from the local tip.
+    # This covers the case where the local tip is not on the latest honest chain anymore.
+
+    # Repeat the sync process until no peer has a tip ahead of the local tip,
+    # because peers' tips may advance during the sync process.
+    block_fetcher = BlockFetcher(peers)
+    rejected_blocks: set[Id] = set()
+    while True:
+        # Fetch blocks from the peers in the range of slots from the local tip to the latest tip.
+        # Gather orphaned blocks, which are blocks from forks that are absent in the local block tree.
+
+        start_slot = local.tip().slot
+        orphans: set[BlockHeader] = set()
+        num_blocks = 0
+        for block in block_fetcher.fetch_blocks_from(start_slot):
+            num_blocks += 1
+            # Reject blocks that have been rejected in the past
+            # or whose parent has been rejected.
+            if {block.id(), block.parent} & rejected_blocks:
+                rejected_blocks.add(block.id())
+                continue
+
+            try:
+                local.on_block(block)
+                orphans.discard(block)
+            except ParentNotFound:
+                orphans.add(block)
+            except Exception:
+                rejected_blocks.add(block.id())
+
+        # Finish the sync process if no block has been fetched,
+        # which means that no peer has a tip ahead of the local tip.
+        if num_blocks == 0:
+            return
+
+        # Backfill the orphan forks starting from the orphan blocks with applying fork choice rule.
+        #
+        # Sort the orphan blocks by slot in descending order to minimize the number of backfillings.
+        for orphan in sorted(orphans, key=lambda b: b.slot, reverse=True):
+            # Skip the orphan block if it has been processed during the previous backfillings
+            # (i.e. if it has been already added to the local block tree).
+            # Or, skip if it has been rejected during the previous backfillings.
+            if (
+                orphan.id() not in local.ledger_state
+                and orphan.id() not in rejected_blocks
+            ):
+                try:
+                    backfill_fork(local, orphan, block_fetcher)
+                except InvalidBlockFromBackfillFork as e:
+                    rejected_blocks.update(block.id() for block in e.invalid_suffix)
+
+
+def backfill_fork(
+    local: Follower,
+    fork_tip: BlockHeader,
+    block_fetcher: "BlockFetcher",
+):
+    # Backfills a fork, which is absent in the local block tree, by fetching blocks from the peers.
+    # During backfilling, the fork choice rule is continuously applied.
+    #
+    # If necessary, the local honest chain is also backfilled for the fork choice rule.
+    # This can happen if the honest chain has been built not from the genesis (i.e. checkpoint sync).
+
+    _, tip_suffix, _, fork_suffix = common_prefix_depth_from_chains(
+        block_fetcher.fetch_chain_backward(local.tip_id(), local),
+        block_fetcher.fetch_chain_backward(fork_tip.id(), local),
+    )
+
+    # First, backfill the local honest chain if some blocks are missing.
+    # In other words, backfill the local block tree, which contains the honest chain.
+    for block in tip_suffix:
+        try:
+            # Just apply the block to the ledger state is enough
+            # instead of calling `on_block` which runs the fork choice rule.
+            local.apply_block_to_ledger_state(block)
+        except Exception as e:
+            raise InvalidBlockTree(e)
+
+    # Then, add blocks in the fork suffix with applying fork choice rule.
+    # After all, add the tip of the fork suffix to apply the fork choice rule.
+    for i, block in enumerate(fork_suffix):
+        try:
+            local.on_block(block)
+        except Exception as e:
+            raise InvalidBlockFromBackfillFork(e, fork_suffix[i:])
+
+
+class BlockFetcher:
+    # NOTE: This class is a mock, which uses a naive approach to fetch blocks from multiple peers.
+    # In real implementation, any optimized way can be used, such as parallel fetching.
+
+    def __init__(self, peers: list[Follower]):
+        self.peers = peers
+
+    def fetch_blocks_from(self, start_slot: Slot) -> Generator[BlockHeader, None, None]:
+        # Filter peers that have a tip ahead of the local tip
+        # and group peers by their tip to minimize the number of fetches.
+        groups = self.filter_and_group_peers_by_tip(start_slot)
+        for group in groups.values():
+            for block in BlockFetcher.fetch_blocks_by_slot(group, start_slot):
+                yield block
+
+    def filter_and_group_peers_by_tip(
+        self, start_slot: Slot
+    ) -> dict[BlockHeader, list[Follower]]:
+        # Group peers by their tip.
+        # Filter only the peers whose tip is ahead of the start_slot.
+        groups: dict[BlockHeader, list[Follower]] = defaultdict(list)
+        for peer in self.peers:
+            if peer.tip().slot.absolute_slot > start_slot.absolute_slot:
+                groups[peer.tip()].append(peer)
+        return groups
+
+    @staticmethod
+    def fetch_blocks_by_slot(
+        peers: list[Follower], start_slot: Slot
+    ) -> Generator[BlockHeader, None, None]:
+        # Fetch blocks in the given range of slots from one of the peers.
+        # Blocks should be returned in order of slot.
+        # If a peer fails, try the next peer.
+        for peer in peers:
+            try:
+                for block in peer.blocks_by_slot(start_slot):
+                    yield block
+                    # Update start_slot for the potential try with the next peer.
+                    start_slot = block.slot
+                # The peer successfully returned all blocks. No need to try the next peer.
+                break
+            except Exception:
+                continue
+
+    def fetch_chain_backward(
+        self, tip: Id, local: Follower
+    ) -> Generator[BlockHeader, None, None]:
+        # Fetches a chain of blocks from the peers, starting from the given tip to the genesis.
+        # Attempts to extend the chain as much as possible by querying multiple peers,
+        # considering that not all peers may have the full chain (from the genesis).
+
+        id = tip
+        # First, try to iterate the chain from the local block tree.
+        for block in iter_chain_blocks(id, local.ledger_state):
+            yield block
+            if block.id() == local.genesis_state.block.id():
+                return
+            id = block.parent
+
+        # Try to continue by fetching the remaining blocks from the peers
+        for peer in self.peers:
+            for block in iter_chain_blocks(id, peer.ledger_state):
+                yield block
+                if block.id() == local.genesis_state.block.id():
+                    return
+                id = block.parent
+
+
+class InvalidBlockTree(Exception):
+    def __init__(self, cause: Exception):
+        super().__init__()
+        self.cause = cause
+
+
+class InvalidBlockFromBackfillFork(Exception):
+    def __init__(self, cause: Exception, invalid_suffix: list[BlockHeader]):
+        super().__init__()
+        self.cause = cause
+        self.invalid_suffix = invalid_suffix
diff --git a/cryptarchia/test_fork_choice.py b/cryptarchia/test_fork_choice.py
index 1a283c5..24b295d 100644
--- a/cryptarchia/test_fork_choice.py
+++ b/cryptarchia/test_fork_choice.py
@@ -36,28 +36,138 @@ class TestForkChoice(TestCase):
             b.id(): LedgerState(block=b) for b in [b0, b1, b2, b3, b4, b5, b6, b7]
         }
 
-        assert (d := common_prefix_depth(b0.id(), b0.id(), states)) == (0, 0), d
-        assert (d := common_prefix_depth(b1.id(), b0.id(), states)) == (1, 0), d
-        assert (d := common_prefix_depth(b0.id(), b1.id(), states)) == (0, 1), d
-        assert (d := common_prefix_depth(b1.id(), b1.id(), states)) == (0, 0), d
-        assert (d := common_prefix_depth(b2.id(), b0.id(), states)) == (2, 0), d
-        assert (d := common_prefix_depth(b0.id(), b2.id(), states)) == (0, 2), d
-        assert (d := common_prefix_depth(b3.id(), b0.id(), states)) == (3, 0), d
-        assert (d := common_prefix_depth(b0.id(), b3.id(), states)) == (0, 3), d
-        assert (d := common_prefix_depth(b1.id(), b4.id(), states)) == (1, 1), d
-        assert (d := common_prefix_depth(b4.id(), b1.id(), states)) == (1, 1), d
-        assert (d := common_prefix_depth(b1.id(), b5.id(), states)) == (1, 2), d
-        assert (d := common_prefix_depth(b5.id(), b1.id(), states)) == (2, 1), d
-        assert (d := common_prefix_depth(b2.id(), b5.id(), states)) == (2, 2), d
-        assert (d := common_prefix_depth(b5.id(), b2.id(), states)) == (2, 2), d
-        assert (d := common_prefix_depth(b3.id(), b5.id(), states)) == (3, 2), d
-        assert (d := common_prefix_depth(b5.id(), b3.id(), states)) == (2, 3), d
-        assert (d := common_prefix_depth(b3.id(), b6.id(), states)) == (1, 1), d
-        assert (d := common_prefix_depth(b6.id(), b3.id(), states)) == (1, 1), d
-        assert (d := common_prefix_depth(b3.id(), b7.id(), states)) == (1, 2), d
-        assert (d := common_prefix_depth(b7.id(), b3.id(), states)) == (2, 1), d
-        assert (d := common_prefix_depth(b5.id(), b7.id(), states)) == (2, 4), d
-        assert (d := common_prefix_depth(b7.id(), b5.id(), states)) == (4, 2), d
+        assert (d := common_prefix_depth(b0.id(), b0.id(), states)) == (
+            0,
+            [b0],
+            0,
+            [b0],
+        ), d
+        assert (d := common_prefix_depth(b1.id(), b0.id(), states)) == (
+            1,
+            [b0, b1],
+            0,
+            [b0],
+        ), d
+        assert (d := common_prefix_depth(b0.id(), b1.id(), states)) == (
+            0,
+            [b0],
+            1,
+            [b0, b1],
+        ), d
+        assert (d := common_prefix_depth(b1.id(), b1.id(), states)) == (
+            0,
+            [b1],
+            0,
+            [b1],
+        ), d
+        assert (d := common_prefix_depth(b2.id(), b0.id(), states)) == (
+            2,
+            [b0, b1, b2],
+            0,
+            [b0],
+        ), d
+        assert (d := common_prefix_depth(b0.id(), b2.id(), states)) == (
+            0,
+            [b0],
+            2,
+            [b0, b1, b2],
+        ), d
+        assert (d := common_prefix_depth(b3.id(), b0.id(), states)) == (
+            3,
+            [b0, b1, b2, b3],
+            0,
+            [b0],
+        ), d
+        assert (d := common_prefix_depth(b0.id(), b3.id(), states)) == (
+            0,
+            [b0],
+            3,
+            [b0, b1, b2, b3],
+        ), d
+        assert (d := common_prefix_depth(b1.id(), b4.id(), states)) == (
+            1,
+            [b0, b1],
+            1,
+            [b0, b4],
+        ), d
+        assert (d := common_prefix_depth(b4.id(), b1.id(), states)) == (
+            1,
+            [b0, b4],
+            1,
+            [b0, b1],
+        ), d
+        assert (d := common_prefix_depth(b1.id(), b5.id(), states)) == (
+            1,
+            [b0, b1],
+            2,
+            [b0, b4, b5],
+        ), d
+        assert (d := common_prefix_depth(b5.id(), b1.id(), states)) == (
+            2,
+            [b0, b4, b5],
+            1,
+            [b0, b1],
+        ), d
+        assert (d := common_prefix_depth(b2.id(), b5.id(), states)) == (
+            2,
+            [b0, b1, b2],
+            2,
+            [b0, b4, b5],
+        ), d
+        assert (d := common_prefix_depth(b5.id(), b2.id(), states)) == (
+            2,
+            [b0, b4, b5],
+            2,
+            [b0, b1, b2],
+        ), d
+        assert (d := common_prefix_depth(b3.id(), b5.id(), states)) == (
+            3,
+            [b0, b1, b2, b3],
+            2,
+            [b0, b4, b5],
+        ), d
+        assert (d := common_prefix_depth(b5.id(), b3.id(), states)) == (
+            2,
+            [b0, b4, b5],
+            3,
+            [b0, b1, b2, b3],
+        ), d
+        assert (d := common_prefix_depth(b3.id(), b6.id(), states)) == (
+            1,
+            [b2, b3],
+            1,
+            [b2, b6],
+        ), d
+        assert (d := common_prefix_depth(b6.id(), b3.id(), states)) == (
+            1,
+            [b2, b6],
+            1,
+            [b2, b3],
+        ), d
+        assert (d := common_prefix_depth(b3.id(), b7.id(), states)) == (
+            1,
+            [b2, b3],
+            2,
+            [b2, b6, b7],
+        ), d
+        assert (d := common_prefix_depth(b7.id(), b3.id(), states)) == (
+            2,
+            [b2, b6, b7],
+            1,
+            [b2, b3],
+        ), d
+        assert (d := common_prefix_depth(b5.id(), b7.id(), states)) == (
+            2,
+            [b0, b4, b5],
+            4,
+            [b0, b1, b2, b6, b7],
+        ), d
+        assert (d := common_prefix_depth(b7.id(), b5.id(), states)) == (
+            4,
+            [b0, b1, b2, b6, b7],
+            2,
+            [b0, b4, b5],
+        ), d
 
     def test_fork_choice_long_sparse_chain(self):
         # The longest chain is not dense after the fork
diff --git a/cryptarchia/test_ledger_state_update.py b/cryptarchia/test_ledger_state_update.py
index d67abd4..d66abf0 100644
--- a/cryptarchia/test_ledger_state_update.py
+++ b/cryptarchia/test_ledger_state_update.py
@@ -1,10 +1,14 @@
 from unittest import TestCase
 
-import numpy as np
-
-from .cryptarchia import Follower, Coin, iter_chain
-
-from .test_common import mk_config, mk_block, mk_genesis_state
+from .cryptarchia import (
+    Coin,
+    Follower,
+    InvalidLeaderProof,
+    MissingOrphanProof,
+    ParentNotFound,
+    iter_chain,
+)
+from .test_common import mk_block, mk_config, mk_genesis_state
 
 
 class TestLedgerStateUpdate(TestCase):
@@ -46,7 +50,8 @@ class TestLedgerStateUpdate(TestCase):
         assert follower.tip_state().verify_unspent(leader_coin.nullifier()) == False
 
         reuse_coin_block = mk_block(slot=1, parent=block, coin=leader_coin)
-        follower.on_block(reuse_coin_block)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(reuse_coin_block)
 
         # Follower should *not* have accepted the block
         assert len(list(iter_chain(follower.tip_id(), follower.ledger_state))) == 2
@@ -126,7 +131,8 @@ class TestLedgerStateUpdate(TestCase):
         # Nothing changes from the local chain and forks.
         unknown_block = mk_block(parent=block_5, slot=2, coin=coins[5])
         block_6 = mk_block(parent=unknown_block, slot=2, coin=coins[6])
-        follower.on_block(block_6)
+        with self.assertRaises(ParentNotFound):
+            follower.on_block(block_6)
         assert follower.tip() == block_3
         assert len(follower.forks) == 2, f"{len(follower.forks)}"
         assert follower.forks[0] == block_4.id()
@@ -169,7 +175,8 @@ class TestLedgerStateUpdate(TestCase):
         # so that the new block can be accepted only if that is the snapshot used
         # first, verify that if we don't change the state, the block is not accepted
         block_4 = mk_block(slot=40, parent=block_3, coin=Coin(sk=4, value=100))
-        follower.on_block(block_4)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(block_4)
         assert follower.tip() == block_3
         # then we add the coin to "spendable commitments" associated with slot 9
         follower.ledger_state[block_2.id()].commitments_spend.add(
@@ -193,7 +200,8 @@ class TestLedgerStateUpdate(TestCase):
 
         # coin can't be reused to win following slots:
         block_2_reuse = mk_block(slot=1, parent=block_1, coin=coin)
-        follower.on_block(block_2_reuse)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(block_2_reuse)
         assert follower.tip() == block_1
 
         # but the evolved coin is eligible
@@ -224,7 +232,8 @@ class TestLedgerStateUpdate(TestCase):
 
         # the new coin is not yet eligible for elections
         block_0_1_attempt = mk_block(slot=1, parent=block_0_0, coin=coin_new)
-        follower.on_block(block_0_1_attempt)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(block_0_1_attempt)
         assert follower.tip() == block_0_0
 
         # whereas the evolved coin from genesis can be spent immediately
@@ -238,7 +247,8 @@ class TestLedgerStateUpdate(TestCase):
         # stake distribution snapshot is taken at the beginning of the previous epoch
 
         block_1_0 = mk_block(slot=20, parent=block_0_1, coin=coin_new)
-        follower.on_block(block_1_0)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(block_1_0)
         assert follower.tip() == block_0_1
 
         # ---- EPOCH 2 ----
@@ -267,7 +277,8 @@ class TestLedgerStateUpdate(TestCase):
         coin_new = coin.evolve()
         coin_new_new = coin_new.evolve()
         block_0_1 = mk_block(slot=1, parent=block_0_0, coin=coin_new_new)
-        follower.on_block(block_0_1)
+        with self.assertRaises(InvalidLeaderProof):
+            follower.on_block(block_0_1)
         # the coin evolved twice should not be accepted as it is not in the lead commitments
         assert follower.tip() == block_0_0
 
@@ -283,7 +294,8 @@ class TestLedgerStateUpdate(TestCase):
             coin=coin_orphan.evolve(),
             orphaned_proofs=[orphan],
         )
-        follower.on_block(block_0_1)
+        with self.assertRaises(MissingOrphanProof):
+            follower.on_block(block_0_1)
 
         # since follower had not seen this orphan prior to being included as
         # an orphan proof, it will be rejected
diff --git a/cryptarchia/test_sync.py b/cryptarchia/test_sync.py
new file mode 100644
index 0000000..101e8e0
--- /dev/null
+++ b/cryptarchia/test_sync.py
@@ -0,0 +1,501 @@
+from unittest import TestCase
+
+from cryptarchia.cryptarchia import BlockHeader, Coin, Follower
+from cryptarchia.sync import InvalidBlockTree, sync
+from cryptarchia.test_common import mk_block, mk_config, mk_genesis_state
+
+
+class TestSync(TestCase):
+    def test_sync_single_chain_from_genesis(self):
+        # Prepare a peer with a single chain:
+        # b0 - b1 - b2 - b3
+        coin = Coin(sk=0, value=10)
+        config = mk_config([coin])
+        genesis = mk_genesis_state([coin])
+        peer = Follower(genesis, config)
+        b0, coin = mk_block(genesis.block, 1, coin), coin.evolve()
+        b1, coin = mk_block(b0, 2, coin), coin.evolve()
+        b2, coin = mk_block(b1, 3, coin), coin.evolve()
+        b3, coin = mk_block(b2, 4, coin), coin.evolve()
+        for b in [b0, b1, b2, b3]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b3)
+        self.assertEqual(peer.forks, [])
+
+        # Start a sync from genesis.
+        # Result: The same block tree as the peer's.
+        local = Follower(genesis, config)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+
+    def test_sync_single_chain_from_middle(self):
+        # Prepare a peer with a single chain:
+        # b0 - b1 - b2 - b3
+        coin = Coin(sk=0, value=10)
+        config = mk_config([coin])
+        genesis = mk_genesis_state([coin])
+        peer = Follower(genesis, config)
+        b0, coin = mk_block(genesis.block, 1, coin), coin.evolve()
+        b1, coin = mk_block(b0, 2, coin), coin.evolve()
+        b2, coin = mk_block(b1, 3, coin), coin.evolve()
+        b3, coin = mk_block(b2, 4, coin), coin.evolve()
+        for b in [b0, b1, b2, b3]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b3)
+        self.assertEqual(peer.forks, [])
+
+        # Start a sync from a tree:
+        # b0 - b1
+        #
+        # Result: The same block tree as the peer's.
+        local = Follower(genesis, config)
+        for b in [b0, b1]:
+            peer.on_block(b)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+
+    def test_sync_forks_from_genesis(self):
+        # Prepare a peer with forks:
+        # b0 - b1 - b2 - b5 == tip
+        #    \
+        #      b3 - b4
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        peer = Follower(genesis, config)
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b3, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b4, c_b = mk_block(b3, 3, c_b), c_b.evolve()
+        b5, c_a = mk_block(b2, 4, c_a), c_a.evolve()
+        for b in [b0, b1, b2, b3, b4, b5]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b4.id()])
+
+        # Start a sync from genesis.
+        # Result: The same block tree as the peer's.
+        local = Follower(genesis, config)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+
+    def test_sync_forks_from_middle(self):
+        # Prepare a peer with forks:
+        # b0 - b1 - b2 - b5 == tip
+        #    \
+        #      b3 - b4
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        peer = Follower(genesis, config)
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b3, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b4, c_b = mk_block(b3, 3, c_b), c_b.evolve()
+        b5, c_a = mk_block(b2, 4, c_a), c_a.evolve()
+        for b in [b0, b1, b2, b3, b4, b5]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b4.id()])
+
+        # Start a sync from a tree:
+        # b0 - b1
+        #    \
+        #      b3
+        #
+        # Result: The same block tree as the peer's.
+        local = Follower(genesis, config)
+        for b in [b0, b1, b3]:
+            peer.on_block(b)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+
+    def test_sync_forks_by_backfilling(self):
+        # Prepare a peer with forks:
+        # b0 - b1 - b2 - b5 == tip
+        #    \
+        #      b3 - b4
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        peer = Follower(genesis, config)
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b3, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b4, c_b = mk_block(b3, 3, c_b), c_b.evolve()
+        b5, c_a = mk_block(b2, 4, c_a), c_a.evolve()
+        for b in [b0, b1, b2, b3, b4, b5]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b4.id()])
+        self.assertEqual(len(peer.ledger_state), 7)
+
+        # Start a sync from a tree without the fork:
+        # b0 - b1
+        #
+        # Result: The same block tree as the peer's.
+        local = Follower(genesis, config)
+        for b in [b0, b1]:
+            peer.on_block(b)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+        self.assertEqual(len(local.ledger_state), len(peer.ledger_state))
+
+    def test_sync_multiple_peers_from_genesis(self):
+        # Prepare multiple peers:
+        # Peer-0:                b5
+        #                      /
+        # Peer-1: b0 - b1 - b2
+        #            \
+        # Peer-2:      b3 - b4
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b3, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b4, c_b = mk_block(b3, 3, c_b), c_b.evolve()
+        b5, c_a = mk_block(b2, 4, c_a), c_a.evolve()
+        peer0 = Follower(genesis, config)
+        for b in [b0, b1, b2, b5]:
+            peer0.on_block(b)
+        self.assertEqual(peer0.tip(), b5)
+        self.assertEqual(peer0.forks, [])
+        peer1 = Follower(genesis, config)
+        for b in [b0, b1, b2]:
+            peer1.on_block(b)
+        self.assertEqual(peer1.tip(), b2)
+        self.assertEqual(peer1.forks, [])
+        peer2 = Follower(genesis, config)
+        for b in [b0, b3, b4]:
+            peer2.on_block(b)
+        self.assertEqual(peer2.tip(), b4)
+        self.assertEqual(peer2.forks, [])
+
+        # Start a sync from genesis.
+        #
+        # Result: A merged block tree
+        #                b5
+        #              /
+        # b0 - b1 - b2
+        #    \
+        #      b3 - b4
+        local = Follower(genesis, config)
+        sync(local, [peer0, peer1, peer2])
+        self.assertEqual(local.tip(), b5)
+        self.assertEqual(local.forks, [b4.id()])
+        self.assertEqual(len(local.ledger_state), 7)
+
+    def test_reject_invalid_blocks(self):
+        # Prepare a peer with invalid blocks:
+        # b0 - b1 - b2 - b3 - (invalid_b4) - (invalid_b5)
+        #
+        # First, build a valid chain (b0 ~ b3):
+        coin = Coin(sk=0, value=10)
+        config = mk_config([coin])
+        genesis = mk_genesis_state([coin])
+        peer = Follower(genesis, config)
+        b0, coin = mk_block(genesis.block, 1, coin), coin.evolve()
+        b1, coin = mk_block(b0, 2, coin), coin.evolve()
+        b2, coin = mk_block(b1, 3, coin), coin.evolve()
+        b3, coin = mk_block(b2, 4, coin), coin.evolve()
+        for b in [b0, b1, b2, b3]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b3)
+        self.assertEqual(peer.forks, [])
+
+        # And deliberately, add invalid blocks (b4 ~ b5):
+        fake_coin = Coin(sk=1, value=10)
+        b4, fake_coin = mk_block(b3, 5, fake_coin), fake_coin.evolve()
+        b5, fake_coin = mk_block(b4, 6, fake_coin), fake_coin.evolve()
+        apply_invalid_block_to_ledger_state(peer, b4)
+        apply_invalid_block_to_ledger_state(peer, b5)
+        # the tip shouldn't be changed.
+        self.assertEqual(peer.tip(), b3)
+        self.assertEqual(peer.forks, [])
+
+        # Start a sync from genesis.
+        #
+        # Result: The same honest chain, but without invalid blocks.
+        # b0 - b1 - b2 - b3 == tip
+        local = Follower(genesis, config)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+
+    def test_reject_invalid_blocks_from_backfilling(self):
+        # Prepare a peer with invalid blocks in a fork:
+        # b0 - b1 - b3 - b4 - b5 == tip
+        #    \
+        #      b2 - (invalid_b6) - (invalid_b7)
+        #
+        # First, build a valid chain (b0 ~ b5):
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        peer = Follower(genesis, config)
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b3, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b4, c_a = mk_block(b3, 4, c_a), c_a.evolve()
+        b5, c_a = mk_block(b4, 5, c_a), c_a.evolve()
+        for b in [b0, b1, b2, b3, b4, b5]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # And deliberately, add invalid blocks (b6 ~ b7):
+        fake_coin = Coin(sk=2, value=10)
+        b6, fake_coin = mk_block(b2, 3, fake_coin), fake_coin.evolve()
+        b7, fake_coin = mk_block(b6, 4, fake_coin), fake_coin.evolve()
+        apply_invalid_block_to_ledger_state(peer, b6)
+        apply_invalid_block_to_ledger_state(peer, b7)
+        # the tip shouldn't be changed.
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # Start a sync from a tree:
+        # b0 - b1 - b3 - b4
+        #
+        # Result: The same forks, but without invalid blocks
+        # b0 - b1 - b3 - b4 - b5 == tip
+        #    \
+        #      b2
+        local = Follower(genesis, config)
+        for b in [b0, b1, b3, b4]:
+            peer.on_block(b)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+        self.assertNotIn(b6.id(), local.ledger_state)
+        self.assertNotIn(b7.id(), local.ledger_state)
+
+
+class TestSyncFromCheckpoint(TestCase):
+    def test_sync_single_chain(self):
+        # Prepare a peer with a single chain:
+        # b0 - b1 - b2 - b3
+        #           ||
+        #       checkpoint
+        coin = Coin(sk=0, value=10)
+        config = mk_config([coin])
+        genesis = mk_genesis_state([coin])
+        peer = Follower(genesis, config)
+        b0, coin = mk_block(genesis.block, 1, coin), coin.evolve()
+        b1, coin = mk_block(b0, 2, coin), coin.evolve()
+        b2, coin = mk_block(b1, 3, coin), coin.evolve()
+        b3, coin = mk_block(b2, 4, coin), coin.evolve()
+        for b in [b0, b1, b2, b3]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b3)
+        self.assertEqual(peer.forks, [])
+
+        # Start a sync from the checkpoint:
+        # () - () - b2
+        #           ||
+        #       checkpoint
+        #
+        # Result: A honest chain without historical blocks
+        # () - () - b2 - b3
+        checkpoint = peer.ledger_state[b2.id()]
+        local = Follower(genesis, config)
+        local.apply_checkpoint(checkpoint)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+        self.assertEqual(
+            set(local.ledger_state.keys()), set([genesis.block.id(), b2.id(), b3.id()])
+        )
+
+    def test_sync_forks(self):
+        # Prepare a peer with forks:
+        #       checkpoint
+        #           ||
+        # b0 - b1 - b2 - b5 == tip
+        #    \
+        #      b3 - b4
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        peer = Follower(genesis, config)
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b3, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b4, c_b = mk_block(b3, 3, c_b), c_b.evolve()
+        b5, c_a = mk_block(b2, 4, c_a), c_a.evolve()
+        for b in [b0, b1, b2, b3, b4, b5]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b4.id()])
+
+        # Start a sync from the checkpoint:
+        #       checkpoint
+        #           ||
+        # () - () - b2
+        #
+        # Result: Backfilled forks.
+        # b0 - b1 - b2 - b5 == tip
+        #    \
+        #      b3 - b4
+        checkpoint = peer.ledger_state[b2.id()]
+        local = Follower(genesis, config)
+        local.apply_checkpoint(checkpoint)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+        self.assertEqual(set(local.ledger_state.keys()), set(peer.ledger_state.keys()))
+
+    def test_sync_from_dishonest_checkpoint(self):
+        # Prepare multiple peers and a dishonest checkpoint:
+        # Peer0: b0 - b1 - b2 - b5 == tip
+        #           \
+        # Peer1:      b3 - b4
+        #                  ||
+        #              checkpoint
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b3, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b4, c_b = mk_block(b3, 3, c_b), c_b.evolve()
+        b5, c_a = mk_block(b2, 4, c_a), c_a.evolve()
+        peer0 = Follower(genesis, config)
+        for b in [b0, b1, b2, b5]:
+            peer0.on_block(b)
+        self.assertEqual(peer0.tip(), b5)
+        self.assertEqual(peer0.forks, [])
+        peer1 = Follower(genesis, config)
+        for b in [b0, b3, b4]:
+            peer1.on_block(b)
+        self.assertEqual(peer1.tip(), b4)
+        self.assertEqual(peer1.forks, [])
+
+        # Start a sync from the dishonest checkpoint:
+        #       checkpoint
+        #           ||
+        # () - () - b4
+        #
+        # Result: The honest chain is found evetually by backfilling.
+        # b0 - b1 - b2 - b5 == tip
+        #    \
+        #      b3 - b4
+        checkpoint = peer1.ledger_state[b4.id()]
+        local = Follower(genesis, config)
+        local.apply_checkpoint(checkpoint)
+        sync(local, [peer0, peer1])
+        self.assertEqual(local.tip(), b5)
+        self.assertEqual(local.forks, [b4.id()])
+        self.assertEqual(len(local.ledger_state.keys()), 7)
+
+    def test_reject_invalid_blocks_from_backfilling_fork(self):
+        # Prepare a peer with invalid blocks in a fork:
+        # b0 - b1 - b3 - b4 - b5 == tip
+        #    \
+        #      b2 - (invalid_b6) - (invalid_b7)
+        #
+        # First, build a valid chain (b0 ~ b5):
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        peer = Follower(genesis, config)
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b3, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b4, c_a = mk_block(b3, 4, c_a), c_a.evolve()
+        b5, c_a = mk_block(b4, 5, c_a), c_a.evolve()
+        for b in [b0, b1, b2, b3, b4, b5]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # And deliberately, add invalid blocks (b6 ~ b7):
+        fake_coin = Coin(sk=2, value=10)
+        b6, fake_coin = mk_block(b2, 3, fake_coin), fake_coin.evolve()
+        b7, fake_coin = mk_block(b6, 4, fake_coin), fake_coin.evolve()
+        apply_invalid_block_to_ledger_state(peer, b6)
+        apply_invalid_block_to_ledger_state(peer, b7)
+        # the tip shouldn't be changed.
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # Start a sync from a checkpoint where all anscestors are valid:
+        #            checkpoint
+        #                ||
+        # () - () - () - b4
+        #
+        # Result: A fork is backfilled, but without invalid blocks.
+        # b0 - b1 - b3 - b4 - b5 == tip
+        #    \
+        #      b2
+        checkpoint = peer.ledger_state[b4.id()]
+        local = Follower(genesis, config)
+        local.apply_checkpoint(checkpoint)
+        sync(local, [peer])
+        self.assertEqual(local.tip(), peer.tip())
+        self.assertEqual(local.forks, peer.forks)
+        self.assertNotIn(b6.id(), local.ledger_state)
+        self.assertNotIn(b7.id(), local.ledger_state)
+
+    def test_reject_invalid_blocks_from_backfilling_block_tree(self):
+        # Prepare a peer with invalid blocks in a fork:
+        # b0 - b1 - b3 - b4 - b5 == tip
+        #    \
+        #      b2 - (invalid_b6) - (invalid_b7)
+        #
+        # First, build a valid chain (b0 ~ b5):
+        c_a, c_b = Coin(sk=0, value=10), Coin(sk=1, value=10)
+        config = mk_config([c_a, c_b])
+        genesis = mk_genesis_state([c_a, c_b])
+        peer = Follower(genesis, config)
+        b0, c_a = mk_block(genesis.block, 1, c_a), c_a.evolve()
+        b1, c_a = mk_block(b0, 2, c_a), c_a.evolve()
+        b2, c_b = mk_block(b0, 2, c_b), c_b.evolve()
+        b3, c_a = mk_block(b1, 3, c_a), c_a.evolve()
+        b4, c_a = mk_block(b3, 4, c_a), c_a.evolve()
+        b5, c_a = mk_block(b4, 5, c_a), c_a.evolve()
+        for b in [b0, b1, b2, b3, b4, b5]:
+            peer.on_block(b)
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # And deliberately, add invalid blocks (b6 ~ b7):
+        fake_coin = Coin(sk=2, value=10)
+        b6, fake_coin = mk_block(b2, 3, fake_coin), fake_coin.evolve()
+        b7, fake_coin = mk_block(b6, 4, fake_coin), fake_coin.evolve()
+        apply_invalid_block_to_ledger_state(peer, b6)
+        apply_invalid_block_to_ledger_state(peer, b7)
+        # the tip shouldn't be changed.
+        self.assertEqual(peer.tip(), b5)
+        self.assertEqual(peer.forks, [b2.id()])
+
+        # Start a sync from a checkpoint where some anscestors are invalid:
+        # ()          checkpoint
+        #   \             ||
+        #   () - () - (invalid_b7)
+        #
+        # Result: `InvalidBlockTree` exception
+        checkpoint = peer.ledger_state[b7.id()]
+        local = Follower(genesis, config)
+        local.apply_checkpoint(checkpoint)
+        with self.assertRaises(InvalidBlockTree):
+            sync(local, [peer])
+
+
+def apply_invalid_block_to_ledger_state(follower: Follower, block: BlockHeader):
+    state = follower.ledger_state[block.parent].copy()
+    state.apply(block)
+    follower.ledger_state[block.id()] = state