feat(core): implement BIP-32 path schemas

core/src/apps/common/keychain.py

@@ -1,7 +1,9 @@
+import sys
+
 from trezor import wire
 from trezor.crypto import bip32
 
-from . import HARDENED, paths, safety_checks
+from . import paths, safety_checks
 from .seed import Slip21Node, get_seed
 
 if False:
@@ -10,10 +12,12 @@ if False:
         Awaitable,
         Callable,
         Dict,
+        Iterable,
         List,
         Optional,
-        Sequence,
+        Tuple,
         TypeVar,
+        Union,
     )
     from typing_extensions import Protocol
 
@@ -85,13 +89,13 @@ class Keychain:
         self,
         seed: bytes,
         curve: str,
-        namespaces: Sequence[paths.Bip32Path],
-        slip21_namespaces: Sequence[paths.Slip21Path] = (),
+        schemas: Iterable[paths.PathSchemaType],
+        slip21_namespaces: Iterable[paths.Slip21Path] = (),
     ) -> None:
         self.seed = seed
         self.curve = curve
-        self.namespaces = namespaces
-        self.slip21_namespaces = slip21_namespaces
+        self.schemas = tuple(schemas)
+        self.slip21_namespaces = tuple(slip21_namespaces)
 
         self._cache = LRUCache(10)
 
@@ -107,11 +111,14 @@ class Keychain:
         if not safety_checks.is_strict():
             return
 
-        if any(ns == path[: len(ns)] for ns in self.namespaces):
+        if self.is_in_keychain(path):
             return
 
         raise FORBIDDEN_KEY_PATH
 
+    def is_in_keychain(self, path: paths.Bip32Path) -> bool:
+        return any(schema.match(path) for schema in self.schemas)
+
     def _derive_with_cache(
         self,
         prefix_len: int,
@@ -159,27 +166,53 @@ class Keychain:
 async def get_keychain(
     ctx: wire.Context,
     curve: str,
-    namespaces: Sequence[paths.Bip32Path],
-    slip21_namespaces: Sequence[paths.Slip21Path] = (),
+    schemas: Iterable[paths.PathSchemaType],
+    slip21_namespaces: Iterable[paths.Slip21Path] = (),
 ) -> Keychain:
     seed = await get_seed(ctx)
-    keychain = Keychain(seed, curve, namespaces, slip21_namespaces)
+    keychain = Keychain(seed, curve, schemas, slip21_namespaces)
     return keychain
 
 
 def with_slip44_keychain(
-    slip44: int, curve: str = "secp256k1", allow_testnet: bool = False
+    *patterns: str,
+    slip44_id: int,
+    curve: str = "secp256k1",
+    allow_testnet: bool = True,
 ) -> Callable[[HandlerWithKeychain[MsgIn, MsgOut]], Handler[MsgIn, MsgOut]]:
-    namespaces = [[44 | HARDENED, slip44 | HARDENED]]
+    if not patterns:
+        raise ValueError  # specify a pattern
+
     if allow_testnet:
-        namespaces.append([44 | HARDENED, 1 | HARDENED])
+        slip44_ids: Union[int, Tuple[int, int]] = (slip44_id, 1)
+    else:
+        slip44_ids = slip44_id
+
+    schemas = []
+    for pattern in patterns:
+        schemas.append(paths.PathSchema(pattern=pattern, slip44_id=slip44_ids))
 
     def decorator(func: HandlerWithKeychain[MsgIn, MsgOut]) -> Handler[MsgIn, MsgOut]:
         async def wrapper(ctx: wire.Context, msg: MsgIn) -> MsgOut:
-            keychain = await get_keychain(ctx, curve, namespaces)
+            keychain = await get_keychain(ctx, curve, schemas)
             with keychain:
                 return await func(ctx, msg, keychain)
 
         return wrapper
 
     return decorator
+
+
+def auto_keychain(
+    modname: str, allow_testnet: bool = True
+) -> Callable[[HandlerWithKeychain[MsgIn, MsgOut]], Handler[MsgIn, MsgOut]]:
+    rdot = modname.rfind(".")
+    parent_modname = modname[:rdot]
+    parent_module = sys.modules[parent_modname]
+
+    pattern = getattr(parent_module, "PATTERN")
+    curve = getattr(parent_module, "CURVE")
+    slip44_id = getattr(parent_module, "SLIP44_ID")
+    return with_slip44_keychain(
+        pattern, slip44_id=slip44_id, curve=curve, allow_testnet=allow_testnet
+    )

core/src/apps/common/paths.py

@@ -8,7 +8,17 @@ from . import HARDENED
 from .confirm import require_confirm
 
 if False:
-    from typing import Any, Callable, List, Sequence, TypeVar
+    from typing import (
+        Any,
+        Callable,
+        Collection,
+        Iterable,
+        List,
+        Sequence,
+        TypeVar,
+        Union,
+    )
+    from typing_extensions import Protocol
     from trezor import wire
 
     # XXX this is a circular import, but it's only for typing
@@ -18,17 +28,226 @@ if False:
     Slip21Path = Sequence[bytes]
     PathType = TypeVar("PathType", Bip32Path, Slip21Path)
 
+    class PathSchemaType(Protocol):
+        def match(self, path: Bip32Path) -> bool:
+            ...
+
+
+class _FastInclusiveRange(range):
+    """Inclusive range with a fast membership test, suitable for PathSchema use.
+
+    Micropython's `range` does not implement the `__contains__` method. This makes
+    checking whether `x in range(BIG_NUMBER)` slow. This class fixes the problem.
+
+    In addition, convenience modifications have been made:
+    * both `min` and `max` belong to the range (so `stop == max + 1`).
+    * both `min` and `max` must be set, `step` is not allowed (we don't need it and it
+      would make the `__contains__` method more complex)
+    """
+
+    def __init__(self, min: int, max: int) -> None:
+        super().__init__(min, max + 1)
+
+    def __contains__(self, x: object) -> bool:
+        if not isinstance(x, int):
+            return False
+        return self.start <= x < self.stop
+
+
+class PathSchema:
+    """General BIP-32 path schema.
+
+    Loosely based on the BIP-32 path template proposal [1].
+
+    Each path component can be one of the following:
+    - constant, e.g., `7`
+    - list of constants, e.g., `[1,2,3]`
+    - range, e.g., `[0-19]`
+
+    Brackets are recommended but not enforced.
+
+    The following substitutions are available:
+    - `coin_type` is substituted with the coin's SLIP-44 identifier
+    - `account` is substituted with `[0-100]`, Trezor's default range of accounts
+    - `change` is substituted with `[0,1]`
+    - `address_index` is substituted with `[0-1000000]`, Trezor's default range of
+      addresses
+
+    Hardened flag is indicated by an apostrophe and applies to the whole path component.
+    It is impossible to specify both hardened and non-hardened values for the same
+    component.
+
+    See examples of valid path formats below and in `apps.bitcoin.keychain`.
+
+    E.g. the following are equivalent definitions of a BIP-84 schema:
+
+        m/84'/coin_type'/[0-100]'/[0,1]/[0-1000000]
+        m/84'/coin_type'/0-100'/0,1/0-1000000
+        m/84'/coin_type'/account'/change/address_index
+
+    Adding an asterisk at the end of the pattern acts as a wildcard for zero or more
+    path components:
+    - m/* can be followed by any number of _unhardened_ path components
+    - m/*' can be followed by any number of _hardened_ path components
+    - m/** can be followed by any number of _any_ path components
+
+    The following is a BIP-44 generic `GetPublicKey` schema:
+
+        m/44'/coin_type'/account'/*
+
+    The asterisk expression can only appear at end of pattern.
+
+    [1] https://github.com/dgpv/bip32_template_parse_tplaplus_spec/blob/master/bip-path-templates.mediawiki
+    """
+
+    REPLACEMENTS = {
+        "account": "0-100",
+        "change": "0,1",
+        "address_index": "0-1000000",
+    }
+
+    WILDCARD_RANGES = {
+        "*": _FastInclusiveRange(0, HARDENED - 1),
+        "*'": _FastInclusiveRange(HARDENED, 0xFFFF_FFFF),
+        "**": _FastInclusiveRange(0, 0xFFFF_FFFF),
+    }
+
+    def __init__(self, pattern: str, slip44_id: Union[int, Iterable[int]]) -> None:
+        if not pattern.startswith("m/"):
+            raise ValueError  # unsupported path template
+        components = pattern[2:].split("/")
+
+        if isinstance(slip44_id, int):
+            slip44_id = (slip44_id,)
+
+        self.schema: List[Collection[int]] = []
+        self.trailing_components: Collection[int] = ()
+
+        for component in components:
+            if component in self.WILDCARD_RANGES:
+                if len(self.schema) != len(components) - 1:
+                    # every component should have resulted in extending self.schema
+                    # so if self.schema does not have the appropriate length (yet),
+                    # the asterisk is not the last item
+                    raise ValueError  # asterisk is not last item of pattern
+
+                self.trailing_components = self.WILDCARD_RANGES[component]
+                break
+
+            # figure out if the component is hardened
+            if component[-1] == "'":
+                component = component[:-1]
+                parse: Callable[[Any], int] = lambda s: int(s) | HARDENED  # noqa: E731
+            else:
+                parse = int
+
+            # strip brackets
+            if component[0] == "[" and component[-1] == "]":
+                component = component[1:-1]
+
+            # optionally replace a keyword
+            component = self.REPLACEMENTS.get(component, component)
+
+            if "-" in component:
+                # parse as a range
+                a, b = [parse(s) for s in component.split("-", 1)]
+                self.schema.append(_FastInclusiveRange(a, b))
+
+            elif "," in component:
+                # parse as a list of values
+                self.schema.append(set(parse(s) for s in component.split(",")))
+
+            elif component == "coin_type":
+                # substitute SLIP-44 ids
+                self.schema.append(set(parse(s) for s in slip44_id))
+
+            else:
+                # plain constant
+                self.schema.append((parse(component),))
+
+    def match(self, path: Bip32Path) -> bool:
+        # The path must not be _shorter_ than schema. It may be longer.
+        if len(path) < len(self.schema):
+            return False
+
+        path_iter = iter(path)
+        # iterate over length of schema, consuming path components
+        for expected in self.schema:
+            value = next(path_iter)
+            if value not in expected:
+                return False
+
+        # iterate over remaining path components
+        for value in path_iter:
+            if value not in self.trailing_components:
+                return False
+
+        return True
+
+    if __debug__:
+
+        def __repr__(self) -> str:
+            components = ["m"]
+
+            def unharden(item: int) -> int:
+                return item ^ (item & HARDENED)
+
+            for component in self.schema:
+                if isinstance(component, range):
+                    a, b = component.start, component.stop - 1
+                    components.append(
+                        "[{}-{}]{}".format(
+                            unharden(a), unharden(b), "'" if a & HARDENED else ""
+                        )
+                    )
+                else:
+                    component_str = ",".join(str(unharden(i)) for i in component)
+                    if len(component) > 1:
+                        component_str = "[" + component_str + "]"
+                    if next(iter(component)) & HARDENED:
+                        component_str += "'"
+                    components.append(component_str)
+
+            if self.trailing_components:
+                for key, val in self.WILDCARD_RANGES.items():
+                    if self.trailing_components is val:
+                        components.append(key)
+                        break
+                else:
+                    components.append("???")
+
+            return "<schema:" + "/".join(components) + ">"
+
+
+class _AlwaysMatchingSchema:
+    @staticmethod
+    def match(path: Bip32Path) -> bool:
+        return True
+
+
+class _NeverMatchingSchema:
+    @staticmethod
+    def match(path: Bip32Path) -> bool:
+        return False
+
+
+# type objects _AlwaysMatchingSchema and _NeverMatching schema conform to the
+# PathSchemaType protocol, but mypy fails to recognize this due to:
+# https://github.com/python/mypy/issues/4536,
+# hence the following trickery
+AlwaysMatchingSchema: PathSchemaType = _AlwaysMatchingSchema  # type: ignore
+NeverMatchingSchema: PathSchemaType = _NeverMatchingSchema  # type: ignore
+
+PATTERN_BIP44 = "m/44'/coin_type'/account'/change/address_index"
+PATTERN_BIP44_PUBKEY = "m/44'/coin_type'/account'/*"
+PATTERN_SEP5 = "m/44'/coin_type'/account'"
+
 
 async def validate_path(
-    ctx: wire.Context,
-    validate_func: Callable[..., bool],
-    keychain: Keychain,
-    path: List[int],
-    curve: str,
-    **kwargs: Any,
+    ctx: wire.Context, keychain: Keychain, path: Bip32Path, *additional_checks: bool
 ) -> None:
     keychain.verify_path(path)
-    if not validate_func(path, **kwargs):
+    if not keychain.is_in_keychain(path) or not all(additional_checks):
         await show_path_warning(ctx, path)
 
 
@@ -41,28 +260,6 @@ async def show_path_warning(ctx: wire.Context, path: Bip32Path) -> None:
     await require_confirm(ctx, text, ButtonRequestType.UnknownDerivationPath)
 
 
-def validate_path_for_get_public_key(path: Bip32Path, slip44_id: int) -> bool:
-    """
-    Checks if path has at least three hardened items and slip44 id matches.
-    The path is allowed to have more than three items, but all the following
-    items have to be non-hardened.
-    """
-    length = len(path)
-    if length < 3 or length > 5:
-        return False
-    if path[0] != 44 | HARDENED:
-        return False
-    if path[1] != slip44_id | HARDENED:
-        return False
-    if path[2] < HARDENED or path[2] > 20 | HARDENED:
-        return False
-    if length > 3 and is_hardened(path[3]):
-        return False
-    if length > 4 and is_hardened(path[4]):
-        return False
-    return True
-
-
 def is_hardened(i: int) -> bool:
     return bool(i & HARDENED)
 
@@ -71,15 +268,19 @@ def path_is_hardened(address_n: Bip32Path) -> bool:
     return all(is_hardened(n) for n in address_n)
 
 
-def break_address_n_to_lines(address_n: Bip32Path) -> List[str]:
+def address_n_to_str(address_n: Bip32Path) -> str:
     def path_item(i: int) -> str:
         if i & HARDENED:
             return str(i ^ HARDENED) + "'"
         else:
             return str(i)
 
+    return "m/" + "/".join([path_item(i) for i in address_n])
+
+
+def break_address_n_to_lines(address_n: Bip32Path) -> List[str]:
     lines = []
-    path_str = "m/" + "/".join([path_item(i) for i in address_n])
+    path_str = address_n_to_str(address_n)
 
     per_line = const(17)
     while len(path_str) > per_line:

core/tests/test_apps.common.keychain.py

@@ -4,8 +4,8 @@ from mock_storage import mock_storage
 
 from storage import cache
 import storage.device
-from apps.common import HARDENED, safety_checks
-from apps.common.paths import path_is_hardened
+from apps.common import safety_checks
+from apps.common.paths import PATTERN_SEP5, PathSchema, path_is_hardened
 from apps.common.keychain import LRUCache, Keychain, with_slip44_keychain, get_keychain
 from trezor import wire
 from trezor.crypto import bip39
@@ -13,26 +13,31 @@ from trezor.messages import SafetyCheckLevel
 
 
 class TestKeychain(unittest.TestCase):
+    def setUp(self):
+        cache.start_session()
+
+    def tearDown(self):
+        cache.clear_all()
+
     @mock_storage
     def test_verify_path(self):
-        n = [
-            [44 | HARDENED, 134 | HARDENED],
-            [44 | HARDENED, 11 | HARDENED],
-        ]
-        keychain = Keychain(b"", "secp256k1", n)
+        schemas = (
+            PathSchema("m/44'/coin_type'", slip44_id=134),
+            PathSchema("m/44'/coin_type'", slip44_id=11),
+        )
+        keychain = Keychain(b"", "secp256k1", schemas)
 
         correct = (
-            [44 | HARDENED, 134 | HARDENED],
-            [44 | HARDENED, 11 | HARDENED],
-            [44 | HARDENED, 11 | HARDENED, 12],
+            [H_(44), H_(134)],
+            [H_(44), H_(11)],
         )
         for path in correct:
             keychain.verify_path(path)
 
         fails = (
-            [44 | HARDENED, 134],  # path does not match
+            [H_(44), 134],  # path does not match
             [44, 134],  # path does not match (non-hardened items)
-            [44 | HARDENED, 13 | HARDENED],  # invalid second item
+            [H_(44), H_(13)],  # invalid second item
         )
         for f in fails:
             with self.assertRaises(wire.DataError):
@@ -42,43 +47,40 @@ class TestKeychain(unittest.TestCase):
         safety_checks.apply_setting(SafetyCheckLevel.PromptTemporarily)
         for path in correct + fails:
             keychain.verify_path(path)
-        # turn on restrictions
-        safety_checks.apply_setting(SafetyCheckLevel.Strict)
 
     def test_verify_path_special_ed25519(self):
-        n = [[44 | HARDENED, 134 | HARDENED]]
-        k = Keychain(b"", "ed25519-keccak", n)
+        schema = PathSchema("m/44'/coin_type'/*", slip44_id=134)
+        k = Keychain(b"", "ed25519-keccak", [schema])
 
         # OK case
-        k.verify_path([44 | HARDENED, 134 | HARDENED])
+        k.verify_path([H_(44), H_(134)])
 
         # failing case: non-hardened component with ed25519-like derivation
         with self.assertRaises(wire.DataError):
-            k.verify_path([44 | HARDENED, 134 | HARDENED, 1])
+            k.verify_path([H_(44), H_(134), 1])
 
-    def test_verify_path_empty_namespace(self):
-        k = Keychain(b"", "secp256k1", [[]])
-        correct = (
+    def test_no_schemas(self):
+        k = Keychain(b"", "secp256k1", [])
+        paths = (
             [],
             [1, 2, 3, 4],
-            [44 | HARDENED, 11 | HARDENED],
-            [44 | HARDENED, 11 | HARDENED, 12],
+            [H_(44), H_(11)],
+            [H_(44), H_(11), 12],
         )
-        for c in correct:
-            k.verify_path(c)
+        for path in paths:
+            self.assertRaises(wire.DataError, k.verify_path, path)
 
     def test_get_keychain(self):
         seed = bip39.seed(" ".join(["all"] * 12), "")
-        cache.start_session()
         cache.set(cache.APP_COMMON_SEED, seed)
 
-        namespaces = [[44 | HARDENED]]
+        schema = PathSchema("m/44'/1'", 0)
         keychain = await_result(
-            get_keychain(wire.DUMMY_CONTEXT, "secp256k1", namespaces)
+            get_keychain(wire.DUMMY_CONTEXT, "secp256k1", [schema])
         )
 
         # valid path:
-        self.assertIsNotNone(keychain.derive([44 | HARDENED, 1 | HARDENED]))
+        self.assertIsNotNone(keychain.derive([H_(44), H_(1)]))
 
         # invalid path:
         with self.assertRaises(wire.DataError):
@@ -86,13 +88,12 @@ class TestKeychain(unittest.TestCase):
 
     def test_with_slip44(self):
         seed = bip39.seed(" ".join(["all"] * 12), "")
-        cache.start_session()
         cache.set(cache.APP_COMMON_SEED, seed)
 
         slip44_id = 42
-        valid_path = [44 | HARDENED, slip44_id | HARDENED]
-        invalid_path = [44 | HARDENED, 99 | HARDENED]
-        testnet_path = [44 | HARDENED, 1 | HARDENED]
+        valid_path = [H_(44), H_(slip44_id), H_(0)]
+        invalid_path = [H_(44), H_(99), H_(0)]
+        testnet_path = [H_(44), H_(1), H_(0)]
 
         def check_valid_paths(keychain, *paths):
             for path in paths:
@@ -102,24 +103,24 @@ class TestKeychain(unittest.TestCase):
             for path in paths:
                 self.assertRaises(wire.DataError, keychain.derive, path)
 
-        @with_slip44_keychain(slip44_id)
+        @with_slip44_keychain(PATTERN_SEP5, slip44_id=slip44_id)
         async def func_id_only(ctx, msg, keychain):
-            check_valid_paths(keychain, valid_path)
-            check_invalid_paths(keychain, testnet_path, invalid_path)
-
-        @with_slip44_keychain(slip44_id, allow_testnet=True)
-        async def func_allow_testnet(ctx, msg, keychain):
             check_valid_paths(keychain, valid_path, testnet_path)
             check_invalid_paths(keychain, invalid_path)
 
-        @with_slip44_keychain(slip44_id, curve="ed25519")
-        async def func_with_curve(ctx, msg, keychain):
-            self.assertEqual(keychain.curve, "ed25519")
+        @with_slip44_keychain(PATTERN_SEP5, slip44_id=slip44_id, allow_testnet=False)
+        async def func_disallow_testnet(ctx, msg, keychain):
             check_valid_paths(keychain, valid_path)
             check_invalid_paths(keychain, testnet_path, invalid_path)
 
+        @with_slip44_keychain(PATTERN_SEP5, slip44_id=slip44_id, curve="ed25519")
+        async def func_with_curve(ctx, msg, keychain):
+            self.assertEqual(keychain.curve, "ed25519")
+            check_valid_paths(keychain, valid_path, testnet_path)
+            check_invalid_paths(keychain, invalid_path)
+
         await_result(func_id_only(wire.DUMMY_CONTEXT, None))
-        await_result(func_allow_testnet(wire.DUMMY_CONTEXT, None))
+        await_result(func_disallow_testnet(wire.DUMMY_CONTEXT, None))
         await_result(func_with_curve(wire.DUMMY_CONTEXT, None))
 
     def test_lru_cache(self):

core/tests/test_apps.common.paths.py

@@ -1,54 +1,163 @@
 from common import *
-from apps.common import HARDENED
-from apps.common.paths import validate_path_for_get_public_key, is_hardened, path_is_hardened
+from trezor.utils import ensure
+from apps.common.paths import *
 
 
 class TestPaths(unittest.TestCase):
-
     def test_is_hardened(self):
-        self.assertTrue(is_hardened(44 | HARDENED))
-        self.assertTrue(is_hardened(0 | HARDENED))
-        self.assertTrue(is_hardened(99999 | HARDENED))
+        self.assertTrue(is_hardened(H_(44)))
+        self.assertTrue(is_hardened(H_(0)))
+        self.assertTrue(is_hardened(H_(99999)))
 
         self.assertFalse(is_hardened(44))
         self.assertFalse(is_hardened(0))
         self.assertFalse(is_hardened(99999))
 
     def test_path_is_hardened(self):
-        self.assertTrue(path_is_hardened([44 | HARDENED, 1 | HARDENED, 0 | HARDENED]))
-        self.assertTrue(path_is_hardened([0 | HARDENED, ]))
-
-        self.assertFalse(path_is_hardened([44, 44 | HARDENED, 0 | HARDENED]))
-        self.assertFalse(path_is_hardened([0, ]))
-        self.assertFalse(path_is_hardened([44 | HARDENED, 1 | HARDENED, 0 | HARDENED, 0 | HARDENED, 0]))
-
-    def test_path_for_get_public_key(self):
-        # 44'/41'/0'
-        self.assertTrue(validate_path_for_get_public_key([44 | HARDENED, 41 | HARDENED, 0 | HARDENED], 41))
-        # 44'/111'/0'
-        self.assertTrue(validate_path_for_get_public_key([44 | HARDENED, 111 | HARDENED, 0 | HARDENED], 111))
-        # 44'/0'/0'/0
-        self.assertTrue(validate_path_for_get_public_key([44 | HARDENED, 0 | HARDENED, 0 | HARDENED, 0], 0))
-        # 44'/0'/0'/0/0
-        self.assertTrue(validate_path_for_get_public_key([44 | HARDENED, 0 | HARDENED, 0 | HARDENED, 0, 0], 0))
-
-        # 44'/41'
-        self.assertFalse(validate_path_for_get_public_key([44 | HARDENED, 41 | HARDENED], 41))
-        # 44'/41'/0
-        self.assertFalse(validate_path_for_get_public_key([44 | HARDENED, 41 | HARDENED, 0], 41))
-        # 44'/41'/0' slip44 mismatch
-        self.assertFalse(validate_path_for_get_public_key([44 | HARDENED, 41 | HARDENED, 0 | HARDENED], 99))
-        # # 44'/41'/0'/0'
-        self.assertFalse(validate_path_for_get_public_key([44 | HARDENED, 41 | HARDENED, 0 | HARDENED, 0 | HARDENED], 41))
-        # # 44'/41'/0'/0'/0
-        self.assertFalse(validate_path_for_get_public_key([44 | HARDENED, 41 | HARDENED, 0 | HARDENED, 0 | HARDENED, 0], 41))
-        # # 44'/41'/0'/0'/0'
-        self.assertFalse(validate_path_for_get_public_key([44 | HARDENED, 41 | HARDENED, 0 | HARDENED, 0 | HARDENED, 0 | HARDENED], 41))
-        # # 44'/41'/0'/0/0/0
-        self.assertFalse(validate_path_for_get_public_key([44 | HARDENED, 41 | HARDENED, 0 | HARDENED, 0, 0, 0], 41))
-        # # 44'/41'/0'/0/0'
-        self.assertFalse(validate_path_for_get_public_key([44 | HARDENED, 41 | HARDENED, 0 | HARDENED, 0, 0 | HARDENED], 41))
-
-
-if __name__ == '__main__':
+        self.assertTrue(path_is_hardened([H_(44), H_(1), H_(0)]))
+        self.assertTrue(path_is_hardened([H_(0)]))
+
+        self.assertFalse(path_is_hardened([44, H_(44), H_(0)]))
+        self.assertFalse(path_is_hardened([0]))
+        self.assertFalse(path_is_hardened([H_(44), H_(1), H_(0), H_(0), 0]))
+
+
+class TestPathSchemas(unittest.TestCase):
+    def assertMatch(self, schema, path):
+        self.assertTrue(
+            schema.match(path),
+            "Expected schema {!r} to match path {}".format(
+                schema, address_n_to_str(path)
+            ),
+        )
+
+    def assertMismatch(self, schema, path):
+        self.assertFalse(
+            schema.match(path),
+            "Expected schema {!r} to not match path {}".format(
+                schema, address_n_to_str(path)
+            ),
+        )
+
+    def assertEqualSchema(self, schema_a, schema_b):
+        def is_equal(a, b):
+            if isinstance(a, range) and isinstance(b, range):
+                return a.start == b.start and a.step == b.step and a.stop == b.stop
+            return a == b
+
+        ensure(
+            all(is_equal(a, b) for a, b in zip(schema_a.schema, schema_b.schema))
+            and is_equal(schema_a.trailing_components, schema_b.trailing_components),
+            "Schemas differ:\nA = {!r}\nB = {!r}".format(schema_a, schema_b),
+        )
+
+    def test_always_never_matching(self):
+        paths = [
+            [],
+            [0],
+            [H_(0)],
+            [44],
+            [H_(44)],
+            [H_(44), H_(0), H_(0), 0, 0],
+            [H_(44), H_(0), H_(0), H_(0), H_(0)],
+            [H_(44), H_(0), H_(0), H_(0), H_(0)] * 10,
+        ]
+        for path in paths:
+            self.assertMatch(SCHEMA_ANY_PATH, path)
+            self.assertMismatch(SCHEMA_NO_MATCH, path)
+
+    def test_pattern_fixed(self):
+        pattern = "m/44'/0'/0'/0/0"
+        schema = PathSchema(pattern, 0)
+
+        self.assertMatch(schema, [H_(44), H_(0), H_(0), 0, 0])
+
+        paths = [
+            [],
+            [0],
+            [H_(0)],
+            [44],
+            [H_(44)],
+            [44, 0, 0, 0, 0],
+            [H_(44), H_(0), H_(0), H_(0), H_(0)],
+            [H_(44), H_(0), H_(0), H_(0), H_(0)] * 10,
+        ]
+        for path in paths:
+            self.assertMismatch(schema, path)
+
+    def test_ranges_sets(self):
+        pattern_ranges = "m/44'/[100-109]'/[0-20]"
+        pattern_sets = "m/44'/[100,105,109]'/[0,10,20]"
+        schema_ranges = PathSchema(pattern_ranges, 0)
+        schema_sets = PathSchema(pattern_sets, 0)
+
+        paths_good = [
+            [H_(44), H_(100), 0],
+            [H_(44), H_(100), 10],
+            [H_(44), H_(100), 20],
+            [H_(44), H_(105), 0],
+            [H_(44), H_(105), 10],
+            [H_(44), H_(105), 20],
+            [H_(44), H_(109), 0],
+            [H_(44), H_(109), 10],
+            [H_(44), H_(109), 20],
+        ]
+        for path in paths_good:
+            self.assertMatch(schema_ranges, path)
+            self.assertMatch(schema_sets, path)
+
+        paths_bad = [
+            [H_(44), H_(100)],
+            [H_(44), H_(100), 0, 0],
+            [H_(44), 100, 0],
+            [H_(44), 100, H_(0)],
+            [H_(44), H_(99), 0],
+            [H_(44), H_(110), 0],
+            [H_(44), H_(100), 21],
+        ]
+        for path in paths_bad:
+            self.assertMismatch(schema_ranges, path)
+            self.assertMismatch(schema_sets, path)
+
+        self.assertMatch(schema_ranges, [H_(44), H_(104), 19])
+        self.assertMismatch(schema_sets, [H_(44), H_(104), 19])
+
+    def test_brackets(self):
+        pattern_a = "m/[0]'/[0-5]'/[0,1,2]'/[0]/[0-5]/[0,1,2]"
+        pattern_b = "m/0'/0-5'/0,1,2'/0/0-5/0,1,2"
+        schema_a = PathSchema(pattern_a, 0)
+        schema_b = PathSchema(pattern_b, 0)
+        self.assertEqualSchema(schema_a, schema_b)
+
+    def test_wildcard(self):
+        pattern = "m/44'/0'/*"
+        schema = PathSchema(pattern, 0)
+
+        paths_good = [
+            [H_(44), H_(0)],
+            [H_(44), H_(0), 0],
+            [H_(44), H_(0), 0, 1, 2, 3, 4, 5, 6, 7, 8],
+        ]
+        for path in paths_good:
+            self.assertMatch(schema, path)
+
+        paths_bad = [
+            [H_(44)],
+            [H_(44), H_(0), H_(0)],
+            [H_(44), H_(0), 0, 1, 2, 3, 4, 5, 6, 7, H_(8)],
+        ]
+        for path in paths_bad:
+            self.assertMismatch(schema, path)
+
+    def test_substitutes(self):
+        pattern_sub = "m/44'/coin_type'/account'/change/address_index"
+        pattern_plain = "m/44'/19'/0-100'/0,1/0-1000000"
+        schema_sub = PathSchema(pattern_sub, slip44_id=19)
+        # use wrong slip44 id to ensure it doesn't affect anything
+        schema_plain = PathSchema(pattern_plain, slip44_id=0)
+
+        self.assertEqualSchema(schema_sub, schema_plain)
+
+
+if __name__ == "__main__":
     unittest.main()