diff --git a/core/src/apps/wallet/sign_tx/multisig.py b/core/src/apps/wallet/sign_tx/multisig.py
index 5cbf62f2e..aff137dd6 100644
--- a/core/src/apps/wallet/sign_tx/multisig.py
+++ b/core/src/apps/wallet/sign_tx/multisig.py
@@ -7,17 +7,20 @@ from trezor.utils import HashWriter, ensure
 
 from apps.wallet.sign_tx.writers import write_bytes_fixed, write_uint32
 
+if False:
+    from typing import List, Optional
+
 
 class MultisigError(ValueError):
     pass
 
 
 class MultisigFingerprint:
-    def __init__(self):
-        self.fingerprint = None  # multisig fingerprint bytes
+    def __init__(self) -> None:
+        self.fingerprint = None  # type: Optional[bytes] # multisig fingerprint bytes
         self.mismatch = False  # flag if multisig input fingerprints are equal
 
-    def add(self, multisig: MultisigRedeemScriptType):
+    def add(self, multisig: MultisigRedeemScriptType) -> None:
         fp = multisig_fingerprint(multisig)
         ensure(fp is not None)
         if self.fingerprint is None:
@@ -25,7 +28,7 @@ class MultisigFingerprint:
         elif self.fingerprint != fp:
             self.mismatch = True
 
-    def matches(self, multisig: MultisigRedeemScriptType):
+    def matches(self, multisig: MultisigRedeemScriptType) -> bool:
         fp = multisig_fingerprint(multisig)
         ensure(fp is not None)
         if self.mismatch is False and self.fingerprint == fp:
@@ -90,14 +93,14 @@ def multisig_get_pubkey(n: HDNodeType, p: list) -> bytes:
     return node.public_key()
 
 
-def multisig_get_pubkeys(multisig: MultisigRedeemScriptType):
+def multisig_get_pubkeys(multisig: MultisigRedeemScriptType) -> List[bytes]:
     if multisig.nodes:
         return [multisig_get_pubkey(hd, multisig.address_n) for hd in multisig.nodes]
     else:
         return [multisig_get_pubkey(hd.node, hd.address_n) for hd in multisig.pubkeys]
 
 
-def multisig_get_pubkey_count(multisig: MultisigRedeemScriptType):
+def multisig_get_pubkey_count(multisig: MultisigRedeemScriptType) -> int:
     if multisig.nodes:
         return len(multisig.nodes)
     else:
diff --git a/core/src/apps/wallet/sign_tx/omni.py b/core/src/apps/wallet/sign_tx/omni.py
index 7d150bedf..81b2a3662 100644
--- a/core/src/apps/wallet/sign_tx/omni.py
+++ b/core/src/apps/wallet/sign_tx/omni.py
@@ -2,6 +2,9 @@ from ustruct import unpack
 
 from trezor.strings import format_amount
 
+if False:
+    from typing import Optional
+
 currencies = {
     1: ("OMNI", True),
     2: ("tOMNI", True),
@@ -14,7 +17,7 @@ def is_valid(data: bytes) -> bool:
     return len(data) >= 8 and data[:4] == b"omni"
 
 
-def parse(data: bytes) -> bool:
+def parse(data: bytes) -> Optional[str]:
     if not is_valid(data):
         return None
     tx_version, tx_type = unpack(">HH", data[4:8])
diff --git a/core/src/apps/wallet/sign_tx/progress.py b/core/src/apps/wallet/sign_tx/progress.py
index 1dc64d29c..0971c6ddf 100644
--- a/core/src/apps/wallet/sign_tx/progress.py
+++ b/core/src/apps/wallet/sign_tx/progress.py
@@ -4,7 +4,7 @@ _progress = 0
 _steps = 0
 
 
-def init(inputs, outputs):
+def init(inputs: int, outputs: int) -> None:
     global _progress, _steps
     _progress = 0
     _steps = inputs + inputs + outputs + inputs
@@ -12,18 +12,18 @@ def init(inputs, outputs):
     report()
 
 
-def advance():
+def advance() -> None:
     global _progress
     _progress += 1
     report()
 
 
-def report_init():
+def report_init() -> None:
     ui.display.clear()
     ui.header("Signing transaction")
 
 
-def report():
+def report() -> None:
     if utils.DISABLE_ANIMATION:
         return
     p = 1000 * _progress // _steps
diff --git a/core/src/apps/wallet/sign_tx/scripts.py b/core/src/apps/wallet/sign_tx/scripts.py
index b1495c785..d02171d0b 100644
--- a/core/src/apps/wallet/sign_tx/scripts.py
+++ b/core/src/apps/wallet/sign_tx/scripts.py
@@ -132,7 +132,7 @@ def input_script_p2wsh_in_p2sh(script_hash: bytes) -> bytearray:
 # ===
 
 
-def witness_p2wpkh(signature: bytes, pubkey: bytes, sighash: int):
+def witness_p2wpkh(signature: bytes, pubkey: bytes, sighash: int) -> bytearray:
     w = empty_bytearray(1 + 5 + len(signature) + 1 + 5 + len(pubkey))
     write_varint(w, 0x02)  # num of segwit items, in P2WPKH it's always 2
     append_signature(w, signature, sighash)
diff --git a/core/src/apps/wallet/sign_tx/zcash.py b/core/src/apps/wallet/sign_tx/zcash.py
index 4f5c8e6ff..cde31b5c4 100644
--- a/core/src/apps/wallet/sign_tx/zcash.py
+++ b/core/src/apps/wallet/sign_tx/zcash.py
@@ -47,7 +47,7 @@ def derive_script_code(txi: TxInputType, pubkeyhash: bytes) -> bytearray:
 
 
 class Zip143:
-    def __init__(self, branch_id):
+    def __init__(self, branch_id: int) -> None:
         self.branch_id = branch_id
         self.h_prevouts = HashWriter(blake2b(outlen=32, personal=b"ZcashPrevoutHash"))
         self.h_sequence = HashWriter(blake2b(outlen=32, personal=b"ZcashSequencHash"))
@@ -119,7 +119,7 @@ class Zip143:
 
 
 class Zip243(Zip143):
-    def __init__(self, branch_id):
+    def __init__(self, branch_id) -> None:
         super().__init__(branch_id)
 
     def preimage_hash(
diff --git a/core/src/trezor/crypto/base58.py b/core/src/trezor/crypto/base58.py
index a472f5c32..310439807 100644
--- a/core/src/trezor/crypto/base58.py
+++ b/core/src/trezor/crypto/base58.py
@@ -13,11 +13,14 @@
 # This module adds shiny packaging and support for python3.
 #
 
+if False:
+    from typing import Callable
+
 # 58 character alphabet used
 _alphabet = "123456789ABCDEFGHJKLMNPQRSTUVWXYZabcdefghijkmnopqrstuvwxyz"
 
 
-def encode(data: bytes, alphabet=_alphabet) -> str:
+def encode(data: bytes, alphabet: str = _alphabet) -> str:
     """
     Convert bytes to base58 encoded string.
     """
@@ -38,7 +41,7 @@ def encode(data: bytes, alphabet=_alphabet) -> str:
     return "".join((c for c in reversed(result + alphabet[0] * (origlen - newlen))))
 
 
-def decode(string: str, alphabet=_alphabet) -> bytes:
+def decode(string: str, alphabet: str = _alphabet) -> bytes:
     """
     Convert base58 encoded string to bytes.
     """
@@ -89,14 +92,16 @@ def ripemd160_32(data: bytes) -> bytes:
     return ripemd160(data).digest()[:4]
 
 
-def encode_check(data: bytes, digestfunc=sha256d_32) -> str:
+def encode_check(data: bytes, digestfunc: Callable[[bytes], bytes] = sha256d_32) -> str:
     """
     Convert bytes to base58 encoded string, append checksum.
     """
     return encode(data + digestfunc(data))
 
 
-def decode_check(string: str, digestfunc=sha256d_32) -> bytes:
+def decode_check(
+    string: str, digestfunc: Callable[[bytes], bytes] = sha256d_32
+) -> bytes:
     """
     Convert base58 encoded string to bytes and verify checksum.
     """
@@ -104,7 +109,7 @@ def decode_check(string: str, digestfunc=sha256d_32) -> bytes:
     return verify_checksum(result, digestfunc)
 
 
-def verify_checksum(data: bytes, digestfunc) -> bytes:
+def verify_checksum(data: bytes, digestfunc: Callable[[bytes], bytes]) -> bytes:
     digestlen = len(digestfunc(b""))
     result, check = data[:-digestlen], data[-digestlen:]
 
diff --git a/core/src/trezor/crypto/bech32.py b/core/src/trezor/crypto/bech32.py
index 212705d55..d7a82cf40 100644
--- a/core/src/trezor/crypto/bech32.py
+++ b/core/src/trezor/crypto/bech32.py
@@ -20,11 +20,13 @@
 
 """Reference implementation for Bech32 and segwit addresses."""
 
+if False:
+    from typing import List, Optional, Tuple
 
 CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l"
 
 
-def bech32_polymod(values):
+def bech32_polymod(values: List[int]) -> int:
     """Internal function that computes the Bech32 checksum."""
     generator = [0x3B6A57B2, 0x26508E6D, 0x1EA119FA, 0x3D4233DD, 0x2A1462B3]
     chk = 1
@@ -36,30 +38,30 @@ def bech32_polymod(values):
     return chk
 
 
-def bech32_hrp_expand(hrp):
+def bech32_hrp_expand(hrp: str) -> List[int]:
     """Expand the HRP into values for checksum computation."""
     return [ord(x) >> 5 for x in hrp] + [0] + [ord(x) & 31 for x in hrp]
 
 
-def bech32_verify_checksum(hrp, data):
+def bech32_verify_checksum(hrp: str, data: List[int]) -> bool:
     """Verify a checksum given HRP and converted data characters."""
     return bech32_polymod(bech32_hrp_expand(hrp) + data) == 1
 
 
-def bech32_create_checksum(hrp, data):
+def bech32_create_checksum(hrp: str, data: List[int]) -> List[int]:
     """Compute the checksum values given HRP and data."""
     values = bech32_hrp_expand(hrp) + data
     polymod = bech32_polymod(values + [0, 0, 0, 0, 0, 0]) ^ 1
     return [(polymod >> 5 * (5 - i)) & 31 for i in range(6)]
 
 
-def bech32_encode(hrp, data):
+def bech32_encode(hrp: str, data: List[int]) -> str:
     """Compute a Bech32 string given HRP and data values."""
     combined = data + bech32_create_checksum(hrp, data)
     return hrp + "1" + "".join([CHARSET[d] for d in combined])
 
 
-def bech32_decode(bech):
+def bech32_decode(bech: str) -> Tuple[Optional[str], Optional[List[int]]]:
     """Validate a Bech32 string, and determine HRP and data."""
     if (any(ord(x) < 33 or ord(x) > 126 for x in bech)) or (
         bech.lower() != bech and bech.upper() != bech
@@ -78,7 +80,9 @@ def bech32_decode(bech):
     return (hrp, data[:-6])
 
 
-def convertbits(data, frombits, tobits, pad=True):
+def convertbits(
+    data: List[int], frombits: int, tobits: int, pad: bool = True
+) -> List[int]:
     """General power-of-2 base conversion."""
     acc = 0
     bits = 0
@@ -87,7 +91,7 @@ def convertbits(data, frombits, tobits, pad=True):
     max_acc = (1 << (frombits + tobits - 1)) - 1
     for value in data:
         if value < 0 or (value >> frombits):
-            return None
+            raise ValueError
         acc = ((acc << frombits) | value) & max_acc
         bits += frombits
         while bits >= tobits:
@@ -97,17 +101,17 @@ def convertbits(data, frombits, tobits, pad=True):
         if bits:
             ret.append((acc << (tobits - bits)) & maxv)
     elif bits >= frombits or ((acc << (tobits - bits)) & maxv):
-        return None
+        raise ValueError
     return ret
 
 
-def decode(hrp, addr):
+def decode(hrp: str, addr: str) -> Tuple[Optional[int], Optional[List[int]]]:
     """Decode a segwit address."""
     hrpgot, data = bech32_decode(addr)
-    if hrpgot != hrp:
+    if data is None or hrpgot != hrp:
         return (None, None)
     decoded = convertbits(data[1:], 5, 8, False)
-    if decoded is None or len(decoded) < 2 or len(decoded) > 40:
+    if len(decoded) < 2 or len(decoded) > 40:
         return (None, None)
     if data[0] > 16:
         return (None, None)
@@ -116,7 +120,7 @@ def decode(hrp, addr):
     return (data[0], decoded)
 
 
-def encode(hrp, witver, witprog):
+def encode(hrp: str, witver: int, witprog: List[int]) -> Optional[str]:
     """Encode a segwit address."""
     ret = bech32_encode(hrp, [witver] + convertbits(witprog, 8, 5))
     if decode(hrp, ret) == (None, None):
diff --git a/core/src/trezor/crypto/cashaddr.py b/core/src/trezor/crypto/cashaddr.py
index c8c8b576b..1ced926d4 100644
--- a/core/src/trezor/crypto/cashaddr.py
+++ b/core/src/trezor/crypto/cashaddr.py
@@ -20,12 +20,15 @@
 # OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
 # THE SOFTWARE.
 
+if False:
+    from typing import Iterable, List, Tuple
+
 CHARSET = "qpzry9x8gf2tvdw0s3jn54khce6mua7l"
 ADDRESS_TYPE_P2KH = 0
 ADDRESS_TYPE_P2SH = 8
 
 
-def cashaddr_polymod(values):
+def cashaddr_polymod(values: List[int]) -> int:
     generator = [0x98F2BC8E61, 0x79B76D99E2, 0xF33E5FB3C4, 0xAE2EABE2A8, 0x1E4F43E470]
     chk = 1
     for value in values:
@@ -36,11 +39,11 @@ def cashaddr_polymod(values):
     return chk ^ 1
 
 
-def prefix_expand(prefix):
+def prefix_expand(prefix: str) -> List[int]:
     return [ord(x) & 0x1F for x in prefix] + [0]
 
 
-def calculate_checksum(prefix, payload):
+def calculate_checksum(prefix: str, payload: List[int]) -> List[int]:
     poly = cashaddr_polymod(prefix_expand(prefix) + payload + [0, 0, 0, 0, 0, 0, 0, 0])
     out = list()
     for i in range(8):
@@ -48,25 +51,27 @@ def calculate_checksum(prefix, payload):
     return out
 
 
-def verify_checksum(prefix, payload):
+def verify_checksum(prefix: str, payload: List[int]) -> bool:
     return cashaddr_polymod(prefix_expand(prefix) + payload) == 0
 
 
-def b32decode(inputs):
+def b32decode(inputs: str) -> List[int]:
     out = list()
     for letter in inputs:
         out.append(CHARSET.find(letter))
     return out
 
 
-def b32encode(inputs):
+def b32encode(inputs: List[int]) -> str:
     out = ""
     for char_code in inputs:
         out += CHARSET[char_code]
     return out
 
 
-def convertbits(data, frombits, tobits, pad=True):
+def convertbits(
+    data: Iterable[int], frombits: int, tobits: int, pad: bool = True
+) -> List[int]:
     acc = 0
     bits = 0
     ret = []
@@ -74,7 +79,7 @@ def convertbits(data, frombits, tobits, pad=True):
     max_acc = (1 << (frombits + tobits - 1)) - 1
     for value in data:
         if value < 0 or (value >> frombits):
-            return None
+            raise ValueError
         acc = ((acc << frombits) | value) & max_acc
         bits += frombits
         while bits >= tobits:
@@ -84,18 +89,18 @@ def convertbits(data, frombits, tobits, pad=True):
         if bits:
             ret.append((acc << (tobits - bits)) & maxv)
     elif bits >= frombits or ((acc << (tobits - bits)) & maxv):
-        return None
+        raise ValueError
     return ret
 
 
-def encode(prefix, version, payload):
-    payload = bytes([version]) + payload
-    payload = convertbits(payload, 8, 5)
+def encode(prefix: str, version: int, payload_bytes: bytes) -> str:
+    payload_bytes = bytes([version]) + payload_bytes
+    payload = convertbits(payload_bytes, 8, 5)
     checksum = calculate_checksum(prefix, payload)
     return prefix + ":" + b32encode(payload + checksum)
 
 
-def decode(prefix, addr):
+def decode(prefix: str, addr: str) -> Tuple[int, bytes]:
     addr = addr.lower()
     decoded = b32decode(addr)
     if not verify_checksum(prefix, decoded):