diff --git a/telethon/client/auth.py b/telethon/client/auth.py
index da864eb3..f310f5d3 100644
--- a/telethon/client/auth.py
+++ b/telethon/client/auth.py
@@ -422,11 +422,15 @@ class AuthMethods(MessageParseMethods, UserMethods):
 
     async def edit_2fa(
             self, current_password=None, new_password=None,
-            *, hint='', email=None):
+            *, hint='', email=None, email_code_callback=None):
         """
         Changes the 2FA settings of the logged in user, according to the
         passed parameters. Take note of the parameter explanations.
 
+        Note that this method may be *incredibly* slow depending on the
+        prime numbers that must be used during the process to make sure
+        that everything is safe.
+
         Has no effect if both current and new password are omitted.
 
         current_password (`str`, optional):
@@ -450,53 +454,42 @@ class AuthMethods(MessageParseMethods, UserMethods):
             if value differs from current one, and has no effect if
             ``new_password`` is not set.
 
+        email_code_callback (`callable`, optional):
+            If an email is provided, a callback that returns the code sent
+            to it must also be set. This callback may be asynchronous.
+
         Returns:
             ``True`` if successful, ``False`` otherwise.
         """
-        raise NotImplemented
-
         if new_password is None and current_password is None:
             return False
 
-        pass_result = await self(functions.account.GetPasswordRequest())
-        if isinstance(
-                pass_result, types.account.NoPassword) and current_password:
+        pwd = await self(functions.account.GetPasswordRequest())
+        assert isinstance(pwd, types.account.Password)
+        if not pwd.has_password and current_password:
             current_password = None
 
-        salt_random = os.urandom(8)
-        salt = pass_result.new_salt + salt_random
-        if not current_password:
-            current_password_hash = salt
+        if current_password:
+            password = pwd_mod.compute_check(pwd, current_password)
         else:
-            current_password = (
-                pass_result.current_salt
-                + current_password.encode()
-                + pass_result.current_salt
-            )
-            current_password_hash = hashlib.sha256(current_password).digest()
+            password = types.InputCheckPasswordEmpty()
 
-        if new_password:  # Setting new password
-            new_password = salt + new_password.encode('utf-8') + salt
-            new_password_hash = hashlib.sha256(new_password).digest()
-            new_settings = types.account.PasswordInputSettings(
-                new_salt=salt,
+        if new_password:
+            new_password_hash = pwd_mod.compute_digest(
+                pwd.new_algo, new_password)
+        else:
+            new_password_hash = b''
+
+        await self(functions.account.UpdatePasswordSettingsRequest(
+            password=password,
+            new_settings=types.account.PasswordInputSettings(
+                new_algo=pwd.new_algo,
                 new_password_hash=new_password_hash,
-                hint=hint
+                hint=hint,
+                email=email,
+                new_secure_settings=None
             )
-            if email:  # If enabling 2FA or changing email
-                new_settings.email = email  # TG counts empty string as None
-            return await self(functions.account.UpdatePasswordSettingsRequest(
-                current_password_hash, new_settings=new_settings
-            ))
-        else:  # Removing existing password
-            return await self(functions.account.UpdatePasswordSettingsRequest(
-                current_password_hash,
-                new_settings=types.account.PasswordInputSettings(
-                    new_salt=bytes(),
-                    new_password_hash=bytes(),
-                    hint=hint
-                )
-            ))
+        ))
 
     # endregion
 
diff --git a/telethon/password.py b/telethon/password.py
index 17d6438d..88b70852 100644
--- a/telethon/password.py
+++ b/telethon/password.py
@@ -11,6 +11,7 @@ def check_prime_and_good_check(prime: int, g: int):
         raise ValueError('bad prime count {}, expected {}'
                          .format(prime.bit_length(), good_prime_bits_count))
 
+    # TODO This is awfully slow
     if factorization.Factorization.factorize(prime)[0] != 1:
         raise ValueError('given "prime" is not prime')
 
@@ -110,13 +111,27 @@ def pbkdf2sha512(password: bytes, salt: bytes, iterations: int):
 
 
 def compute_hash(algo: types.PasswordKdfAlgoSHA256SHA256PBKDF2HMACSHA512iter100000SHA256ModPow,
-                 password: bytes):
-    hash1 = sha256(algo.salt1, password, algo.salt1)
+                 password: str):
+    hash1 = sha256(algo.salt1, password.encode('utf-8'), algo.salt1)
     hash2 = sha256(algo.salt2, hash1, algo.salt2)
     hash3 = pbkdf2sha512(hash2, algo.salt1, 100000)
     return sha256(algo.salt2, hash3, algo.salt2)
 
 
+def compute_digest(algo: types.PasswordKdfAlgoSHA256SHA256PBKDF2HMACSHA512iter100000SHA256ModPow,
+                   password: str):
+    try:
+        check_prime_and_good(algo.p, algo.g)
+    except ValueError:
+        raise ValueError('bad p/g in password')
+
+    value = pow(algo.g,
+                int.from_bytes(compute_hash(algo, password), 'big'),
+                int.from_bytes(algo.p, 'big'))
+
+    return big_num_for_hash(value)
+
+
 # https://github.com/telegramdesktop/tdesktop/blob/18b74b90451a7db2379a9d753c9cbaf8734b4d5d/Telegram/SourceFiles/core/core_cloud_password.cpp
 def compute_check(request: types.account.Password, password: str):
     algo = request.current_algo
@@ -124,7 +139,7 @@ def compute_check(request: types.account.Password, password: str):
         raise ValueError('unsupported password algorithm {}'
                          .format(algo.__class__.__name__))
 
-    pw_hash = compute_hash(algo, password.encode('utf-8'))
+    pw_hash = compute_hash(algo, password)
 
     p = int.from_bytes(algo.p, 'big')
     g = algo.g