diff --git a/max/auth/__init__.py b/max/auth/__init__.py
index 27525f0..b041bca 100644
--- a/max/auth/__init__.py
+++ b/max/auth/__init__.py
@@ -1,4 +1,9 @@
-from .auth import change_password, check_password, hash_password  # noqa
+from .auth import (  # noqa
+    change_password,
+    check_password,
+    hash_password,
+    validate_password,
+)
 from .middlewares import AuthMiddleware, no_authentication_required  # noqa
 from .routes import init_routes
 
diff --git a/max/auth/auth.py b/max/auth/auth.py
index 4bb1c29..8ddbc19 100644
--- a/max/auth/auth.py
+++ b/max/auth/auth.py
@@ -1,16 +1,31 @@
 import base64
 import hashlib
-import os
 
-from flask import session
+import bcrypt
+from flask import current_app, session
 
 from max.crypto import constant_time_compare, force_bytes
 from max.db import get_user_by_email, update_user
+from max.exceptions import InvalidPassword
 from max.sessions import session_storage
 from max.translations import t
 
+BLF_CRYPT_PREFIX = "{BLF-CRYPT}"
 SSHA512_PREFIX = "{SSHA512}"
+BCRYPT_ROUNDS = 12
+# bcrypt only uses the first 72 bytes
+MAX_PASSWORD_BYTES = 72
+# Hash of a random, unknown password. It is checked for unknown users, so the
+# response time does not tell whether an email exists.
+DUMMY_HASH = (
+    BLF_CRYPT_PREFIX + "$2b$12$J27D9dEpQ5ff/I48HG05p.97oJGTO7UiaKGIbVuzV6nw0lo6gZ5wq"
+)
+
 LOGIN_FAILED_MESSAGE = "Email or password is wrong, or the account is deactivated"
+PASSWORD_TOO_LONG_MESSAGE = (
+    "The password must be at most 72 bytes long "
+    "(72 characters, fewer with umlauts or special characters)"
+)
 
 
 def login(email, password):
@@ -21,6 +36,7 @@ def login(email, password):
 
     user = get_user_by_email(email)
     if user is None:
+        check_password(password, DUMMY_HASH)
         return t(LOGIN_FAILED_MESSAGE)
 
     if not check_password(password, user.passwordhash):
@@ -29,6 +45,8 @@ def login(email, password):
     if not user.enabled:
         return t(LOGIN_FAILED_MESSAGE)
 
+    rehash_password_if_needed(user, password)
+
     # Start a new session (new id, new CSRF token) against session fixation.
     session.clear()
     session["user_id"] = user.id
@@ -51,10 +69,63 @@ def change_password(user, password):
         session_storage.remove_user_sessions(user.id)
 
 
-def hash_password(password: str, salt: bytes = None):
-    if salt is None:
-        salt = os.urandom(32)
+def rehash_password_if_needed(user, password):
+    """Replaces an outdated hash, the plain password is only known at the login"""
+    if not needs_rehash(user.passwordhash):
+        return
+    error = validate_password(password)
+    if error:
+        current_app.logger.warning(
+            'Cannot rehash the password of user %s: "%s"', user.id, error
+        )
+        return
+    update_user(user.id, passwordhash=hash_password(password))
+    current_app.logger.info("Rehashed the password of user %s", user.id)
 
+
+def validate_password(password: str):
+    """Returns the (untranslated) error message, or None if the password is valid"""
+    if len(force_bytes(password)) > MAX_PASSWORD_BYTES:
+        return PASSWORD_TOO_LONG_MESSAGE
+    return None
+
+
+def hash_password(password: str):
+    error = validate_password(password)
+    if error:
+        raise InvalidPassword(error)
+
+    hash = bcrypt.hashpw(force_bytes(password), bcrypt.gensalt(rounds=BCRYPT_ROUNDS))
+    return BLF_CRYPT_PREFIX + hash.decode()
+
+
+def needs_rehash(hash: str):
+    if not hash.startswith(BLF_CRYPT_PREFIX):
+        return True
+    # "$2b$12$…": the cost factor follows the version
+    rounds = int(hash[len(BLF_CRYPT_PREFIX) :].split("$")[2])  # noqa
+    return rounds < BCRYPT_ROUNDS
+
+
+def check_password(password: str, hash: str):
+    if hash.startswith(BLF_CRYPT_PREFIX):
+        # Such a password cannot have been set, and bcrypt would raise
+        if validate_password(password):
+            return False
+        bcrypt_hash = hash[len(BLF_CRYPT_PREFIX) :]  # noqa
+        return bcrypt.checkpw(force_bytes(password), force_bytes(bcrypt_hash))
+
+    if hash.startswith(SSHA512_PREFIX):
+        return check_ssha512_password(password, hash)
+
+    raise RuntimeError("The hash has an unknown scheme")
+
+
+# {SSHA512} is outdated. Existing hashes are still checked and replaced at the
+# next login. Remove this once no hash uses it anymore (see F-08).
+
+
+def hash_ssha512_password(password: str, salt: bytes):
     sha = hashlib.sha512()
     sha.update(force_bytes(password))
     sha.update(salt)
@@ -62,16 +133,13 @@ def hash_password(password: str, salt: bytes = None):
     return SSHA512_PREFIX + sha_and_salt.decode()
 
 
-def get_salt(hash: str):
-    if not hash.startswith(SSHA512_PREFIX):
-        raise RuntimeError(f"The hash does not start with '{SSHA512_PREFIX}''")
-
+def get_ssha512_salt(hash: str):
     sha_and_salt = base64.b64decode(hash[len(SSHA512_PREFIX) :])  # noqa
     return sha_and_salt[64:]
 
 
-def check_password(password: str, hash: str):
-    salt = get_salt(hash)
-    hash_from_password = hash_password(password, salt=salt)
+def check_ssha512_password(password: str, hash: str):
+    salt = get_ssha512_salt(hash)
+    hash_from_password = hash_ssha512_password(password, salt)
 
     return constant_time_compare(hash, hash_from_password)
diff --git a/max/cli.py b/max/cli.py
index f74a80f..6e5fb67 100644
--- a/max/cli.py
+++ b/max/cli.py
@@ -1,6 +1,10 @@
 import click
 
-from .auth import check_password as auth_check_password, hash_password
+from .auth import (
+    check_password as auth_check_password,
+    hash_password,
+    validate_password,
+)
 from .db import (
     add_domain as db_add_domain,
     remove_domain as db_remove_domain,
@@ -17,10 +21,17 @@ def register_cli(app):
     app.cli.command("remove-domain")(remove_domain)
 
 
+def abort_if_password_invalid(password):
+    error = validate_password(password)
+    if error:
+        raise click.ClickException(error)
+
+
 @click.argument("email")
 @click.argument("password")
 def reset_user(email, password):
     """Resets or create a user given by the email"""
+    abort_if_password_invalid(password)
     hash = hash_password(password)
     reset_or_create_user(email, hash, False)
 
@@ -29,6 +40,7 @@ def reset_user(email, password):
 @click.argument("password")
 def reset_admin(email, password):
     """Resets or create an admin given by the email"""
+    abort_if_password_invalid(password)
     hash = hash_password(password)
     reset_or_create_user(email, hash, True)
 
@@ -36,6 +48,7 @@ def reset_admin(email, password):
 @click.argument("password")
 def make_hash(password):
     """Creates a salted hash from the password"""
+    abort_if_password_invalid(password)
     print(hash_password(password))
 
 
diff --git a/max/exceptions.py b/max/exceptions.py
index cf94b62..025fbd4 100644
--- a/max/exceptions.py
+++ b/max/exceptions.py
@@ -21,6 +21,12 @@ class PermissionDenied(MaxException):
     """
 
 
+class InvalidPassword(MaxException):
+    """
+    Callers must check the password with validate_password before hashing it.
+    """
+
+
 class LanguageNotSet(MaxException):
     """
     Something is translated outside of the I18NMiddleware, which sets the
diff --git a/max/private_static/i18n/de.json b/max/private_static/i18n/de.json
index 9229a64..145b238 100644
--- a/max/private_static/i18n/de.json
+++ b/max/private_static/i18n/de.json
@@ -50,6 +50,7 @@
     "Note changed successfully!": "Notiz wurde erfolgreich bearbeitet!",
     "Both passwords must be given": "Beide Passwörter müssen angegeben werden",
     "Both passwords must be the same": "Beide Passwörter müssen übereinstimmen",
+    "The password must be at most 72 bytes long (72 characters, fewer with umlauts or special characters)": "Das Passwort darf höchstens 72 Bytes lang sein (72 Zeichen, mit Umlauten oder Sonderzeichen weniger)",
     "Current password": "Aktuelles Passwort",
     "The current password must be given": "Das aktuelle Passwort muss angegeben werden",
     "The current password is wrong": "Das aktuelle Passwort ist falsch",
diff --git a/max/routes/user/change_password.py b/max/routes/user/change_password.py
index 1654362..6f58c55 100644
--- a/max/routes/user/change_password.py
+++ b/max/routes/user/change_password.py
@@ -1,6 +1,6 @@
 from flask import flash
 
-from max.auth import change_password, check_password
+from max.auth import change_password, check_password, validate_password
 from max.permissions import AllowAdminOrSelf
 from max.translations import t
 
@@ -45,6 +45,11 @@ class UserChangePassword(AllowAdminOrSelf, BackToUsersMixin, FetchUserTemplateGe
             flash(t("Both passwords must be the same"), category="error")
             return
 
+        password_error = validate_password(pw1)
+        if password_error:
+            flash(t(password_error), category="error")
+            return
+
         change_password(self.user, pw1)
         flash(t("Password changed successfully!"), category="success")
         return self.redirect()
diff --git a/max/routes/user/create.py b/max/routes/user/create.py
index af06428..f9a6b16 100644
--- a/max/routes/user/create.py
+++ b/max/routes/user/create.py
@@ -1,6 +1,6 @@
 from flask import flash, url_for
 
-from max.auth import hash_password
+from max.auth import hash_password, validate_password
 from max.db import EmailAlreadyExists, create_user, get_domains
 from max.permissions import AllowAdmin
 from max.translations import t
@@ -48,7 +48,12 @@ class UserCreate(AllowAdmin, CheckEmailMixin, BaseTemplateGetView):
             flash(t("Both passwords must be the same"), category="error")
             error = True
         else:
-            self.password = pw1
+            password_error = validate_password(pw1)
+            if password_error:
+                flash(t(password_error), category="error")
+                error = True
+            else:
+                self.password = pw1
 
         enabled = self.request.form.get("enabled")
         if enabled == "on":
diff --git a/max/templates/user/change-password.html b/max/templates/user/change-password.html
index 1da5ccf..e65432c 100644
--- a/max/templates/user/change-password.html
+++ b/max/templates/user/change-password.html
@@ -14,12 +14,12 @@
         {% endif %}
         <div class="pure-control-group">
             <label for="password1">{{ t("Password") }}</label>
-            <input id="password1" type="password" name="password1" autocomplete="new-password" placeholder="{{ t("New password") }}">
+            <input id="password1" type="password" name="password1" autocomplete="new-password" maxlength="72" placeholder="{{ t("New password") }}">
         </div>
 
         <div class="pure-control-group">
             <label for="password2">{{ t("Re-enter password") }}</label>
-            <input id="password2" type="password" name="password2" autocomplete="new-password" placeholder="{{ t("New password") }}">
+            <input id="password2" type="password" name="password2" autocomplete="new-password" maxlength="72" placeholder="{{ t("New password") }}">
         </div>
 
         <div class="pure-controls">
diff --git a/max/templates/user/create.html b/max/templates/user/create.html
index 5b114f2..013a2bc 100644
--- a/max/templates/user/create.html
+++ b/max/templates/user/create.html
@@ -19,12 +19,12 @@
 
         <div class="pure-control-group">
             <label for="password1">{{ t("Password") }}</label>
-            <input id="password1" type="password" name="password1" autocomplete="new-password" placeholder="{{ t("Password") }}">
+            <input id="password1" type="password" name="password1" autocomplete="new-password" maxlength="72" placeholder="{{ t("Password") }}">
         </div>
 
         <div class="pure-control-group">
             <label for="password2">{{ t("Re-enter password") }}</label>
-            <input id="password2" type="password" name="password2" autocomplete="new-password" placeholder="{{ t("Re-enter password") }}">
+            <input id="password2" type="password" name="password2" autocomplete="new-password" maxlength="72" placeholder="{{ t("Re-enter password") }}">
         </div>
 
         <div class="pure-controls checkbox">
diff --git a/requirements.in b/requirements.in
index 8e01e7c..3fff729 100644
--- a/requirements.in
+++ b/requirements.in
@@ -1,5 +1,6 @@
 # Direct dependencies of MAX. Pinned versions with hashes are in requirements.txt,
 # generated by `make lock-deps` (see README).
+bcrypt>=5,<6
 Flask>=3.1,<4
 gunicorn>=26,<27
 psycopg2>=2.9,<3
diff --git a/requirements.txt b/requirements.txt
index 525dd37..2159df0 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -4,6 +4,71 @@
 #
 #    pip-compile --allow-unsafe --generate-hashes --strip-extras requirements.in
 #
+bcrypt==5.0.0 \
+    --hash=sha256:046ad6db88edb3c5ece4369af997938fb1c19d6a699b9c1b27b0db432faae4c4 \
+    --hash=sha256:0c418ca99fd47e9c59a301744d63328f17798b5947b0f791e9af3c1c499c2d0a \
+    --hash=sha256:0c8e093ea2532601a6f686edbc2c6b2ec24131ff5c52f7610dd64fa4553b5464 \
+    --hash=sha256:0cae4cb350934dfd74c020525eeae0a5f79257e8a201c0c176f4b84fdbf2a4b4 \
+    --hash=sha256:137c5156524328a24b9fac1cb5db0ba618bc97d11970b39184c1d87dc4bf1746 \
+    --hash=sha256:200af71bc25f22006f4069060c88ed36f8aa4ff7f53e67ff04d2ab3f1e79a5b2 \
+    --hash=sha256:212139484ab3207b1f0c00633d3be92fef3c5f0af17cad155679d03ff2ee1e41 \
+    --hash=sha256:2b732e7d388fa22d48920baa267ba5d97cca38070b69c0e2d37087b381c681fd \
+    --hash=sha256:35a77ec55b541e5e583eb3436ffbbf53b0ffa1fa16ca6782279daf95d146dcd9 \
+    --hash=sha256:38cac74101777a6a7d3b3e3cfefa57089b5ada650dce2baf0cbdd9d65db22a9e \
+    --hash=sha256:3abeb543874b2c0524ff40c57a4e14e5d3a66ff33fb423529c88f180fd756538 \
+    --hash=sha256:3ca8a166b1140436e058298a34d88032ab62f15aae1c598580333dc21d27ef10 \
+    --hash=sha256:3cf67a804fc66fc217e6914a5635000259fbbbb12e78a99488e4d5ba445a71eb \
+    --hash=sha256:4870a52610537037adb382444fefd3706d96d663ac44cbb2f37e3919dca3d7ef \
+    --hash=sha256:48f753100931605686f74e27a7b49238122aa761a9aefe9373265b8b7aa43ea4 \
+    --hash=sha256:4bfd2a34de661f34d0bda43c3e4e79df586e4716ef401fe31ea39d69d581ef23 \
+    --hash=sha256:560ddb6ec730386e7b3b26b8b4c88197aaed924430e7b74666a586ac997249ef \
+    --hash=sha256:5b1589f4839a0899c146e8892efe320c0fa096568abd9b95593efac50a87cb75 \
+    --hash=sha256:5feebf85a9cefda32966d8171f5db7e3ba964b77fdfe31919622256f80f9cf42 \
+    --hash=sha256:611f0a17aa4a25a69362dcc299fda5c8a3d4f160e2abb3831041feb77393a14a \
+    --hash=sha256:61afc381250c3182d9078551e3ac3a41da14154fbff647ddf52a769f588c4172 \
+    --hash=sha256:64d7ce196203e468c457c37ec22390f1a61c85c6f0b8160fd752940ccfb3a683 \
+    --hash=sha256:64ee8434b0da054d830fa8e89e1c8bf30061d539044a39524ff7dec90481e5c2 \
+    --hash=sha256:6b8f520b61e8781efee73cba14e3e8c9556ccfb375623f4f97429544734545b4 \
+    --hash=sha256:741449132f64b3524e95cd30e5cd3343006ce146088f074f31ab26b94e6c75ba \
+    --hash=sha256:744d3c6b164caa658adcb72cb8cc9ad9b4b75c7db507ab4bc2480474a51989da \
+    --hash=sha256:79cfa161eda8d2ddf29acad370356b47f02387153b11d46042e93a0a95127493 \
+    --hash=sha256:7aeef54b60ceddb6f30ee3db090351ecf0d40ec6e2abf41430997407a46d2254 \
+    --hash=sha256:7edda91d5ab52b15636d9c30da87d2cc84f426c72b9dba7a9b4fe142ba11f534 \
+    --hash=sha256:7f277a4b3390ab4bebe597800a90da0edae882c6196d3038a73adf446c4f969f \
+    --hash=sha256:7f4c94dec1b5ab5d522750cb059bb9409ea8872d4494fd152b53cca99f1ddd8c \
+    --hash=sha256:801cad5ccb6b87d1b430f183269b94c24f248dddbbc5c1f78b6ed231743e001c \
+    --hash=sha256:83e787d7a84dbbfba6f250dd7a5efd689e935f03dd83b0f919d39349e1f23f83 \
+    --hash=sha256:89042e61b5e808b67daf24a434d89bab164d4de1746b37a8d173b6b14f3db9ff \
+    --hash=sha256:92864f54fb48b4c718fc92a32825d0e42265a627f956bc0361fe869f1adc3e7d \
+    --hash=sha256:9d52ed507c2488eddd6a95bccee4e808d3234fa78dd370e24bac65a21212b861 \
+    --hash=sha256:9fffdb387abe6aa775af36ef16f55e318dcda4194ddbf82007a6f21da29de8f5 \
+    --hash=sha256:a28bc05039bdf3289d757f49d616ab3efe8cf40d8e8001ccdd621cd4f98f4fc9 \
+    --hash=sha256:a5393eae5722bcef046a990b84dff02b954904c36a194f6cfc817d7dca6c6f0b \
+    --hash=sha256:a71f70ee269671460b37a449f5ff26982a6f2ba493b3eabdd687b4bf35f875ac \
+    --hash=sha256:b17366316c654e1ad0306a6858e189fc835eca39f7eb2cafd6aaca8ce0c40a2e \
+    --hash=sha256:baade0a5657654c2984468efb7d6c110db87ea63ef5a4b54732e7e337253e44f \
+    --hash=sha256:c2388ca94ffee269b6038d48747f4ce8df0ffbea43f31abfa18ac72f0218effb \
+    --hash=sha256:c58b56cdfb03202b3bcc9fd8daee8e8e9b6d7e3163aa97c631dfcfcc24d36c86 \
+    --hash=sha256:cde08734f12c6a4e28dc6755cd11d3bdfea608d93d958fffbe95a7026ebe4980 \
+    --hash=sha256:d79e5c65dcc9af213594d6f7f1fa2c98ad3fc10431e7aa53c176b441943efbdd \
+    --hash=sha256:d8d65b564ec849643d9f7ea05c6d9f0cd7ca23bdd4ac0c2dbef1104ab504543d \
+    --hash=sha256:db99dca3b1fdc3db87d7c57eac0c82281242d1eabf19dcb8a6b10eb29a2e72d1 \
+    --hash=sha256:dcd58e2b3a908b5ecc9b9df2f0085592506ac2d5110786018ee5e160f28e0911 \
+    --hash=sha256:dd19cf5184a90c873009244586396a6a884d591a5323f0e8a5922560718d4993 \
+    --hash=sha256:ddb4e1500f6efdd402218ffe34d040a1196c072e07929b9820f363a1fd1f4191 \
+    --hash=sha256:e3cf5b2560c7b5a142286f69bde914494b6d8f901aaa71e453078388a50881c4 \
+    --hash=sha256:ed2e1365e31fc73f1825fa830f1c8f8917ca1b3ca6185773b349c20fd606cec2 \
+    --hash=sha256:edfcdcedd0d0f05850c52ba3127b1fce70b9f89e0fe5ff16517df7e81fa3cbb8 \
+    --hash=sha256:f0ce778135f60799d89c9693b9b398819d15f1921ba15fe719acb3178215a7db \
+    --hash=sha256:f2347d3534e76bf50bca5500989d6c1d05ed64b440408057a37673282c654927 \
+    --hash=sha256:f3c08197f3039bec79cee59a606d62b96b16669cff3949f21e74796b6e3cd2be \
+    --hash=sha256:f632fd56fc4e61564f78b46a2269153122db34988e78b6be8b32d28507b7eaeb \
+    --hash=sha256:f6984a24db30548fd39a44360532898c33528b74aedf81c26cf29c51ee47057e \
+    --hash=sha256:f70aadb7a809305226daedf75d90379c397b094755a710d7014b8b117df1ebbf \
+    --hash=sha256:f748f7c2d6fd375cc93d3fba7ef4a9e3a092421b8dbf34d8d4dc06be9492dfdd \
+    --hash=sha256:f8429e1c410b4073944f03bd778a9e066e7fad723564a52ff91841d278dfc822 \
+    --hash=sha256:fc746432b951e92b58317af8e0ca746efe93e66555f1b40888865ef5bf56446b
+    # via -r requirements.in
 blinker==1.9.0 \
     --hash=sha256:b4ce2265a7abece45e7cc896e98dbebe6cead56bcf805a3d23136d145f5445bf \
     --hash=sha256:ba0efaa9080b619ff2f3459d1d500c57bddea4a6b424b60a91141db6fd2f08bc