diff --git a/README.rst b/README.rst
index 849f6184f..f54bdb6ba 100644
--- a/README.rst
+++ b/README.rst
@@ -149,7 +149,7 @@ Optional Dependencies
 
 PTB can be installed with optional dependencies:
 
-* ``pip install python-telegram-bot[passport]`` installs the `cryptography>=3.0 <https://cryptography.io/en/stable>`_ library. Use this, if you want to use Telegram Passport related functionality.
+* ``pip install python-telegram-bot[passport]`` installs the `cryptography>=39.0.1 <https://cryptography.io/en/stable>`_ library. Use this, if you want to use Telegram Passport related functionality.
 * ``pip install python-telegram-bot[socks]`` installs `httpx[socks] <https://www.python-httpx.org/#dependencies>`_. Use this, if you want to work behind a Socks5 server.
 * ``pip install python-telegram-bot[rate-limiter]`` installs `aiolimiter~=1.0.0 <https://aiolimiter.readthedocs.io/en/stable/>`_. Use this, if you want to use ``telegram.ext.AIORateLimiter``.
 * ``pip install python-telegram-bot[webhooks]`` installs the `tornado~=6.2 <https://www.tornadoweb.org/en/stable/>`_ library. Use this, if you want to use ``telegram.ext.Updater.start_webhook``/``telegram.ext.Application.run_webhook``.
diff --git a/README_RAW.rst b/README_RAW.rst
index 71fb9b18a..81fc1420b 100644
--- a/README_RAW.rst
+++ b/README_RAW.rst
@@ -150,7 +150,7 @@ Optional Dependencies
 
 PTB can be installed with optional dependencies:
 
-* ``pip install python-telegram-bot-raw[passport]`` installs the `cryptography>=3.0 <https://cryptography.io/en/stable>`_ library. Use this, if you want to use Telegram Passport related functionality.
+* ``pip install python-telegram-bot-raw[passport]`` installs the `cryptography>=39.0.1 <https://cryptography.io/en/stable>`_ library. Use this, if you want to use Telegram Passport related functionality.
 * ``pip install python-telegram-bot-raw[socks]`` installs `httpx[socks] <https://www.python-httpx.org/#dependencies>`_. Use this, if you want to work behind a Socks5 server.
 
 To install multiple optional dependencies, separate them by commas, e.g. ``pip install python-telegram-bot-raw[passport,socks]``.
diff --git a/requirements-opts.txt b/requirements-opts.txt
index 190d65cfe..834f6fe51 100644
--- a/requirements-opts.txt
+++ b/requirements-opts.txt
@@ -11,7 +11,7 @@
 # versions and only increase the lower bound if necessary
 
 httpx[socks] # socks
-cryptography!=3.4,!=3.4.1,!=3.4.2,!=3.4.3,>=3.0 # passport
+cryptography!=3.4,!=3.4.1,!=3.4.2,!=3.4.3,>=39.0.1 # passport
 aiolimiter~=1.0.0 # rate-limiter!ext
 
 # tornado is rather stable, but let's not allow the next mayor release without prior testing