diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index adf9e3ef5..2b79f5b59 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -67,6 +67,7 @@ jobs:
     strategy:
       matrix:
         TEST:
+          - {CONTAINER: "ubuntu-bionic", TOXENV: "py36"}
           # cryptographyMain used since there's no wheel
           - {CONTAINER: "ubuntu-rolling", TOXENV: "py39-cryptographyMain"}
     name: "${{ matrix.TEST.TOXENV }} on ${{ matrix.TEST.CONTAINER }}"
diff --git a/setup.py b/setup.py
index 5797abcc6..ef7a0b937 100755
--- a/setup.py
+++ b/setup.py
@@ -96,7 +96,7 @@ def find_meta(meta):
         package_dir={"": "src"},
         install_requires=[
             # Fix cryptographyMinimum in tox.ini when changing this!
-            "cryptography>=36.0",
+            "cryptography>=37.0",
         ],
         extras_require={
             "test": ["flaky", "pretend", "pytest>=3.0.1"],
diff --git a/tox.ini b/tox.ini
index a69486744..cba267169 100644
--- a/tox.ini
+++ b/tox.ini
@@ -10,7 +10,7 @@ extras =
 deps =
     coverage>=4.2
     cryptographyMain: git+https://github.com/pyca/cryptography.git
-    cryptographyMinimum: cryptography==36.0
+    cryptographyMinimum: cryptography==37.0
     randomorder: pytest-randomly
 setenv =
     # Do not allow the executing environment to pollute the test environment