diff --git a/.cirrus.yml b/.cirrus.yml
index 1762007c60..9d3807f4eb 100644
--- a/.cirrus.yml
+++ b/.cirrus.yml
@@ -93,7 +93,7 @@ task:
     - env:
         CC: clang-snapshot
   test_script:
-    - ./ci/cirrus.sh
+    - ./ci/ci.sh
   << : *CAT_LOGS
 
 task:
@@ -111,7 +111,7 @@ task:
     - env:
         CC: clang --target=i686-pc-linux-gnu -isystem /usr/i686-linux-gnu/include
   test_script:
-    - ./ci/cirrus.sh
+    - ./ci/ci.sh
   << : *CAT_LOGS
 
 task:
@@ -130,7 +130,7 @@ task:
   test_script:
     # https://sourceware.org/bugzilla/show_bug.cgi?id=27008
     - rm /etc/ld.so.cache
-    - ./ci/cirrus.sh
+    - ./ci/ci.sh
   << : *CAT_LOGS
 
 task:
@@ -150,7 +150,7 @@ task:
     - env: {}
     - env: {EXPERIMENTAL: yes, ASM: arm32}
   test_script:
-    - ./ci/cirrus.sh
+    - ./ci/ci.sh
   << : *CAT_LOGS
 
 task:
@@ -167,7 +167,7 @@ task:
     ELLSWIFT: yes
     CTIMETESTS: no
   test_script:
-    - ./ci/cirrus.sh
+    - ./ci/ci.sh
   << : *CAT_LOGS
 
 task:
@@ -184,28 +184,7 @@ task:
     ELLSWIFT: yes
     CTIMETESTS: no
   test_script:
-    - ./ci/cirrus.sh
-  << : *CAT_LOGS
-
-task:
-  << : *LINUX_CONTAINER
-  env:
-    WRAPPER_CMD: wine
-    WITH_VALGRIND: no
-    ECDH: yes
-    RECOVERY: yes
-    SCHNORRSIG: yes
-    ELLSWIFT: yes
-    CTIMETESTS: no
-  matrix:
-    - name: "x86_64 (mingw32-w64): Windows (Debian stable, Wine)"
-      env:
-        HOST: x86_64-w64-mingw32
-    - name: "i686 (mingw32-w64): Windows (Debian stable, Wine)"
-      env:
-        HOST: i686-w64-mingw32
-  test_script:
-    - ./ci/cirrus.sh
+    - ./ci/ci.sh
   << : *CAT_LOGS
 
 # Sanitizers
@@ -249,7 +228,7 @@ task:
         HOST: i686-linux-gnu
         CC: i686-linux-gnu-gcc
   test_script:
-    - ./ci/cirrus.sh
+    - ./ci/ci.sh
   << : *CAT_LOGS
 
 # Memory sanitizers
@@ -276,7 +255,7 @@ task:
         ECMULTWINDOW: 2
         CFLAGS: "-fsanitize=memory -g -O3"
   test_script:
-    - ./ci/cirrus.sh
+    - ./ci/ci.sh
   << : *CAT_LOGS
 
 task:
@@ -292,7 +271,7 @@ task:
     SCHNORRSIG: yes
     ELLSWIFT: yes
   test_script:
-    - ./ci/cirrus.sh
+    - ./ci/ci.sh
   << : *CAT_LOGS
 
 task:
diff --git a/.github/actions/run-in-docker-action/action.yml b/.github/actions/run-in-docker-action/action.yml
new file mode 100644
index 0000000000..203383d0b1
--- /dev/null
+++ b/.github/actions/run-in-docker-action/action.yml
@@ -0,0 +1,37 @@
+name: 'Run in Docker with environment'
+description: 'Run a command in a Docker container, while passing explicitly set environment variables into the container.'
+inputs:
+  dockerfile:
+    description: 'A Dockerfile that defines an image'
+    required: true
+  tag:
+    description: 'A tag of an image'
+    required: true
+  command:
+    description: 'A command to run in a container'
+    required: true
+runs:
+  using: "composite"
+  steps:
+    - uses: docker/setup-buildx-action@v2
+      with:
+        # See: https://github.com/moby/buildkit/issues/3969.
+        driver-opts: |
+          network=host
+
+    - uses: docker/build-push-action@v4
+      with:
+        context: .
+        file: ${{ inputs.dockerfile }}
+        tags: ${{ inputs.tag }}
+        load: true
+        cache-from: type=gha
+
+    - # Tell Docker to pass environment variables in `env` into the container.
+      run: >
+        docker run \
+          $(echo '${{ toJSON(env) }}' | jq -r 'keys[] | "--env \(.) "') \
+          --volume ${{ github.workspace }}:${{ github.workspace }} \
+          --workdir ${{ github.workspace }} \
+          ${{ inputs.tag }} bash -c "${{ inputs.command }}"
+      shell: bash
diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index c172abb0ee..f9518c4ac4 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -42,6 +42,82 @@ env:
   EXAMPLES: 'yes'
 
 jobs:
+  docker_cache:
+    name: "Build Docker image"
+    runs-on: ubuntu-latest
+    steps:
+      - name: Set up Docker Buildx
+        uses: docker/setup-buildx-action@v2
+        with:
+          # See: https://github.com/moby/buildkit/issues/3969.
+          driver-opts: |
+            network=host
+
+      - name: Build container
+        uses: docker/build-push-action@v4
+        with:
+          file: ./ci/linux-debian.Dockerfile
+          tags: linux-debian-image
+          cache-from: type=gha
+          cache-to: type=gha,mode=min
+
+  mingw_debian:
+    name: ${{ matrix.configuration.job_name }}
+    runs-on: ubuntu-latest
+    needs: docker_cache
+
+    env:
+      WRAPPER_CMD: 'wine'
+      WITH_VALGRIND: 'no'
+      ECDH: 'yes'
+      RECOVERY: 'yes'
+      SCHNORRSIG: 'yes'
+      ELLSWIFT: 'yes'
+      CTIMETESTS: 'no'
+
+    strategy:
+      fail-fast: false
+      matrix:
+        configuration:
+          - job_name: 'x86_64 (mingw32-w64): Windows (Debian stable, Wine)'
+            env_vars:
+              HOST: 'x86_64-w64-mingw32'
+          - job_name: 'i686 (mingw32-w64): Windows (Debian stable, Wine)'
+            env_vars:
+              HOST: 'i686-w64-mingw32'
+
+    steps:
+      - name: Checkout
+        uses: actions/checkout@v3
+
+      - name: CI script
+        env: ${{ matrix.configuration.env_vars }}
+        uses: ./.github/actions/run-in-docker-action
+        with:
+          dockerfile: ./ci/linux-debian.Dockerfile
+          tag: linux-debian-image
+          command: >
+            git config --global --add safe.directory ${{ github.workspace }} &&
+            ./ci/ci.sh
+
+      - run: cat tests.log || true
+        if: ${{ always() }}
+      - run: cat noverify_tests.log || true
+        if: ${{ always() }}
+      - run: cat exhaustive_tests.log || true
+        if: ${{ always() }}
+      - run: cat ctime_tests.log || true
+        if: ${{ always() }}
+      - run: cat bench.log || true
+        if: ${{ always() }}
+      - run: cat config.log || true
+        if: ${{ always() }}
+      - run: cat test_env.log || true
+        if: ${{ always() }}
+      - name: CI env
+        run: env
+        if: ${{ always() }}
+
   macos-native:
     name: "x86_64: macOS Ventura"
     # See: https://github.com/actions/runner-images#available-images.
@@ -80,7 +156,7 @@ jobs:
 
       - name: CI script
         env: ${{ matrix.env_vars }}
-        run: ./ci/cirrus.sh
+        run: ./ci/ci.sh
 
       - run: cat tests.log || true
         if: ${{ always() }}
diff --git a/ci/cirrus.sh b/ci/ci.sh
similarity index 100%
rename from ci/cirrus.sh
rename to ci/ci.sh