diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 5fcdc321..ef472d56 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -94,6 +94,7 @@ jobs:
       matrix:
         target:
           - x86_64-unknown-linux-gnu
+          - i686-unknown-linux-gnu
         toolchain:
           - stable
           - "1.66.0" # MSRV
@@ -105,8 +106,13 @@ jobs:
           toolchain: ${{ matrix.toolchain }}
       - name: Install SoftHSM
         run: |
-          sudo apt-get update -y -qq &&
-          sudo apt-get install -y -qq libsofthsm2 &&
+          sudo apt-get update -y -qq
+          if [ "{{ matrix.target }}" = "i686-unknown-linux-gnu" ]; then
+            sudo dpkg --add-architecture i386 &&
+            sudo apt-get install -y -qq gcc-multilib:i386 libsofthsm2:i386
+          else
+            sudo apt-get install -y -qq libsofthsm2
+          fi
           mkdir /tmp/tokens
           echo "directories.tokendir = /tmp/tokens" > /tmp/softhsm2.conf
       - name: Install Rust target
diff --git a/cryptoki/tests/basic.rs b/cryptoki/tests/basic.rs
index 2cd3d4ab..aca611d1 100644
--- a/cryptoki/tests/basic.rs
+++ b/cryptoki/tests/basic.rs
@@ -1771,6 +1771,7 @@ fn sha256_digest_multipart_already_initialized() -> TestResult {
     Ok(())
 }
 
+#[cfg(target_pointer_width = "64")]
 #[test]
 #[serial]
 fn gcm_param_graceful_failure() -> TestResult {