diff --git a/Dockerfile.cross b/Dockerfile.cross
index f41d0e5..2cc6471 100644
--- a/Dockerfile.cross
+++ b/Dockerfile.cross
@@ -16,6 +16,18 @@ RUN apt-get update -qq && \
     apt-get clean -y && \
     rm -rf /var/lib/apt/lists/*
 
+# Install Autoconf 2.71. Ubuntu 20.04 comes with Autoconf 2.69, but
+# libffi 3.4.3 or newer requres Autoconf 2.71.
+RUN curl -LO https://ftp.gnu.org/gnu/autoconf/autoconf-2.71.tar.xz && \
+    tar -Jxvf autoconf-*.tar.xz && \
+    rm autoconf-*.tar.xz && \
+    cd autoconf-* && \
+    ./configure --prefix=/opt/autotools && \
+    make -j$(nproc) install && \
+    rm -rf autoconf-*
+
+ENV PATH=/opt/autotools/bin:$PATH
+
 COPY build-python.sh .
 
 ARG WITH_PYTHON
diff --git a/build-python.sh b/build-python.sh
index e167186..2584163 100755
--- a/build-python.sh
+++ b/build-python.sh
@@ -16,7 +16,7 @@
 
 set -e
 
-: ${LIBFFI_VERSION:=v3.4.2}
+: ${LIBFFI_VERSION:=v3.4.4}
 : ${PYTHON_VERSION:=v3.11.4}
 : ${PYTHON_VERSION_MINGW:=95b1546da60ce10fc038f51790bf799d3780d37a}