diff --git a/src/secp256k1/.travis.yml b/src/secp256k1/.travis.yml
--- a/src/secp256k1/.travis.yml
+++ b/src/secp256k1/.travis.yml
@@ -8,6 +8,9 @@
       - ninja-build
 install:
   - ./travis/install_cmake.sh
+cache:
+  directories:
+    - /opt/cmake
 compiler:
   - clang
   - gcc
diff --git a/src/secp256k1/travis/build_cmake.sh b/src/secp256k1/travis/build_cmake.sh
--- a/src/secp256k1/travis/build_cmake.sh
+++ b/src/secp256k1/travis/build_cmake.sh
@@ -18,8 +18,8 @@
 mkdir -p buildcmake/install
 pushd buildcmake
 
-# Use the cmake version installed via APT instead of the Travis custom one.
-CMAKE_COMMAND=/usr/bin/cmake
+# Use the cmake version installed via the install_cmake.sh script.
+CMAKE_COMMAND=/opt/cmake/bin/cmake
 ${CMAKE_COMMAND} --version
 
 ${CMAKE_COMMAND} -GNinja .. \
diff --git a/src/secp256k1/travis/install_cmake.sh b/src/secp256k1/travis/install_cmake.sh
--- a/src/secp256k1/travis/install_cmake.sh
+++ b/src/secp256k1/travis/install_cmake.sh
@@ -4,12 +4,36 @@
 
 set -euxo pipefail
 
-# Fetch Kitware signing key
-wget -O - https://apt.kitware.com/keys/kitware-archive-latest.asc 2>/dev/null | sudo apt-key add -
-	
-# Add the Kitware PPA
-sudo apt-add-repository 'deb https://apt.kitware.com/ubuntu/ xenial main'
-sudo apt-get update
-
-# Install cmake
-sudo apt-get -y install cmake
+### Change these values to select the cmake version to install
+CMAKE_VERSION_MAJOR=3
+CMAKE_VERSION_MINOR=13
+CMAKE_VERSION_PATCH=0
+
+CMAKE_INSTALL_SCRIPT_SHA256SUM=97220140fb5be4f1fa35600f7b45dd82d168c966dfbb877cae2bad4064b0d31b
+
+### Installation
+
+CMAKE_VERSION_FULL=${CMAKE_VERSION_MAJOR}.${CMAKE_VERSION_MINOR}.${CMAKE_VERSION_PATCH}
+
+# If cmake is already installed with the expected version (from cache), skip the
+# installation process.
+if /opt/cmake/bin/cmake --version | grep "${CMAKE_VERSION_FULL}"; then
+  exit 0
+fi
+
+# Download the pre-built binary from the cmake.org website.
+# It is distributed as a script containing a self extractible archive.
+URL_PREFIX=https://cmake.org/files/v${CMAKE_VERSION_MAJOR}.${CMAKE_VERSION_MINOR}
+CMAKE_INSTALL_SCRIPT=cmake-${CMAKE_VERSION_MAJOR}.${CMAKE_VERSION_MINOR}.${CMAKE_VERSION_PATCH}-Linux-x86_64.sh
+
+wget ${URL_PREFIX}/${CMAKE_INSTALL_SCRIPT}
+echo "${CMAKE_INSTALL_SCRIPT_SHA256SUM} ${CMAKE_INSTALL_SCRIPT}" | sha256sum -c
+
+# Make it executable
+sudo chmod +x ${CMAKE_INSTALL_SCRIPT}
+
+# Install to /opt/cmake
+CMAKE_INSTALL_PREFIX=/opt/cmake
+
+sudo mkdir -p ${CMAKE_INSTALL_PREFIX}
+sudo ./${CMAKE_INSTALL_SCRIPT} --prefix=${CMAKE_INSTALL_PREFIX} --skip-license