diff --git a/src/secp256k1/.travis.yml b/src/secp256k1/.travis.yml
--- a/src/secp256k1/.travis.yml
+++ b/src/secp256k1/.travis.yml
@@ -50,7 +50,7 @@
             - libgmp-dev:i386
             - ninja-build
     - compiler: clang
-      env: HOST=i686-linux-gnu
+      env: HOST=i686-linux-gnu BIGNUM=no
       addons:
         apt:
           sources:
@@ -61,7 +61,7 @@
             - gcc-multilib
             - ninja-build
     - compiler: gcc
-      env: HOST=i686-linux-gnu ENDOMORPHISM=yes
+      env: HOST=i686-linux-gnu ENDOMORPHISM=yes BIGNUM=no
       addons:
         apt:
           sources:
diff --git a/src/secp256k1/CMakeLists.txt b/src/secp256k1/CMakeLists.txt
--- a/src/secp256k1/CMakeLists.txt
+++ b/src/secp256k1/CMakeLists.txt
@@ -37,9 +37,10 @@
 add_library(secp256k1 src/secp256k1.c)
 target_include_directories(secp256k1 PUBLIC include)
 
-# We need to link in GMP
-find_package(GMP)
-if(GMP_FOUND)
+option(SECP256K1_ENABLE_BIGNUM "Use the GMP bignum implementation" OFF)
+if(SECP256K1_ENABLE_BIGNUM)
+	# We need to link in GMP
+	find_package(GMP REQUIRED)
 	target_include_directories(secp256k1 PUBLIC ${GMP_INCLUDE_DIR})
 	target_link_libraries(secp256k1 ${GMP_LIBRARY})
 	set(USE_NUM_GMP 1)
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
@@ -5,11 +5,7 @@
 set -ex
 
 if [ "x$HOST" = "xi686-linux-gnu" ]; then
-  TOOLCHAIN_FILE="-DCMAKE_TOOLCHAIN_FILE=../cmake/platforms/Linux32.cmake"
-fi
-
-if [ "x$BIGNUM" = "xno" ]; then
-  USE_GMP="-DGMP_LIBRARY=OFF"
+  CMAKE_EXTRA_FLAGS="-DCMAKE_C_FLAGS=-m32"
 fi
 
 mkdir -p buildcmake
@@ -26,11 +22,11 @@
   -DSECP256K1_ENABLE_MODULE_SCHNORR=$SCHNORR \
   -DSECP256K1_ENABLE_JNI=$JNI \
   -DSECP256K1_ENABLE_ENDOMORPHISM=$ENDOMORPHISM \
+  -DSECP256K1_ENABLE_BIGNUM=$BIGNUM \
   -DUSE_ASM_X86_64=$ASM \
   -DUSE_FIELD=$FIELD \
   -DUSE_SCALAR=$SCALAR \
-  $USE_GMP \
-  $TOOLCHAIN_FILE \
+  $CMAKE_EXTRA_FLAGS
 
 ninja check-secp256k1