diff --git a/contrib/gitian-descriptors/gitian-linux.yml b/contrib/gitian-descriptors/gitian-linux.yml
--- a/contrib/gitian-descriptors/gitian-linux.yml
+++ b/contrib/gitian-descriptors/gitian-linux.yml
@@ -54,6 +54,13 @@
   CMAKE_TOOLCHAIN_FILE[arm-linux-gnueabihf]=LinuxARM.cmake
   CMAKE_TOOLCHAIN_FILE[aarch64-linux-gnu]=LinuxAArch64.cmake
 
+  # Allow extra cmake option to be specified for each host
+  declare -A CMAKE_EXTRA_OPTIONS
+  CMAKE_EXTRA_OPTIONS[i686-pc-linux-gnu]="-DSECP256K1_USE_ASM=OFF"
+  CMAKE_EXTRA_OPTIONS[aarch64-linux-gnu]="-DSECP256K1_USE_ASM=OFF"
+  # ARM assembly is supported but experimental, disable it for the release
+  CMAKE_EXTRA_OPTIONS[arm-linux-gnueabihf]="-DSECP256K1_USE_ASM=OFF"
+
   INSTALL_COMPONENTS="bitcoind bitcoin-qt bitcoin-seeder"
 
   FAKETIME_HOST_PROGS=""
@@ -164,7 +171,8 @@
       -DENABLE_GLIBC_BACK_COMPAT=ON \
       -DCMAKE_INSTALL_PREFIX=${INSTALLPATH} \
       -DCCACHE=OFF \
-      -DUSE_LD_GOLD=OFF
+      -DUSE_LD_GOLD=OFF \
+      ${CMAKE_EXTRA_OPTIONS[${i}]}
 
     ninja
     ninja security-check
diff --git a/contrib/gitian-descriptors/gitian-win.yml b/contrib/gitian-descriptors/gitian-win.yml
--- a/contrib/gitian-descriptors/gitian-win.yml
+++ b/contrib/gitian-descriptors/gitian-win.yml
@@ -164,7 +164,7 @@
 
   # Allow extra cmake option to be specified for each host
   declare -A CMAKE_EXTRA_OPTIONS
-  CMAKE_EXTRA_OPTIONS[i686-w64-mingw32]="-DCPACK_PACKAGE_FILE_NAME=${DISTNAME}-win32-setup-unsigned"
+  CMAKE_EXTRA_OPTIONS[i686-w64-mingw32]="-DCPACK_PACKAGE_FILE_NAME=${DISTNAME}-win32-setup-unsigned -DSECP256K1_USE_ASM=OFF"
   CMAKE_EXTRA_OPTIONS[x86_64-w64-mingw32]="-DCPACK_PACKAGE_FILE_NAME=${DISTNAME}-win64-setup-unsigned"
 
   ORIGPATH="$PATH"
diff --git a/src/secp256k1/CMakeLists.txt b/src/secp256k1/CMakeLists.txt
--- a/src/secp256k1/CMakeLists.txt
+++ b/src/secp256k1/CMakeLists.txt
@@ -65,19 +65,42 @@
 	set(USE_SCALAR_INV_BUILTIN 1)
 endif()
 
-# We check if amd64 asm is supported.
 option(SECP256K1_USE_ASM "Use assembly if available" ON)
-if($SECP256K1_USE_ASM)
-	check_c_source_compiles("
-		#include <stdint.h>
-		int main() {
-			uint64_t a = 11, tmp;
-			__asm__ __volatile__(\"movq \$0x100000000,%1; mulq %%rsi\" : \"+a\"(a) : \"S\"(tmp) : \"cc\", \"%rdx\");
-			return 0;
-		}
-	" USE_ASM_X86_64)
-else()
-	set(USE_ASM_X86_64 0)
+
+if(SECP256K1_USE_ASM)
+	macro(unsupported_asm_error)
+		message(FATAL_ERROR
+			"Assembly is not supported for your target architecture."
+			"Re-run cmake with -DSECP256k1_USE_ASM=OFF to disable ASM support"
+		)
+	endmacro()
+
+	# Guess the target architecture.
+	# First check if the CMAKE_C_COMPILER_TARGET is set (should be when
+	# cross compiling), then CMAKE_SYSTEM_PROCESSOR as a fallback if meaningful
+	# (this is not the case for ARM as the content is highly non standard).
+	if(CMAKE_C_COMPILER_TARGET MATCHES "x86_64" OR CMAKE_SYSTEM_PROCESSOR MATCHES "x86_64")
+		# We check if amd64 asm is supported.
+		check_c_source_compiles("
+			#include <stdint.h>
+			int main() {
+				uint64_t a = 11, tmp;
+				__asm__ __volatile__(\"movq \$0x100000000,%1; mulq %%rsi\" : \"+a\"(a) : \"S\"(tmp) : \"cc\", \"%rdx\");
+				return 0;
+			}
+		" USE_ASM_X86_64)
+
+		if(NOT USE_ASM_X86_64)
+			unsupported_asm_error()
+		endif()
+	elseif(CMAKE_C_COMPILER_TARGET MATCHES "arm-linux-gnueabihf")
+		enable_language(ASM)
+		set(USE_EXTERNAL_ASM 1)
+		add_library(secp256k1_common src/asm/field_10x26_arm.s)
+		target_link_libraries(secp256k1 secp256k1_common)
+	else()
+		unsupported_asm_error()
+	endif()
 endif()
 
 # We make sure __int128 is defined
diff --git a/src/secp256k1/src/libsecp256k1-config.h.cmake.in b/src/secp256k1/src/libsecp256k1-config.h.cmake.in
--- a/src/secp256k1/src/libsecp256k1-config.h.cmake.in
+++ b/src/secp256k1/src/libsecp256k1-config.h.cmake.in
@@ -20,6 +20,7 @@
 #cmakedefine USE_FIELD_10X26
 
 #cmakedefine USE_ASM_X86_64
+#cmakedefine USE_EXTERNAL_ASM
 
 #cmakedefine USE_ENDOMORPHISM
 #cmakedefine USE_EXTERNAL_DEFAULT_CALLBACKS