diff --git a/Makefile.certificate b/Makefile.certificate
index 4f9d55d..cc88c52 100644
--- a/Makefile.certificate
+++ b/Makefile.certificate
@@ -1,8 +1,11 @@
 UTF8 := $(shell locale -c LC_CTYPE -k | grep -q charmap.*UTF-8 && echo -utf8)
-SERIAL=0
 DAYS=365
 KEYLEN=2048
 TYPE=rsa:$(KEYLEN)
+EXTRA_FLAGS=
+ifdef SERIAL
+	EXTRA_FLAGS+=-set_serial $(SERIAL)
+endif
 
 .PHONY: usage
 .SUFFIXES: .key .csr .crt .pem
@@ -23,8 +26,9 @@ usage:
 	@echo "To create a CSR for use with Apache, run \"make certreq\"."
 	@echo "To create a test certificate for use with Apache, run \"make testcert\"."
 	@echo
-	@echo "To create a test certificate with serial number other than zero, add SERIAL=num"
+	@echo "To create a test certificate with serial number other than random, add SERIAL=num"
 	@echo "You can also specify key length with KEYLEN=n and expiration in days with DAYS=n"
+	@echo "Any additional options can be passed to openssl req via EXTRA_FLAGS"
 	@echo
 	@echo Examples:
 	@echo "  make server.key"
@@ -35,14 +39,14 @@ usage:
 	@echo "  make certreq"
 	@echo "  make testcert"
 	@echo "  make server.crt SERIAL=1"
-	@echo "  make stunnel.pem SERIAL=2"
-	@echo "  make testcert SERIAL=3"
+	@echo "  make stunnel.pem EXTRA_FLAGS=-sha384"
+	@echo "  make testcert DAYS=600"
 
 %.pem:
 	umask 77 ; \
 	PEM1=`/bin/mktemp /tmp/openssl.XXXXXX` ; \
 	PEM2=`/bin/mktemp /tmp/openssl.XXXXXX` ; \
-	/usr/bin/openssl req $(UTF8) -newkey $(TYPE) -keyout $$PEM1 -nodes -x509 -days $(DAYS) -out $$PEM2 -set_serial $(SERIAL) ; \
+	/usr/bin/openssl req $(UTF8) -newkey $(TYPE) -keyout $$PEM1 -nodes -x509 -days $(DAYS) -out $$PEM2 $(EXTRA_FLAGS) ; \
 	cat $$PEM1 >  $@ ; \
 	echo ""    >> $@ ; \
 	cat $$PEM2 >> $@ ; \
@@ -58,7 +62,7 @@ usage:
 
 %.crt: %.key
 	umask 77 ; \
-	/usr/bin/openssl req $(UTF8) -new -key $^ -x509 -days $(DAYS) -out $@ -set_serial $(SERIAL)
+	/usr/bin/openssl req $(UTF8) -new -key $^ -x509 -days $(DAYS) -out $@ $(EXTRA_FLAGS)
 
 TLSROOT=/etc/pki/tls
 KEY=$(TLSROOT)/private/localhost.key
@@ -75,4 +79,4 @@ $(CSR): $(KEY)
 
 $(CRT): $(KEY)
 	umask 77 ; \
-	/usr/bin/openssl req $(UTF8) -new -key $(KEY) -x509 -days $(DAYS) -out $(CRT) -set_serial $(SERIAL)
+	/usr/bin/openssl req $(UTF8) -new -key $(KEY) -x509 -days $(DAYS) -out $(CRT) $(EXTRA_FLAGS)
diff --git a/openssl.spec b/openssl.spec
index fa18769..6d27b92 100644
--- a/openssl.spec
+++ b/openssl.spec
@@ -227,6 +227,9 @@ if ! echo %{_target} | grep -q i686 ; then
 	sslflags="no-asm 386"
 fi
 %endif
+%ifarch x86_64
+sslflags=enable-ec_nistp_64_gcc_128
+%endif
 %ifarch sparcv9
 sslarch=linux-sparcv9
 sslflags=no-asm
@@ -243,21 +246,25 @@ sslarch="linux-generic32 -DB_ENDIAN"
 %endif
 %ifarch s390x
 sslarch="linux64-s390x"
+sslflags=enable-ec_nistp_64_gcc_128
 %endif
 %ifarch %{arm}
 sslarch=linux-armv4
 %endif
 %ifarch aarch64
 sslarch=linux-aarch64
+sslflags=enable-ec_nistp_64_gcc_128
 %endif
 %ifarch sh3 sh4
 sslarch=linux-generic32
 %endif
 %ifarch ppc64 ppc64p7
 sslarch=linux-ppc64
+sslflags=enable-ec_nistp_64_gcc_128
 %endif
 %ifarch ppc64le
 sslarch="linux-ppc64le"
+sslflags=enable-ec_nistp_64_gcc_128
 %endif
 
 # ia64, x86_64, ppc are OK by default
@@ -268,7 +275,7 @@ sslarch="linux-ppc64le"
 	--prefix=%{_prefix} --openssldir=%{_sysconfdir}/pki/tls ${sslflags} \
 	--system-ciphers-file=%{_sysconfdir}/crypto-policies/back-ends/openssl.config \
 	zlib enable-camellia enable-seed enable-tlsext enable-rfc3779 \
-	enable-cms enable-md2 enable-ec_nistp_64_gcc_128 \
+	enable-cms enable-md2 \
 	no-mdc2 no-rc5 no-ec2m no-gost no-srp \
 	--with-krb5-flavor=MIT --enginesdir=%{_libdir}/openssl/engines \
 	--with-krb5-dir=/usr shared  ${sslarch} %{?!nofips:fips}
@@ -488,6 +495,7 @@ rm -rf $RPM_BUILD_ROOT/%{_libdir}/fipscanister.*
 - enable fast assembler implementation for NIST P-256 and P-521
   elliptic curves (#1164210)
 - filter out unwanted link options from the .pc files (#1257836)
+- do not set serial to 0 in Makefile.certificate (#1135719)
 
 * Mon Nov 16 2015 Tomáš Mráz <tmraz@redhat.com> 1.0.2d-3
 - fix sigill on some AMD CPUs (#1278194)