diff --git a/swtpm.spec b/swtpm.spec
index 0aa2560..1400353 100644
--- a/swtpm.spec
+++ b/swtpm.spec
@@ -29,7 +29,7 @@
 BuildRequires:  trousers >= 0.3.9
 %endif
 %if %{with gnutls}
-BuildRequires:  gnutls >= 3.1.0
+BuildRequires:  gnutls >= 3.4.0
 BuildRequires:  gnutls-devel
 BuildRequires:  gnutls-utils
 BuildRequires:  libtasn1-devel
diff --git a/swtpm.spec.in b/swtpm.spec.in
index a91220e..df1f20e 100644
--- a/swtpm.spec.in
+++ b/swtpm.spec.in
@@ -29,7 +29,7 @@
 BuildRequires:  trousers >= 0.3.9
 %endif
 %if %{with gnutls}
-BuildRequires:  gnutls >= 3.1.0
+BuildRequires:  gnutls >= 3.4.0
 BuildRequires:  gnutls-devel
 BuildRequires:  gnutls-utils
 BuildRequires:  libtasn1-devel