diff --git a/cmd/kubeadm/app/util/pkiutil/pki_helpers.go b/cmd/kubeadm/app/util/pkiutil/pki_helpers.go
index 95386cafabf..7887a2fbac3 100644
--- a/cmd/kubeadm/app/util/pkiutil/pki_helpers.go
+++ b/cmd/kubeadm/app/util/pkiutil/pki_helpers.go
@@ -631,10 +631,12 @@ func GeneratePrivateKey(keyType x509.PublicKeyAlgorithm) (crypto.Signer, error)
 
 // NewSignedCert creates a signed certificate using the given CA certificate and key
 func NewSignedCert(cfg *CertConfig, key crypto.Signer, caCert *x509.Certificate, caKey crypto.Signer, isCA bool) (*x509.Certificate, error) {
-	serial, err := cryptorand.Int(cryptorand.Reader, new(big.Int).SetInt64(math.MaxInt64))
+	// returns a uniform random value in [0, max-1), then add 1 to serial to make it a uniform random value in [1, max).
+	serial, err := cryptorand.Int(cryptorand.Reader, new(big.Int).SetInt64(math.MaxInt64-1))
 	if err != nil {
 		return nil, err
 	}
+	serial = new(big.Int).Add(serial, big.NewInt(1))
 	if len(cfg.CommonName) == 0 {
 		return nil, errors.New("must specify a CommonName")
 	}
diff --git a/staging/src/k8s.io/client-go/util/cert/cert.go b/staging/src/k8s.io/client-go/util/cert/cert.go
index 4be1dfe4935..37b023ef25d 100644
--- a/staging/src/k8s.io/client-go/util/cert/cert.go
+++ b/staging/src/k8s.io/client-go/util/cert/cert.go
@@ -25,6 +25,7 @@ import (
 	"crypto/x509/pkix"
 	"encoding/pem"
 	"fmt"
+	"math"
 	"math/big"
 	"net"
 	"os"
@@ -57,8 +58,14 @@ type AltNames struct {
 // NewSelfSignedCACert creates a CA certificate
 func NewSelfSignedCACert(cfg Config, key crypto.Signer) (*x509.Certificate, error) {
 	now := time.Now()
+	// returns a uniform random value in [0, max-1), then add 1 to serial to make it a uniform random value in [1, max).
+	serial, err := cryptorand.Int(cryptorand.Reader, new(big.Int).SetInt64(math.MaxInt64-1))
+	if err != nil {
+		return nil, err
+	}
+	serial = new(big.Int).Add(serial, big.NewInt(1))
 	tmpl := x509.Certificate{
-		SerialNumber: new(big.Int).SetInt64(0),
+		SerialNumber: serial,
 		Subject: pkix.Name{
 			CommonName:   cfg.CommonName,
 			Organization: cfg.Organization,
@@ -116,9 +123,14 @@ func GenerateSelfSignedCertKeyWithFixtures(host string, alternateIPs []net.IP, a
 	if err != nil {
 		return nil, nil, err
 	}
-
+	// returns a uniform random value in [0, max-1), then add 1 to serial to make it a uniform random value in [1, max).
+	serial, err := cryptorand.Int(cryptorand.Reader, new(big.Int).SetInt64(math.MaxInt64-1))
+	if err != nil {
+		return nil, nil, err
+	}
+	serial = new(big.Int).Add(serial, big.NewInt(1))
 	caTemplate := x509.Certificate{
-		SerialNumber: big.NewInt(1),
+		SerialNumber: serial,
 		Subject: pkix.Name{
 			CommonName: fmt.Sprintf("%s-ca@%d", host, time.Now().Unix()),
 		},
@@ -144,9 +156,14 @@ func GenerateSelfSignedCertKeyWithFixtures(host string, alternateIPs []net.IP, a
 	if err != nil {
 		return nil, nil, err
 	}
-
+	// returns a uniform random value in [0, max-1), then add 1 to serial to make it a uniform random value in [1, max).
+	serial, err = cryptorand.Int(cryptorand.Reader, new(big.Int).SetInt64(math.MaxInt64-1))
+	if err != nil {
+		return nil, nil, err
+	}
+	serial = new(big.Int).Add(serial, big.NewInt(1))
 	template := x509.Certificate{
-		SerialNumber: big.NewInt(2),
+		SerialNumber: serial,
 		Subject: pkix.Name{
 			CommonName: fmt.Sprintf("%s@%d", host, time.Now().Unix()),
 		},
diff --git a/test/integration/apiserver/podlogs/podlogs_test.go b/test/integration/apiserver/podlogs/podlogs_test.go
index 1d2ad10061e..b1d0edc4c98 100644
--- a/test/integration/apiserver/podlogs/podlogs_test.go
+++ b/test/integration/apiserver/podlogs/podlogs_test.go
@@ -346,11 +346,12 @@ func generateClientCert(t *testing.T) testCerts {
 		t.Fatal(err)
 	}
 
-	serial, err := rand.Int(rand.Reader, new(big.Int).SetInt64(math.MaxInt64))
+	// returns a uniform random value in [0, max-1), then add 1 to serial to make it a uniform random value in [1, max).
+	serial, err := rand.Int(rand.Reader, new(big.Int).SetInt64(math.MaxInt64-1))
 	if err != nil {
 		t.Fatal(err)
 	}
-
+	serial = new(big.Int).Add(serial, big.NewInt(1))
 	certTmpl := x509.Certificate{
 		Subject: pkix.Name{
 			CommonName: "the-api-server-user",
diff --git a/test/integration/client/cert_rotation_test.go b/test/integration/client/cert_rotation_test.go
index 44089b91128..41f9f45a446 100644
--- a/test/integration/client/cert_rotation_test.go
+++ b/test/integration/client/cert_rotation_test.go
@@ -183,10 +183,12 @@ func writeCerts(t *testing.T, clientSigningCert *x509.Certificate, clientSigning
 		t.Fatal(err)
 	}
 
-	serial, err := rand.Int(rand.Reader, new(big.Int).SetInt64(math.MaxInt64))
+	// returns a uniform random value in [0, max-1), then add 1 to serial to make it a uniform random value in [1, max).
+	serial, err := rand.Int(rand.Reader, new(big.Int).SetInt64(math.MaxInt64-1))
 	if err != nil {
 		t.Fatal(err)
 	}
+	serial = new(big.Int).Add(serial, big.NewInt(1))
 
 	certTmpl := x509.Certificate{
 		Subject: pkix.Name{
diff --git a/test/utils/pki_helpers.go b/test/utils/pki_helpers.go
index 06c3290493d..c96e5855cac 100644
--- a/test/utils/pki_helpers.go
+++ b/test/utils/pki_helpers.go
@@ -53,10 +53,12 @@ func EncodeCertPEM(cert *x509.Certificate) []byte {
 
 // NewSignedCert creates a signed certificate using the given CA certificate and key
 func NewSignedCert(cfg *certutil.Config, key crypto.Signer, caCert *x509.Certificate, caKey crypto.Signer) (*x509.Certificate, error) {
-	serial, err := cryptorand.Int(cryptorand.Reader, new(big.Int).SetInt64(math.MaxInt64))
+	// returns a uniform random value in [0, max-1), then add 1 to serial to make it a uniform random value in [1, max).
+	serial, err := cryptorand.Int(cryptorand.Reader, new(big.Int).SetInt64(math.MaxInt64-1))
 	if err != nil {
 		return nil, err
 	}
+	serial = new(big.Int).Add(serial, big.NewInt(1))
 	if len(cfg.CommonName) == 0 {
 		return nil, fmt.Errorf("must specify a CommonName")
 	}