diff --git a/cmd/certs.go b/cmd/certs.go
index 78f147b68..609263c2b 100644
--- a/cmd/certs.go
+++ b/cmd/certs.go
@@ -17,6 +17,8 @@
 package cmd
 
 import (
+	"crypto"
+	"crypto/ecdsa"
 	"crypto/tls"
 	"crypto/x509"
 	"encoding/pem"
@@ -142,6 +144,16 @@ func getSSLConfig() (x509Certs []*x509.Certificate, rootCAs *x509.CertPool, tlsC
 	if cert, err = loadX509KeyPair(getPublicCertFile(), getPrivateKeyFile()); err != nil {
 		return nil, nil, nil, false, err
 	}
+	// Ensure that the private key is not a P-384 or P-521 EC key.
+	// The Go TLS stack does not provide constant-time implementations of P-384 and P-521.
+	if priv, ok := cert.PrivateKey.(crypto.Signer); ok {
+		if pub, ok := priv.Public().(*ecdsa.PublicKey); ok {
+			if name := pub.Params().Name; name == "P-384" || name == "P-521" { // unfortunately there is no cleaner way to check
+				return nil, nil, nil, false, fmt.Errorf("TLS: the ECDSA curve '%s' is not supported", name)
+			}
+		}
+
+	}
 
 	tlsCert = &cert
 
diff --git a/cmd/http/server.go b/cmd/http/server.go
index 91ad0e84e..964a17389 100644
--- a/cmd/http/server.go
+++ b/cmd/http/server.go
@@ -172,6 +172,9 @@ var defaultCipherSuites = []uint16{
 	tls.TLS_ECDHE_ECDSA_WITH_AES_256_GCM_SHA384,
 }
 
+// Go only provides constant-time implementations of Curve25519 and NIST P-256 curve.
+var secureCurves = []tls.CurveID{tls.X25519, tls.CurveP256}
+
 // NewServer - creates new HTTP server using given arguments.
 func NewServer(addrs []string, handler http.Handler, certificate *tls.Certificate) *Server {
 	var tlsConfig *tls.Config
@@ -179,6 +182,7 @@ func NewServer(addrs []string, handler http.Handler, certificate *tls.Certificat
 		tlsConfig = &tls.Config{
 			PreferServerCipherSuites: true,
 			CipherSuites:             defaultCipherSuites,
+			CurvePreferences:         secureCurves,
 			MinVersion:               tls.VersionTLS12,
 			NextProtos:               []string{"http/1.1", "h2"},
 		}
diff --git a/docs/tls/README.md b/docs/tls/README.md
index b5c9bfc05..43f16777c 100644
--- a/docs/tls/README.md
+++ b/docs/tls/README.md
@@ -43,6 +43,9 @@ or protect the private key additionally with a password:
 ```sh
 openssl ecparam -genkey -name prime256v1 | openssl ec -aes256 -out private.key -passout pass:PASSWORD
 ```
+
+Notice that the NIST curves P-384 and P-521 are not supported yet.
+
 2. **RSA:**
 ```sh
 openssl genrsa -out private.key 2048