Support NIST curve P256 (#769)

* Support NIST curve P256 This change adds support for NIST curve P256. When you use `nebula-cert ca` or `nebula-cert keygen`, you can specify `-curve P256` to enable it. The curve to use is based on the curve defined in your CA certificate. Internally, we use ECDSA P256 to sign certificates, and ECDH P256 to do Noise handshakes. P256 is not supported natively in Noise Protocol, so we define `DHP256` in the `noiseutil` package to implement support for it. You cannot have a mixed network of Curve25519 and P256 certificates, since the Noise protocol will only attempt to parse using the Curve defined in the host's certificate. * verify the curves match in VerifyPrivateKey This would have failed anyways once we tried to actually use the bytes in the private key, but its better to detect the issue up front with a better error message. * add cert.Curve argument to Sign method * fix mismerge * use crypto/ecdh This is the preferred method for doing ECDH functions now, and also has a boringcrypto specific codepath. * remove other ecdh uses of crypto/elliptic use crypto/ecdh instead
2025-11-22 16:34:25 +01:00 · 2023-05-04 17:50:23 -04:00
parent 702e1c59bd
commit e0185c4b01
21 changed files with 857 additions and 165 deletions
--- a/cmd/nebula-cert/ca.go
+++ b/cmd/nebula-cert/ca.go
@@ -1,6 +1,8 @@
 package main

 import (
+	"crypto/ecdsa"
+	"crypto/elliptic"
 	"crypto/rand"
 	"flag"
 	"fmt"
@@ -31,6 +33,8 @@ type caFlags struct {
 	argonIterations  *uint
 	argonParallelism *uint
 	encryption       *bool
+
+	curve *string
 }

 func newCaFlags() *caFlags {
@@ -48,6 +52,7 @@ func newCaFlags() *caFlags {
 	cf.argonParallelism = cf.set.Uint("argon-parallelism", 4, "Optional: Argon2 parallelism parameter used for encrypted private key passphrase")
 	cf.argonIterations = cf.set.Uint("argon-iterations", 1, "Optional: Argon2 iterations parameter used for encrypted private key passphrase")
 	cf.encryption = cf.set.Bool("encrypt", false, "Optional: prompt for passphrase and write out-key in an encrypted format")
+	cf.curve = cf.set.String("curve", "25519", "EdDSA/ECDSA Curve (25519, P256)")
 	return &cf
 }

@@ -160,9 +165,25 @@ func ca(args []string, out io.Writer, errOut io.Writer, pr PasswordReader) error
 		}
 	}

-	pub, rawPriv, err := ed25519.GenerateKey(rand.Reader)
-	if err != nil {
-		return fmt.Errorf("error while generating ed25519 keys: %s", err)
+	var curve cert.Curve
+	var pub, rawPriv []byte
+	switch *cf.curve {
+	case "25519", "X25519", "Curve25519", "CURVE25519":
+		curve = cert.Curve_CURVE25519
+		pub, rawPriv, err = ed25519.GenerateKey(rand.Reader)
+		if err != nil {
+			return fmt.Errorf("error while generating ed25519 keys: %s", err)
+		}
+	case "P256":
+		var key *ecdsa.PrivateKey
+		curve = cert.Curve_P256
+		key, err = ecdsa.GenerateKey(elliptic.P256(), rand.Reader)
+		if err != nil {
+			return fmt.Errorf("error while generating ecdsa keys: %s", err)
+		}
+		// ref: https://github.com/golang/go/blob/go1.19/src/crypto/x509/sec1.go#L60
+		rawPriv = key.D.FillBytes(make([]byte, 32))
+		pub = elliptic.Marshal(elliptic.P256(), key.X, key.Y)
 	}

 	nc := cert.NebulaCertificate{
@@ -175,6 +196,7 @@ func ca(args []string, out io.Writer, errOut io.Writer, pr PasswordReader) error
 			NotAfter:  time.Now().Add(*cf.duration),
 			PublicKey: pub,
 			IsCA:      true,
+			Curve:     curve,
 		},
 	}

@@ -186,20 +208,20 @@ func ca(args []string, out io.Writer, errOut io.Writer, pr PasswordReader) error
 		return fmt.Errorf("refusing to overwrite existing CA cert: %s", *cf.outCertPath)
 	}

-	err = nc.Sign(rawPriv)
+	err = nc.Sign(curve, rawPriv)
 	if err != nil {
 		return fmt.Errorf("error while signing: %s", err)
 	}

 	if *cf.encryption {
-		b, err := cert.EncryptAndMarshalEd25519PrivateKey(rawPriv, passphrase, kdfParams)
+		b, err := cert.EncryptAndMarshalSigningPrivateKey(curve, rawPriv, passphrase, kdfParams)
 		if err != nil {
 			return fmt.Errorf("error while encrypting out-key: %s", err)
 		}

 		err = ioutil.WriteFile(*cf.outKeyPath, b, 0600)
 	} else {
-		err = ioutil.WriteFile(*cf.outKeyPath, cert.MarshalEd25519PrivateKey(rawPriv), 0600)
+		err = ioutil.WriteFile(*cf.outKeyPath, cert.MarshalSigningPrivateKey(curve, rawPriv), 0600)
 	}

 	if err != nil {
--- a/cmd/nebula-cert/ca_test.go
+++ b/cmd/nebula-cert/ca_test.go
@@ -35,6 +35,8 @@ func Test_caHelp(t *testing.T) {
 			"    \tOptional: Argon2 memory parameter (in KiB) used for encrypted private key passphrase (default 2097152)\n"+
 			"  -argon-parallelism uint\n"+
 			"    \tOptional: Argon2 parallelism parameter used for encrypted private key passphrase (default 4)\n"+
+			"  -curve string\n"+
+			"    \tEdDSA/ECDSA Curve (25519, P256) (default \"25519\")\n"+
 			"  -duration duration\n"+
 			"    \tOptional: amount of time the certificate should be valid for. Valid time units are seconds: \"s\", minutes: \"m\", hours: \"h\" (default 8760h0m0s)\n"+
 			"  -encrypt\n"+
@@ -174,7 +176,9 @@ func Test_ca(t *testing.T) {
 	assert.Equal(t, uint32(1), ned.EncryptionMetadata.Argon2Parameters.Iterations)

 	// verify the key is valid and decrypt-able
-	lKey, b, err = cert.DecryptAndUnmarshalEd25519PrivateKey(passphrase, rb)
+	var curve cert.Curve
+	curve, lKey, b, err = cert.DecryptAndUnmarshalSigningPrivateKey(passphrase, rb)
+	assert.Equal(t, cert.Curve_CURVE25519, curve)
 	assert.Nil(t, err)
 	assert.Len(t, b, 0)
 	assert.Len(t, lKey, 64)
--- a/cmd/nebula-cert/keygen.go
+++ b/cmd/nebula-cert/keygen.go
@@ -14,6 +14,8 @@ type keygenFlags struct {
 	set        *flag.FlagSet
 	outKeyPath *string
 	outPubPath *string
+
+	curve *string
 }

 func newKeygenFlags() *keygenFlags {
@@ -21,6 +23,7 @@ func newKeygenFlags() *keygenFlags {
 	cf.set.Usage = func() {}
 	cf.outPubPath = cf.set.String("out-pub", "", "Required: path to write the public key to")
 	cf.outKeyPath = cf.set.String("out-key", "", "Required: path to write the private key to")
+	cf.curve = cf.set.String("curve", "25519", "ECDH Curve (25519, P256)")
 	return &cf
 }

@@ -38,14 +41,25 @@ func keygen(args []string, out io.Writer, errOut io.Writer) error {
 		return err
 	}

-	pub, rawPriv := x25519Keypair()
+	var pub, rawPriv []byte
+	var curve cert.Curve
+	switch *cf.curve {
+	case "25519", "X25519", "Curve25519", "CURVE25519":
+		pub, rawPriv = x25519Keypair()
+		curve = cert.Curve_CURVE25519
+	case "P256":
+		pub, rawPriv = p256Keypair()
+		curve = cert.Curve_P256
+	default:
+		return fmt.Errorf("invalid curve: %s", *cf.curve)
+	}

-	err = ioutil.WriteFile(*cf.outKeyPath, cert.MarshalX25519PrivateKey(rawPriv), 0600)
+	err = ioutil.WriteFile(*cf.outKeyPath, cert.MarshalPrivateKey(curve, rawPriv), 0600)
 	if err != nil {
 		return fmt.Errorf("error while writing out-key: %s", err)
 	}

-	err = ioutil.WriteFile(*cf.outPubPath, cert.MarshalX25519PublicKey(pub), 0600)
+	err = ioutil.WriteFile(*cf.outPubPath, cert.MarshalPublicKey(curve, pub), 0600)
 	if err != nil {
 		return fmt.Errorf("error while writing out-pub: %s", err)
 	}
--- a/cmd/nebula-cert/keygen_test.go
+++ b/cmd/nebula-cert/keygen_test.go
@@ -22,6 +22,8 @@ func Test_keygenHelp(t *testing.T) {
 	assert.Equal(
 		t,
 		"Usage of "+os.Args[0]+" keygen <flags>: create a public/private key pair. the public key can be passed to `nebula-cert sign`\n"+
+			"  -curve string\n"+
+			"    \tECDH Curve (25519, P256) (default \"25519\")\n"+
 			"  -out-key string\n"+
 			"    \tRequired: path to write the private key to\n"+
 			"  -out-pub string\n"+
--- a/cmd/nebula-cert/print_test.go
+++ b/cmd/nebula-cert/print_test.go
@@ -87,7 +87,7 @@ func Test_printCert(t *testing.T) {
 	assert.Nil(t, err)
 	assert.Equal(
 		t,
-		"NebulaCertificate {\n\tDetails {\n\t\tName: test\n\t\tIps: []\n\t\tSubnets: []\n\t\tGroups: [\n\t\t\t\"hi\"\n\t\t]\n\t\tNot before: 0001-01-01 00:00:00 +0000 UTC\n\t\tNot After: 0001-01-01 00:00:00 +0000 UTC\n\t\tIs CA: false\n\t\tIssuer: \n\t\tPublic key: 0102030405060708090001020304050607080900010203040506070809000102\n\t}\n\tFingerprint: cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\n\tSignature: 0102030405060708090001020304050607080900010203040506070809000102\n}\nNebulaCertificate {\n\tDetails {\n\t\tName: test\n\t\tIps: []\n\t\tSubnets: []\n\t\tGroups: [\n\t\t\t\"hi\"\n\t\t]\n\t\tNot before: 0001-01-01 00:00:00 +0000 UTC\n\t\tNot After: 0001-01-01 00:00:00 +0000 UTC\n\t\tIs CA: false\n\t\tIssuer: \n\t\tPublic key: 0102030405060708090001020304050607080900010203040506070809000102\n\t}\n\tFingerprint: cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\n\tSignature: 0102030405060708090001020304050607080900010203040506070809000102\n}\nNebulaCertificate {\n\tDetails {\n\t\tName: test\n\t\tIps: []\n\t\tSubnets: []\n\t\tGroups: [\n\t\t\t\"hi\"\n\t\t]\n\t\tNot before: 0001-01-01 00:00:00 +0000 UTC\n\t\tNot After: 0001-01-01 00:00:00 +0000 UTC\n\t\tIs CA: false\n\t\tIssuer: \n\t\tPublic key: 0102030405060708090001020304050607080900010203040506070809000102\n\t}\n\tFingerprint: cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\n\tSignature: 0102030405060708090001020304050607080900010203040506070809000102\n}\n",
+		"NebulaCertificate {\n\tDetails {\n\t\tName: test\n\t\tIps: []\n\t\tSubnets: []\n\t\tGroups: [\n\t\t\t\"hi\"\n\t\t]\n\t\tNot before: 0001-01-01 00:00:00 +0000 UTC\n\t\tNot After: 0001-01-01 00:00:00 +0000 UTC\n\t\tIs CA: false\n\t\tIssuer: \n\t\tPublic key: 0102030405060708090001020304050607080900010203040506070809000102\n\t\tCurve: CURVE25519\n\t}\n\tFingerprint: cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\n\tSignature: 0102030405060708090001020304050607080900010203040506070809000102\n}\nNebulaCertificate {\n\tDetails {\n\t\tName: test\n\t\tIps: []\n\t\tSubnets: []\n\t\tGroups: [\n\t\t\t\"hi\"\n\t\t]\n\t\tNot before: 0001-01-01 00:00:00 +0000 UTC\n\t\tNot After: 0001-01-01 00:00:00 +0000 UTC\n\t\tIs CA: false\n\t\tIssuer: \n\t\tPublic key: 0102030405060708090001020304050607080900010203040506070809000102\n\t\tCurve: CURVE25519\n\t}\n\tFingerprint: cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\n\tSignature: 0102030405060708090001020304050607080900010203040506070809000102\n}\nNebulaCertificate {\n\tDetails {\n\t\tName: test\n\t\tIps: []\n\t\tSubnets: []\n\t\tGroups: [\n\t\t\t\"hi\"\n\t\t]\n\t\tNot before: 0001-01-01 00:00:00 +0000 UTC\n\t\tNot After: 0001-01-01 00:00:00 +0000 UTC\n\t\tIs CA: false\n\t\tIssuer: \n\t\tPublic key: 0102030405060708090001020304050607080900010203040506070809000102\n\t\tCurve: CURVE25519\n\t}\n\tFingerprint: cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\n\tSignature: 0102030405060708090001020304050607080900010203040506070809000102\n}\n",
 		ob.String(),
 	)
 	assert.Equal(t, "", eb.String())
@@ -115,7 +115,7 @@ func Test_printCert(t *testing.T) {
 	assert.Nil(t, err)
 	assert.Equal(
 		t,
-		"{\"details\":{\"groups\":[\"hi\"],\"ips\":[],\"isCa\":false,\"issuer\":\"\",\"name\":\"test\",\"notAfter\":\"0001-01-01T00:00:00Z\",\"notBefore\":\"0001-01-01T00:00:00Z\",\"publicKey\":\"0102030405060708090001020304050607080900010203040506070809000102\",\"subnets\":[]},\"fingerprint\":\"cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\",\"signature\":\"0102030405060708090001020304050607080900010203040506070809000102\"}\n{\"details\":{\"groups\":[\"hi\"],\"ips\":[],\"isCa\":false,\"issuer\":\"\",\"name\":\"test\",\"notAfter\":\"0001-01-01T00:00:00Z\",\"notBefore\":\"0001-01-01T00:00:00Z\",\"publicKey\":\"0102030405060708090001020304050607080900010203040506070809000102\",\"subnets\":[]},\"fingerprint\":\"cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\",\"signature\":\"0102030405060708090001020304050607080900010203040506070809000102\"}\n{\"details\":{\"groups\":[\"hi\"],\"ips\":[],\"isCa\":false,\"issuer\":\"\",\"name\":\"test\",\"notAfter\":\"0001-01-01T00:00:00Z\",\"notBefore\":\"0001-01-01T00:00:00Z\",\"publicKey\":\"0102030405060708090001020304050607080900010203040506070809000102\",\"subnets\":[]},\"fingerprint\":\"cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\",\"signature\":\"0102030405060708090001020304050607080900010203040506070809000102\"}\n",
+		"{\"details\":{\"curve\":\"CURVE25519\",\"groups\":[\"hi\"],\"ips\":[],\"isCa\":false,\"issuer\":\"\",\"name\":\"test\",\"notAfter\":\"0001-01-01T00:00:00Z\",\"notBefore\":\"0001-01-01T00:00:00Z\",\"publicKey\":\"0102030405060708090001020304050607080900010203040506070809000102\",\"subnets\":[]},\"fingerprint\":\"cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\",\"signature\":\"0102030405060708090001020304050607080900010203040506070809000102\"}\n{\"details\":{\"curve\":\"CURVE25519\",\"groups\":[\"hi\"],\"ips\":[],\"isCa\":false,\"issuer\":\"\",\"name\":\"test\",\"notAfter\":\"0001-01-01T00:00:00Z\",\"notBefore\":\"0001-01-01T00:00:00Z\",\"publicKey\":\"0102030405060708090001020304050607080900010203040506070809000102\",\"subnets\":[]},\"fingerprint\":\"cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\",\"signature\":\"0102030405060708090001020304050607080900010203040506070809000102\"}\n{\"details\":{\"curve\":\"CURVE25519\",\"groups\":[\"hi\"],\"ips\":[],\"isCa\":false,\"issuer\":\"\",\"name\":\"test\",\"notAfter\":\"0001-01-01T00:00:00Z\",\"notBefore\":\"0001-01-01T00:00:00Z\",\"publicKey\":\"0102030405060708090001020304050607080900010203040506070809000102\",\"subnets\":[]},\"fingerprint\":\"cc3492c0e9c48f17547f5987ea807462ebb3451e622590a10bb3763c344c82bd\",\"signature\":\"0102030405060708090001020304050607080900010203040506070809000102\"}\n",
 		ob.String(),
 	)
 	assert.Equal(t, "", eb.String())
--- a/cmd/nebula-cert/sign.go
+++ b/cmd/nebula-cert/sign.go
@@ -1,7 +1,7 @@
 package main

 import (
-	"crypto/ed25519"
+	"crypto/ecdh"
 	"crypto/rand"
 	"flag"
 	"fmt"
@@ -78,10 +78,11 @@ func signCert(args []string, out io.Writer, errOut io.Writer, pr PasswordReader)
 		return fmt.Errorf("error while reading ca-key: %s", err)
 	}

-	var caKey ed25519.PrivateKey
+	var curve cert.Curve
+	var caKey []byte

 	// naively attempt to decode the private key as though it is not encrypted
-	caKey, _, err = cert.UnmarshalEd25519PrivateKey(rawCAKey)
+	caKey, _, curve, err = cert.UnmarshalSigningPrivateKey(rawCAKey)
 	if err == cert.ErrPrivateKeyEncrypted {
 		// ask for a passphrase until we get one
 		var passphrase []byte
@@ -103,7 +104,7 @@ func signCert(args []string, out io.Writer, errOut io.Writer, pr PasswordReader)
 			return fmt.Errorf("cannot open encrypted ca-key without passphrase")
 		}

-		caKey, _, err = cert.DecryptAndUnmarshalEd25519PrivateKey(passphrase, rawCAKey)
+		curve, caKey, _, err = cert.DecryptAndUnmarshalSigningPrivateKey(passphrase, rawCAKey)
 		if err != nil {
 			return fmt.Errorf("error while parsing encrypted ca-key: %s", err)
 		}
@@ -121,7 +122,7 @@ func signCert(args []string, out io.Writer, errOut io.Writer, pr PasswordReader)
 		return fmt.Errorf("error while parsing ca-crt: %s", err)
 	}

-	if err := caCert.VerifyPrivateKey(caKey); err != nil {
+	if err := caCert.VerifyPrivateKey(curve, caKey); err != nil {
 		return fmt.Errorf("refusing to sign, root certificate does not match private key")
 	}

@@ -181,12 +182,16 @@ func signCert(args []string, out io.Writer, errOut io.Writer, pr PasswordReader)
 		if err != nil {
 			return fmt.Errorf("error while reading in-pub: %s", err)
 		}
-		pub, _, err = cert.UnmarshalX25519PublicKey(rawPub)
+		var pubCurve cert.Curve
+		pub, _, pubCurve, err = cert.UnmarshalPublicKey(rawPub)
 		if err != nil {
 			return fmt.Errorf("error while parsing in-pub: %s", err)
 		}
+		if pubCurve != curve {
+			return fmt.Errorf("curve of in-pub does not match ca")
+		}
 	} else {
-		pub, rawPriv = x25519Keypair()
+		pub, rawPriv = newKeypair(curve)
 	}

 	nc := cert.NebulaCertificate{
@@ -200,6 +205,7 @@ func signCert(args []string, out io.Writer, errOut io.Writer, pr PasswordReader)
 			PublicKey: pub,
 			IsCA:      false,
 			Issuer:    issuer,
+			Curve:     curve,
 		},
 	}

@@ -219,7 +225,7 @@ func signCert(args []string, out io.Writer, errOut io.Writer, pr PasswordReader)
 		return fmt.Errorf("refusing to overwrite existing cert: %s", *sf.outCertPath)
 	}

-	err = nc.Sign(caKey)
+	err = nc.Sign(curve, caKey)
 	if err != nil {
 		return fmt.Errorf("error while signing: %s", err)
 	}
@@ -229,7 +235,7 @@ func signCert(args []string, out io.Writer, errOut io.Writer, pr PasswordReader)
 			return fmt.Errorf("refusing to overwrite existing key: %s", *sf.outKeyPath)
 		}

-		err = ioutil.WriteFile(*sf.outKeyPath, cert.MarshalX25519PrivateKey(rawPriv), 0600)
+		err = ioutil.WriteFile(*sf.outKeyPath, cert.MarshalPrivateKey(curve, rawPriv), 0600)
 		if err != nil {
 			return fmt.Errorf("error while writing out-key: %s", err)
 		}
@@ -260,6 +266,17 @@ func signCert(args []string, out io.Writer, errOut io.Writer, pr PasswordReader)
 	return nil
 }

+func newKeypair(curve cert.Curve) ([]byte, []byte) {
+	switch curve {
+	case cert.Curve_CURVE25519:
+		return x25519Keypair()
+	case cert.Curve_P256:
+		return p256Keypair()
+	default:
+		return nil, nil
+	}
+}
+
 func x25519Keypair() ([]byte, []byte) {
 	privkey := make([]byte, 32)
 	if _, err := io.ReadFull(rand.Reader, privkey); err != nil {
@@ -274,6 +291,15 @@ func x25519Keypair() ([]byte, []byte) {
 	return pubkey, privkey
 }

+func p256Keypair() ([]byte, []byte) {
+	privkey, err := ecdh.P256().GenerateKey(rand.Reader)
+	if err != nil {
+		panic(err)
+	}
+	pubkey := privkey.PublicKey()
+	return pubkey.Bytes(), privkey.Bytes()
+}
+
 func signSummary() string {
 	return "sign <flags>: create and sign a certificate"
 }
--- a/cmd/nebula-cert/sign_test.go
+++ b/cmd/nebula-cert/sign_test.go
@@ -359,7 +359,7 @@ func Test_signCert(t *testing.T) {
 	// generate the encrypted key
 	caPub, caPriv, _ = ed25519.GenerateKey(rand.Reader)
 	kdfParams := cert.NewArgon2Parameters(64*1024, 4, 3)
-	b, _ = cert.EncryptAndMarshalEd25519PrivateKey(caPriv, passphrase, kdfParams)
+	b, _ = cert.EncryptAndMarshalSigningPrivateKey(cert.Curve_CURVE25519, caPriv, passphrase, kdfParams)
 	caKeyF.Write(b)

 	ca = cert.NebulaCertificate{
--- a/cmd/nebula-cert/verify_test.go
+++ b/cmd/nebula-cert/verify_test.go
@@ -77,7 +77,7 @@ func Test_verify(t *testing.T) {
 			IsCA:      true,
 		},
 	}
-	ca.Sign(caPriv)
+	ca.Sign(cert.Curve_CURVE25519, caPriv)
 	b, _ := ca.MarshalToPEM()
 	caFile.Truncate(0)
 	caFile.Seek(0, 0)
@@ -117,7 +117,7 @@ func Test_verify(t *testing.T) {
 		},
 	}

-	crt.Sign(badPriv)
+	crt.Sign(cert.Curve_CURVE25519, badPriv)
 	b, _ = crt.MarshalToPEM()
 	certFile.Truncate(0)
 	certFile.Seek(0, 0)
@@ -129,7 +129,7 @@ func Test_verify(t *testing.T) {
 	assert.EqualError(t, err, "certificate signature did not match")

 	// verified cert at path
-	crt.Sign(caPriv)
+	crt.Sign(cert.Curve_CURVE25519, caPriv)
 	b, _ = crt.MarshalToPEM()
 	certFile.Truncate(0)
 	certFile.Seek(0, 0)