vendor/github.com/docker/libtrust/ec_key.go - third_party/github.com/moby/moby - Git at Google

 package libtrust

 import (
 	"crypto"
 	"crypto/ecdsa"
 	"crypto/elliptic"
 	"crypto/rand"
 	"crypto/x509"
 	"encoding/json"
 	"encoding/pem"
 	"errors"
 	"fmt"
 	"io"
 	"math/big"
 )

 /*
  * EC DSA PUBLIC KEY
  */

 // ecPublicKey implements a libtrust.PublicKey using elliptic curve digital
 // signature algorithms.
 type ecPublicKey struct {
 	*ecdsa.PublicKey
 	curveName          string
 	signatureAlgorithm *signatureAlgorithm
 	extended           map[string]interface{}
 }

 func fromECPublicKey(cryptoPublicKey *ecdsa.PublicKey) (*ecPublicKey, error) {
 	curve := cryptoPublicKey.Curve

 	switch {
 	case curve == elliptic.P256():
 		return &ecPublicKey{cryptoPublicKey, "P-256", es256, map[string]interface{}{}}, nil
 	case curve == elliptic.P384():
 		return &ecPublicKey{cryptoPublicKey, "P-384", es384, map[string]interface{}{}}, nil
 	case curve == elliptic.P521():
 		return &ecPublicKey{cryptoPublicKey, "P-521", es512, map[string]interface{}{}}, nil
 	default:
 		return nil, errors.New("unsupported elliptic curve")
 	}
 }

 // KeyType returns the key type for elliptic curve keys, i.e., "EC".
 func (k *ecPublicKey) KeyType() string {
 	return "EC"
 }

 // CurveName returns the elliptic curve identifier.
 // Possible values are "P-256", "P-384", and "P-521".
 func (k *ecPublicKey) CurveName() string {
 	return k.curveName
 }

 // KeyID returns a distinct identifier which is unique to this Public Key.
 func (k *ecPublicKey) KeyID() string {
 	return keyIDFromCryptoKey(k)
 }

 func (k *ecPublicKey) String() string {
 	return fmt.Sprintf("EC Public Key <%s>", k.KeyID())
 }

 // Verify verifyies the signature of the data in the io.Reader using this
 // PublicKey. The alg parameter should identify the digital signature
 // algorithm which was used to produce the signature and should be supported
 // by this public key. Returns a nil error if the signature is valid.
 func (k *ecPublicKey) Verify(data io.Reader, alg string, signature []byte) error {
 	// For EC keys there is only one supported signature algorithm depending
 	// on the curve parameters.
 	if k.signatureAlgorithm.HeaderParam() != alg {
 		return fmt.Errorf("unable to verify signature: EC Public Key with curve %q does not support signature algorithm %q", k.curveName, alg)
 	}

 	// signature is the concatenation of (r, s), base64Url encoded.
 	sigLength := len(signature)
 	expectedOctetLength := 2 * ((k.Params().BitSize + 7) >> 3)
 	if sigLength != expectedOctetLength {
 		return fmt.Errorf("signature length is %d octets long, should be %d", sigLength, expectedOctetLength)
 	}

 	rBytes, sBytes := signature[:sigLength/2], signature[sigLength/2:]
 	r := new(big.Int).SetBytes(rBytes)
 	s := new(big.Int).SetBytes(sBytes)

 	hasher := k.signatureAlgorithm.HashID().New()
 	_, err := io.Copy(hasher, data)
 	if err != nil {
 		return fmt.Errorf("error reading data to sign: %s", err)
 	}
 	hash := hasher.Sum(nil)

 	if !ecdsa.Verify(k.PublicKey, hash, r, s) {
 		return errors.New("invalid signature")
 	}

 	return nil
 }

 // CryptoPublicKey returns the internal object which can be used as a
 // crypto.PublicKey for use with other standard library operations. The type
 // is either *rsa.PublicKey or *ecdsa.PublicKey
 func (k *ecPublicKey) CryptoPublicKey() crypto.PublicKey {
 	return k.PublicKey
 }

 func (k *ecPublicKey) toMap() map[string]interface{} {
 	jwk := make(map[string]interface{})
 	for k, v := range k.extended {
 		jwk[k] = v
 	}
 	jwk["kty"] = k.KeyType()
 	jwk["kid"] = k.KeyID()
 	jwk["crv"] = k.CurveName()

 	xBytes := k.X.Bytes()
 	yBytes := k.Y.Bytes()
 	octetLength := (k.Params().BitSize + 7) >> 3
 	// MUST include leading zeros in the output so that x, y are each
 	// *octetLength* bytes long.
 	xBuf := make([]byte, octetLength-len(xBytes), octetLength)
 	yBuf := make([]byte, octetLength-len(yBytes), octetLength)
 	xBuf = append(xBuf, xBytes...)
 	yBuf = append(yBuf, yBytes...)

 	jwk["x"] = joseBase64UrlEncode(xBuf)
 	jwk["y"] = joseBase64UrlEncode(yBuf)

 	return jwk
 }

 // MarshalJSON serializes this Public Key using the JWK JSON serialization format for
 // elliptic curve keys.
 func (k *ecPublicKey) MarshalJSON() (data []byte, err error) {
 	return json.Marshal(k.toMap())
 }

 // PEMBlock serializes this Public Key to DER-encoded PKIX format.
 func (k *ecPublicKey) PEMBlock() (*pem.Block, error) {
 	derBytes, err := x509.MarshalPKIXPublicKey(k.PublicKey)
 	if err != nil {
 		return nil, fmt.Errorf("unable to serialize EC PublicKey to DER-encoded PKIX format: %s", err)
 	}
 	k.extended["kid"] = k.KeyID() // For display purposes.
 	return createPemBlock("PUBLIC KEY", derBytes, k.extended)
 }

 func (k *ecPublicKey) AddExtendedField(field string, value interface{}) {
 	k.extended[field] = value
 }

 func (k *ecPublicKey) GetExtendedField(field string) interface{} {
 	v, ok := k.extended[field]
 	if !ok {
 		return nil
 	}
 	return v
 }

 func ecPublicKeyFromMap(jwk map[string]interface{}) (*ecPublicKey, error) {
 	// JWK key type (kty) has already been determined to be "EC".
 	// Need to extract 'crv', 'x', 'y', and 'kid' and check for
 	// consistency.

 	// Get the curve identifier value.
 	crv, err := stringFromMap(jwk, "crv")
 	if err != nil {
 		return nil, fmt.Errorf("JWK EC Public Key curve identifier: %s", err)
 	}

 	var (
 		curve  elliptic.Curve
 		sigAlg *signatureAlgorithm
 	)

 	switch {
 	case crv == "P-256":
 		curve = elliptic.P256()
 		sigAlg = es256
 	case crv == "P-384":
 		curve = elliptic.P384()
 		sigAlg = es384
 	case crv == "P-521":
 		curve = elliptic.P521()
 		sigAlg = es512
 	default:
 		return nil, fmt.Errorf("JWK EC Public Key curve identifier not supported: %q\n", crv)
 	}

 	// Get the X and Y coordinates for the public key point.
 	xB64Url, err := stringFromMap(jwk, "x")
 	if err != nil {
 		return nil, fmt.Errorf("JWK EC Public Key x-coordinate: %s", err)
 	}
 	x, err := parseECCoordinate(xB64Url, curve)
 	if err != nil {
 		return nil, fmt.Errorf("JWK EC Public Key x-coordinate: %s", err)
 	}

 	yB64Url, err := stringFromMap(jwk, "y")
 	if err != nil {
 		return nil, fmt.Errorf("JWK EC Public Key y-coordinate: %s", err)
 	}
 	y, err := parseECCoordinate(yB64Url, curve)
 	if err != nil {
 		return nil, fmt.Errorf("JWK EC Public Key y-coordinate: %s", err)
 	}

 	key := &ecPublicKey{
 		PublicKey: &ecdsa.PublicKey{Curve: curve, X: x, Y: y},
 		curveName: crv, signatureAlgorithm: sigAlg,
 	}

 	// Key ID is optional too, but if it exists, it should match the key.
 	_, ok := jwk["kid"]
 	if ok {
 		kid, err := stringFromMap(jwk, "kid")
 		if err != nil {
 			return nil, fmt.Errorf("JWK EC Public Key ID: %s", err)
 		}
 		if kid != key.KeyID() {
 			return nil, fmt.Errorf("JWK EC Public Key ID does not match: %s", kid)
 		}
 	}

 	key.extended = jwk

 	return key, nil
 }

 /*
  * EC DSA PRIVATE KEY
  */

 // ecPrivateKey implements a JWK Private Key using elliptic curve digital signature
 // algorithms.
 type ecPrivateKey struct {
 	ecPublicKey
 	*ecdsa.PrivateKey
 }

 func fromECPrivateKey(cryptoPrivateKey *ecdsa.PrivateKey) (*ecPrivateKey, error) {
 	publicKey, err := fromECPublicKey(&cryptoPrivateKey.PublicKey)
 	if err != nil {
 		return nil, err
 	}

 	return &ecPrivateKey{*publicKey, cryptoPrivateKey}, nil
 }

 // PublicKey returns the Public Key data associated with this Private Key.
 func (k *ecPrivateKey) PublicKey() PublicKey {
 	return &k.ecPublicKey
 }

 func (k *ecPrivateKey) String() string {
 	return fmt.Sprintf("EC Private Key <%s>", k.KeyID())
 }

 // Sign signs the data read from the io.Reader using a signature algorithm supported
 // by the elliptic curve private key. If the specified hashing algorithm is
 // supported by this key, that hash function is used to generate the signature
 // otherwise the the default hashing algorithm for this key is used. Returns
 // the signature and the name of the JWK signature algorithm used, e.g.,
 // "ES256", "ES384", "ES512".
 func (k *ecPrivateKey) Sign(data io.Reader, hashID crypto.Hash) (signature []byte, alg string, err error) {
 	// Generate a signature of the data using the internal alg.
 	// The given hashId is only a suggestion, and since EC keys only support
 	// on signature/hash algorithm given the curve name, we disregard it for
 	// the elliptic curve JWK signature implementation.
 	hasher := k.signatureAlgorithm.HashID().New()
 	_, err = io.Copy(hasher, data)
 	if err != nil {
 		return nil, "", fmt.Errorf("error reading data to sign: %s", err)
 	}
 	hash := hasher.Sum(nil)

 	r, s, err := ecdsa.Sign(rand.Reader, k.PrivateKey, hash)
 	if err != nil {
 		return nil, "", fmt.Errorf("error producing signature: %s", err)
 	}
 	rBytes, sBytes := r.Bytes(), s.Bytes()
 	octetLength := (k.ecPublicKey.Params().BitSize + 7) >> 3
 	// MUST include leading zeros in the output
 	rBuf := make([]byte, octetLength-len(rBytes), octetLength)
 	sBuf := make([]byte, octetLength-len(sBytes), octetLength)

 	rBuf = append(rBuf, rBytes...)
 	sBuf = append(sBuf, sBytes...)

 	signature = append(rBuf, sBuf...)
 	alg = k.signatureAlgorithm.HeaderParam()

 	return
 }

 // CryptoPrivateKey returns the internal object which can be used as a
 // crypto.PublicKey for use with other standard library operations. The type
 // is either *rsa.PublicKey or *ecdsa.PublicKey
 func (k *ecPrivateKey) CryptoPrivateKey() crypto.PrivateKey {
 	return k.PrivateKey
 }

 func (k *ecPrivateKey) toMap() map[string]interface{} {
 	jwk := k.ecPublicKey.toMap()

 	dBytes := k.D.Bytes()
 	// The length of this octet string MUST be ceiling(log-base-2(n)/8)
 	// octets (where n is the order of the curve). This is because the private
 	// key d must be in the interval [1, n-1] so the bitlength of d should be
 	// no larger than the bitlength of n-1. The easiest way to find the octet
 	// length is to take bitlength(n-1), add 7 to force a carry, and shift this
 	// bit sequence right by 3, which is essentially dividing by 8 and adding
 	// 1 if there is any remainder. Thus, the private key value d should be
 	// output to (bitlength(n-1)+7)>>3 octets.
 	n := k.ecPublicKey.Params().N
 	octetLength := (new(big.Int).Sub(n, big.NewInt(1)).BitLen() + 7) >> 3
 	// Create a buffer with the necessary zero-padding.
 	dBuf := make([]byte, octetLength-len(dBytes), octetLength)
 	dBuf = append(dBuf, dBytes...)

 	jwk["d"] = joseBase64UrlEncode(dBuf)

 	return jwk
 }

 // MarshalJSON serializes this Private Key using the JWK JSON serialization format for
 // elliptic curve keys.
 func (k *ecPrivateKey) MarshalJSON() (data []byte, err error) {
 	return json.Marshal(k.toMap())
 }

 // PEMBlock serializes this Private Key to DER-encoded PKIX format.
 func (k *ecPrivateKey) PEMBlock() (*pem.Block, error) {
 	derBytes, err := x509.MarshalECPrivateKey(k.PrivateKey)
 	if err != nil {
 		return nil, fmt.Errorf("unable to serialize EC PrivateKey to DER-encoded PKIX format: %s", err)
 	}
 	k.extended["keyID"] = k.KeyID() // For display purposes.
 	return createPemBlock("EC PRIVATE KEY", derBytes, k.extended)
 }

 func ecPrivateKeyFromMap(jwk map[string]interface{}) (*ecPrivateKey, error) {
 	dB64Url, err := stringFromMap(jwk, "d")
 	if err != nil {
 		return nil, fmt.Errorf("JWK EC Private Key: %s", err)
 	}

 	// JWK key type (kty) has already been determined to be "EC".
 	// Need to extract the public key information, then extract the private
 	// key value 'd'.
 	publicKey, err := ecPublicKeyFromMap(jwk)
 	if err != nil {
 		return nil, err
 	}

 	d, err := parseECPrivateParam(dB64Url, publicKey.Curve)
 	if err != nil {
 		return nil, fmt.Errorf("JWK EC Private Key d-param: %s", err)
 	}

 	key := &ecPrivateKey{
 		ecPublicKey: *publicKey,
 		PrivateKey: &ecdsa.PrivateKey{
 			PublicKey: *publicKey.PublicKey,
 			D:         d,
 		},
 	}

 	return key, nil
 }

 /*
  *	Key Generation Functions.
  */

 func generateECPrivateKey(curve elliptic.Curve) (k *ecPrivateKey, err error) {
 	k = new(ecPrivateKey)
 	k.PrivateKey, err = ecdsa.GenerateKey(curve, rand.Reader)
 	if err != nil {
 		return nil, err
 	}

 	k.ecPublicKey.PublicKey = &k.PrivateKey.PublicKey
 	k.extended = make(map[string]interface{})

 	return
 }

 // GenerateECP256PrivateKey generates a key pair using elliptic curve P-256.
 func GenerateECP256PrivateKey() (PrivateKey, error) {
 	k, err := generateECPrivateKey(elliptic.P256())
 	if err != nil {
 		return nil, fmt.Errorf("error generating EC P-256 key: %s", err)
 	}

 	k.curveName = "P-256"
 	k.signatureAlgorithm = es256

 	return k, nil
 }

 // GenerateECP384PrivateKey generates a key pair using elliptic curve P-384.
 func GenerateECP384PrivateKey() (PrivateKey, error) {
 	k, err := generateECPrivateKey(elliptic.P384())
 	if err != nil {
 		return nil, fmt.Errorf("error generating EC P-384 key: %s", err)
 	}

 	k.curveName = "P-384"
 	k.signatureAlgorithm = es384

 	return k, nil
 }

 // GenerateECP521PrivateKey generates aß key pair using elliptic curve P-521.
 func GenerateECP521PrivateKey() (PrivateKey, error) {
 	k, err := generateECPrivateKey(elliptic.P521())
 	if err != nil {
 		return nil, fmt.Errorf("error generating EC P-521 key: %s", err)
 	}

 	k.curveName = "P-521"
 	k.signatureAlgorithm = es512

 	return k, nil
 }
	package libtrust

	import (
	"crypto"
	"crypto/ecdsa"
	"crypto/elliptic"
	"crypto/rand"
	"crypto/x509"
	"encoding/json"
	"encoding/pem"
	"errors"
	"fmt"
	"io"
	"math/big"
	)

	/*
	* EC DSA PUBLIC KEY
	*/

	// ecPublicKey implements a libtrust.PublicKey using elliptic curve digital
	// signature algorithms.
	type ecPublicKey struct {
	*ecdsa.PublicKey
	curveName string
	signatureAlgorithm *signatureAlgorithm
	extended map[string]interface{}
	}

	func fromECPublicKey(cryptoPublicKey ecdsa.PublicKey) (ecPublicKey, error) {
	curve := cryptoPublicKey.Curve

	switch {
	case curve == elliptic.P256():
	return &ecPublicKey{cryptoPublicKey, "P-256", es256, map[string]interface{}{}}, nil
	case curve == elliptic.P384():
	return &ecPublicKey{cryptoPublicKey, "P-384", es384, map[string]interface{}{}}, nil
	case curve == elliptic.P521():
	return &ecPublicKey{cryptoPublicKey, "P-521", es512, map[string]interface{}{}}, nil
	default:
	return nil, errors.New("unsupported elliptic curve")
	}
	}

	// KeyType returns the key type for elliptic curve keys, i.e., "EC".
	func (k *ecPublicKey) KeyType() string {
	return "EC"
	}

	// CurveName returns the elliptic curve identifier.
	// Possible values are "P-256", "P-384", and "P-521".
	func (k *ecPublicKey) CurveName() string {
	return k.curveName
	}

	// KeyID returns a distinct identifier which is unique to this Public Key.
	func (k *ecPublicKey) KeyID() string {
	return keyIDFromCryptoKey(k)
	}

	func (k *ecPublicKey) String() string {
	return fmt.Sprintf("EC Public Key <%s>", k.KeyID())
	}

	// Verify verifyies the signature of the data in the io.Reader using this
	// PublicKey. The alg parameter should identify the digital signature
	// algorithm which was used to produce the signature and should be supported
	// by this public key. Returns a nil error if the signature is valid.
	func (k *ecPublicKey) Verify(data io.Reader, alg string, signature []byte) error {
	// For EC keys there is only one supported signature algorithm depending
	// on the curve parameters.
	if k.signatureAlgorithm.HeaderParam() != alg {
	return fmt.Errorf("unable to verify signature: EC Public Key with curve %q does not support signature algorithm %q", k.curveName, alg)
	}

	// signature is the concatenation of (r, s), base64Url encoded.
	sigLength := len(signature)
	expectedOctetLength := 2 * ((k.Params().BitSize + 7) >> 3)
	if sigLength != expectedOctetLength {
	return fmt.Errorf("signature length is %d octets long, should be %d", sigLength, expectedOctetLength)
	}

	rBytes, sBytes := signature[:sigLength/2], signature[sigLength/2:]
	r := new(big.Int).SetBytes(rBytes)
	s := new(big.Int).SetBytes(sBytes)

	hasher := k.signatureAlgorithm.HashID().New()
	_, err := io.Copy(hasher, data)
	if err != nil {
	return fmt.Errorf("error reading data to sign: %s", err)
	}
	hash := hasher.Sum(nil)

	if !ecdsa.Verify(k.PublicKey, hash, r, s) {
	return errors.New("invalid signature")
	}

	return nil
	}

	// CryptoPublicKey returns the internal object which can be used as a
	// crypto.PublicKey for use with other standard library operations. The type
	// is either rsa.PublicKey or ecdsa.PublicKey
	func (k *ecPublicKey) CryptoPublicKey() crypto.PublicKey {
	return k.PublicKey
	}

	func (k *ecPublicKey) toMap() map[string]interface{} {
	jwk := make(map[string]interface{})
	for k, v := range k.extended {
	jwk[k] = v
	}
	jwk["kty"] = k.KeyType()
	jwk["kid"] = k.KeyID()
	jwk["crv"] = k.CurveName()

	xBytes := k.X.Bytes()
	yBytes := k.Y.Bytes()
	octetLength := (k.Params().BitSize + 7) >> 3
	// MUST include leading zeros in the output so that x, y are each
	// octetLength bytes long.
	xBuf := make([]byte, octetLength-len(xBytes), octetLength)
	yBuf := make([]byte, octetLength-len(yBytes), octetLength)
	xBuf = append(xBuf, xBytes...)
	yBuf = append(yBuf, yBytes...)

	jwk["x"] = joseBase64UrlEncode(xBuf)
	jwk["y"] = joseBase64UrlEncode(yBuf)

	return jwk
	}

	// MarshalJSON serializes this Public Key using the JWK JSON serialization format for
	// elliptic curve keys.
	func (k *ecPublicKey) MarshalJSON() (data []byte, err error) {
	return json.Marshal(k.toMap())
	}

	// PEMBlock serializes this Public Key to DER-encoded PKIX format.
	func (k ecPublicKey) PEMBlock() (pem.Block, error) {
	derBytes, err := x509.MarshalPKIXPublicKey(k.PublicKey)
	if err != nil {
	return nil, fmt.Errorf("unable to serialize EC PublicKey to DER-encoded PKIX format: %s", err)
	}
	k.extended["kid"] = k.KeyID() // For display purposes.
	return createPemBlock("PUBLIC KEY", derBytes, k.extended)
	}

	func (k *ecPublicKey) AddExtendedField(field string, value interface{}) {
	k.extended[field] = value
	}

	func (k *ecPublicKey) GetExtendedField(field string) interface{} {
	v, ok := k.extended[field]
	if !ok {
	return nil
	}
	return v
	}

	func ecPublicKeyFromMap(jwk map[string]interface{}) (*ecPublicKey, error) {
	// JWK key type (kty) has already been determined to be "EC".
	// Need to extract 'crv', 'x', 'y', and 'kid' and check for
	// consistency.

	// Get the curve identifier value.
	crv, err := stringFromMap(jwk, "crv")
	if err != nil {
	return nil, fmt.Errorf("JWK EC Public Key curve identifier: %s", err)
	}

	var (
	curve elliptic.Curve
	sigAlg *signatureAlgorithm
	)

	switch {
	case crv == "P-256":
	curve = elliptic.P256()
	sigAlg = es256
	case crv == "P-384":
	curve = elliptic.P384()
	sigAlg = es384
	case crv == "P-521":
	curve = elliptic.P521()
	sigAlg = es512
	default:
	return nil, fmt.Errorf("JWK EC Public Key curve identifier not supported: %q\n", crv)
	}

	// Get the X and Y coordinates for the public key point.
	xB64Url, err := stringFromMap(jwk, "x")
	if err != nil {
	return nil, fmt.Errorf("JWK EC Public Key x-coordinate: %s", err)
	}
	x, err := parseECCoordinate(xB64Url, curve)
	if err != nil {
	return nil, fmt.Errorf("JWK EC Public Key x-coordinate: %s", err)
	}

	yB64Url, err := stringFromMap(jwk, "y")
	if err != nil {
	return nil, fmt.Errorf("JWK EC Public Key y-coordinate: %s", err)
	}
	y, err := parseECCoordinate(yB64Url, curve)
	if err != nil {
	return nil, fmt.Errorf("JWK EC Public Key y-coordinate: %s", err)
	}

	key := &ecPublicKey{
	PublicKey: &ecdsa.PublicKey{Curve: curve, X: x, Y: y},
	curveName: crv, signatureAlgorithm: sigAlg,
	}

	// Key ID is optional too, but if it exists, it should match the key.
	_, ok := jwk["kid"]
	if ok {
	kid, err := stringFromMap(jwk, "kid")
	if err != nil {
	return nil, fmt.Errorf("JWK EC Public Key ID: %s", err)
	}
	if kid != key.KeyID() {
	return nil, fmt.Errorf("JWK EC Public Key ID does not match: %s", kid)
	}
	}

	key.extended = jwk

	return key, nil
	}

	/*
	* EC DSA PRIVATE KEY
	*/

	// ecPrivateKey implements a JWK Private Key using elliptic curve digital signature
	// algorithms.
	type ecPrivateKey struct {
	ecPublicKey
	*ecdsa.PrivateKey
	}

	func fromECPrivateKey(cryptoPrivateKey ecdsa.PrivateKey) (ecPrivateKey, error) {
	publicKey, err := fromECPublicKey(&cryptoPrivateKey.PublicKey)
	if err != nil {
	return nil, err
	}

	return &ecPrivateKey{*publicKey, cryptoPrivateKey}, nil
	}

	// PublicKey returns the Public Key data associated with this Private Key.
	func (k *ecPrivateKey) PublicKey() PublicKey {
	return &k.ecPublicKey
	}

	func (k *ecPrivateKey) String() string {
	return fmt.Sprintf("EC Private Key <%s>", k.KeyID())
	}

	// Sign signs the data read from the io.Reader using a signature algorithm supported
	// by the elliptic curve private key. If the specified hashing algorithm is
	// supported by this key, that hash function is used to generate the signature
	// otherwise the the default hashing algorithm for this key is used. Returns
	// the signature and the name of the JWK signature algorithm used, e.g.,
	// "ES256", "ES384", "ES512".
	func (k *ecPrivateKey) Sign(data io.Reader, hashID crypto.Hash) (signature []byte, alg string, err error) {
	// Generate a signature of the data using the internal alg.
	// The given hashId is only a suggestion, and since EC keys only support
	// on signature/hash algorithm given the curve name, we disregard it for
	// the elliptic curve JWK signature implementation.
	hasher := k.signatureAlgorithm.HashID().New()
	_, err = io.Copy(hasher, data)
	if err != nil {
	return nil, "", fmt.Errorf("error reading data to sign: %s", err)
	}
	hash := hasher.Sum(nil)

	r, s, err := ecdsa.Sign(rand.Reader, k.PrivateKey, hash)
	if err != nil {
	return nil, "", fmt.Errorf("error producing signature: %s", err)
	}
	rBytes, sBytes := r.Bytes(), s.Bytes()
	octetLength := (k.ecPublicKey.Params().BitSize + 7) >> 3
	// MUST include leading zeros in the output
	rBuf := make([]byte, octetLength-len(rBytes), octetLength)
	sBuf := make([]byte, octetLength-len(sBytes), octetLength)

	rBuf = append(rBuf, rBytes...)
	sBuf = append(sBuf, sBytes...)

	signature = append(rBuf, sBuf...)
	alg = k.signatureAlgorithm.HeaderParam()

	return
	}

	// CryptoPrivateKey returns the internal object which can be used as a
	// crypto.PublicKey for use with other standard library operations. The type
	// is either rsa.PublicKey or ecdsa.PublicKey
	func (k *ecPrivateKey) CryptoPrivateKey() crypto.PrivateKey {
	return k.PrivateKey
	}

	func (k *ecPrivateKey) toMap() map[string]interface{} {
	jwk := k.ecPublicKey.toMap()

	dBytes := k.D.Bytes()
	// The length of this octet string MUST be ceiling(log-base-2(n)/8)
	// octets (where n is the order of the curve). This is because the private
	// key d must be in the interval [1, n-1] so the bitlength of d should be
	// no larger than the bitlength of n-1. The easiest way to find the octet
	// length is to take bitlength(n-1), add 7 to force a carry, and shift this
	// bit sequence right by 3, which is essentially dividing by 8 and adding
	// 1 if there is any remainder. Thus, the private key value d should be
	// output to (bitlength(n-1)+7)>>3 octets.
	n := k.ecPublicKey.Params().N
	octetLength := (new(big.Int).Sub(n, big.NewInt(1)).BitLen() + 7) >> 3
	// Create a buffer with the necessary zero-padding.
	dBuf := make([]byte, octetLength-len(dBytes), octetLength)
	dBuf = append(dBuf, dBytes...)

	jwk["d"] = joseBase64UrlEncode(dBuf)

	return jwk
	}

	// MarshalJSON serializes this Private Key using the JWK JSON serialization format for
	// elliptic curve keys.
	func (k *ecPrivateKey) MarshalJSON() (data []byte, err error) {
	return json.Marshal(k.toMap())
	}

	// PEMBlock serializes this Private Key to DER-encoded PKIX format.
	func (k ecPrivateKey) PEMBlock() (pem.Block, error) {
	derBytes, err := x509.MarshalECPrivateKey(k.PrivateKey)
	if err != nil {
	return nil, fmt.Errorf("unable to serialize EC PrivateKey to DER-encoded PKIX format: %s", err)
	}
	k.extended["keyID"] = k.KeyID() // For display purposes.
	return createPemBlock("EC PRIVATE KEY", derBytes, k.extended)
	}

	func ecPrivateKeyFromMap(jwk map[string]interface{}) (*ecPrivateKey, error) {
	dB64Url, err := stringFromMap(jwk, "d")
	if err != nil {
	return nil, fmt.Errorf("JWK EC Private Key: %s", err)
	}

	// JWK key type (kty) has already been determined to be "EC".
	// Need to extract the public key information, then extract the private
	// key value 'd'.
	publicKey, err := ecPublicKeyFromMap(jwk)
	if err != nil {
	return nil, err
	}

	d, err := parseECPrivateParam(dB64Url, publicKey.Curve)
	if err != nil {
	return nil, fmt.Errorf("JWK EC Private Key d-param: %s", err)
	}

	key := &ecPrivateKey{
	ecPublicKey: *publicKey,
	PrivateKey: &ecdsa.PrivateKey{
	PublicKey: *publicKey.PublicKey,
	D: d,
	},
	}

	return key, nil
	}

	/*
	* Key Generation Functions.
	*/

	func generateECPrivateKey(curve elliptic.Curve) (k *ecPrivateKey, err error) {
	k = new(ecPrivateKey)
	k.PrivateKey, err = ecdsa.GenerateKey(curve, rand.Reader)
	if err != nil {
	return nil, err
	}

	k.ecPublicKey.PublicKey = &k.PrivateKey.PublicKey
	k.extended = make(map[string]interface{})

	return
	}

	// GenerateECP256PrivateKey generates a key pair using elliptic curve P-256.
	func GenerateECP256PrivateKey() (PrivateKey, error) {
	k, err := generateECPrivateKey(elliptic.P256())
	if err != nil {
	return nil, fmt.Errorf("error generating EC P-256 key: %s", err)
	}

	k.curveName = "P-256"
	k.signatureAlgorithm = es256

	return k, nil
	}

	// GenerateECP384PrivateKey generates a key pair using elliptic curve P-384.
	func GenerateECP384PrivateKey() (PrivateKey, error) {
	k, err := generateECPrivateKey(elliptic.P384())
	if err != nil {
	return nil, fmt.Errorf("error generating EC P-384 key: %s", err)
	}

	k.curveName = "P-384"
	k.signatureAlgorithm = es384

	return k, nil
	}

	// GenerateECP521PrivateKey generates aß key pair using elliptic curve P-521.
	func GenerateECP521PrivateKey() (PrivateKey, error) {
	k, err := generateECPrivateKey(elliptic.P521())
	if err != nil {
	return nil, fmt.Errorf("error generating EC P-521 key: %s", err)
	}

	k.curveName = "P-521"
	k.signatureAlgorithm = es512

	return k, nil
	}