ssl/test/runner/key_agreement.go

// Copyright 2010 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package runner

import (
	"crypto"
	"crypto/ecdsa"
	"crypto/elliptic"
	"crypto/md5"
	"crypto/rand"
	"crypto/rsa"
	"crypto/sha1"
	"crypto/x509"
	"encoding/asn1"
	"errors"
	"fmt"
	"io"
	"math/big"
)

var errClientKeyExchange = errors.New("tls: invalid ClientKeyExchange message")
var errServerKeyExchange = errors.New("tls: invalid ServerKeyExchange message")

// rsaKeyAgreement implements the standard TLS key agreement where the client
// encrypts the pre-master secret to the server's public key.
type rsaKeyAgreement struct {
	version       uint16
	clientVersion uint16
	exportKey     *rsa.PrivateKey
}

func (ka *rsaKeyAgreement) generateServerKeyExchange(config *Config, cert *Certificate, clientHello *clientHelloMsg, hello *serverHelloMsg) (*serverKeyExchangeMsg, error) {
	// Save the client version for comparison later.
	ka.clientVersion = versionToWire(clientHello.vers, clientHello.isDTLS)

	if !config.Bugs.RSAEphemeralKey {
		return nil, nil
	}

	// Generate an ephemeral RSA key to use instead of the real
	// one, as in RSA_EXPORT.
	key, err := rsa.GenerateKey(config.rand(), 512)
	if err != nil {
		return nil, err
	}
	ka.exportKey = key

	modulus := key.N.Bytes()
	exponent := big.NewInt(int64(key.E)).Bytes()
	serverRSAParams := make([]byte, 0, 2+len(modulus)+2+len(exponent))
	serverRSAParams = append(serverRSAParams, byte(len(modulus)>>8), byte(len(modulus)))
	serverRSAParams = append(serverRSAParams, modulus...)
	serverRSAParams = append(serverRSAParams, byte(len(exponent)>>8), byte(len(exponent)))
	serverRSAParams = append(serverRSAParams, exponent...)

	var tls12HashId uint8
	if ka.version >= VersionTLS12 {
		if tls12HashId, err = pickTLS12HashForSignature(signatureRSA, clientHello.signatureAndHashes, config.signatureAndHashesForServer()); err != nil {
			return nil, err
		}
	}

	digest, hashFunc, err := hashForServerKeyExchange(signatureRSA, tls12HashId, ka.version, clientHello.random, hello.random, serverRSAParams)
	if err != nil {
		return nil, err
	}
	privKey, ok := cert.PrivateKey.(*rsa.PrivateKey)
	if !ok {
		return nil, errors.New("RSA ephemeral key requires an RSA server private key")
	}
	sig, err := rsa.SignPKCS1v15(config.rand(), privKey, hashFunc, digest)
	if err != nil {
		return nil, errors.New("failed to sign RSA parameters: " + err.Error())
	}

	skx := new(serverKeyExchangeMsg)
	sigAndHashLen := 0
	if ka.version >= VersionTLS12 {
		sigAndHashLen = 2
	}
	skx.key = make([]byte, len(serverRSAParams)+sigAndHashLen+2+len(sig))
	copy(skx.key, serverRSAParams)
	k := skx.key[len(serverRSAParams):]
	if ka.version >= VersionTLS12 {
		k[0] = tls12HashId
		k[1] = signatureRSA
		k = k[2:]
	}
	k[0] = byte(len(sig) >> 8)
	k[1] = byte(len(sig))
	copy(k[2:], sig)

	return skx, nil
}

func (ka *rsaKeyAgreement) processClientKeyExchange(config *Config, cert *Certificate, ckx *clientKeyExchangeMsg, version uint16) ([]byte, error) {
	preMasterSecret := make([]byte, 48)
	_, err := io.ReadFull(config.rand(), preMasterSecret[2:])
	if err != nil {
		return nil, err
	}

	if len(ckx.ciphertext) < 2 {
		return nil, errClientKeyExchange
	}

	ciphertext := ckx.ciphertext
	if version != VersionSSL30 {
		ciphertextLen := int(ckx.ciphertext[0])<<8 | int(ckx.ciphertext[1])
		if ciphertextLen != len(ckx.ciphertext)-2 {
			return nil, errClientKeyExchange
		}
		ciphertext = ckx.ciphertext[2:]
	}

	key := cert.PrivateKey.(*rsa.PrivateKey)
	if ka.exportKey != nil {
		key = ka.exportKey
	}
	err = rsa.DecryptPKCS1v15SessionKey(config.rand(), key, ciphertext, preMasterSecret)
	if err != nil {
		return nil, err
	}
	// This check should be done in constant-time, but this is a testing
	// implementation. See the discussion at the end of section 7.4.7.1 of
	// RFC 4346.
	vers := uint16(preMasterSecret[0])<<8 | uint16(preMasterSecret[1])
	if ka.clientVersion != vers {
		return nil, errors.New("tls: invalid version in RSA premaster")
	}
	return preMasterSecret, nil
}

func (ka *rsaKeyAgreement) processServerKeyExchange(config *Config, clientHello *clientHelloMsg, serverHello *serverHelloMsg, cert *x509.Certificate, skx *serverKeyExchangeMsg) error {
	return errors.New("tls: unexpected ServerKeyExchange")
}

func (ka *rsaKeyAgreement) generateClientKeyExchange(config *Config, clientHello *clientHelloMsg, cert *x509.Certificate) ([]byte, *clientKeyExchangeMsg, error) {
	bad := config.Bugs.BadRSAClientKeyExchange
	preMasterSecret := make([]byte, 48)
	vers := clientHello.vers
	if bad == RSABadValueWrongVersion {
		vers ^= 1
	}
	vers = versionToWire(vers, clientHello.isDTLS)
	preMasterSecret[0] = byte(vers >> 8)
	preMasterSecret[1] = byte(vers)
	_, err := io.ReadFull(config.rand(), preMasterSecret[2:])
	if err != nil {
		return nil, nil, err
	}

	sentPreMasterSecret := preMasterSecret
	if bad == RSABadValueTooLong {
		sentPreMasterSecret = make([]byte, len(sentPreMasterSecret)+1)
		copy(sentPreMasterSecret, preMasterSecret)
	} else if bad == RSABadValueTooShort {
		sentPreMasterSecret = sentPreMasterSecret[:len(sentPreMasterSecret)-1]
	}

	encrypted, err := rsa.EncryptPKCS1v15(config.rand(), cert.PublicKey.(*rsa.PublicKey), sentPreMasterSecret)
	if err != nil {
		return nil, nil, err
	}
	if bad == RSABadValueCorrupt {
		encrypted[len(encrypted)-1] ^= 1
		// Clear the high byte to ensure |encrypted| is still below the RSA modulus.
		encrypted[0] = 0
	}
	ckx := new(clientKeyExchangeMsg)
	if clientHello.vers != VersionSSL30 {
		ckx.ciphertext = make([]byte, len(encrypted)+2)
		ckx.ciphertext[0] = byte(len(encrypted) >> 8)
		ckx.ciphertext[1] = byte(len(encrypted))
		copy(ckx.ciphertext[2:], encrypted)
	} else {
		ckx.ciphertext = encrypted
	}
	return preMasterSecret, ckx, nil
}

// sha1Hash calculates a SHA1 hash over the given byte slices.
func sha1Hash(slices [][]byte) []byte {
	hsha1 := sha1.New()
	for _, slice := range slices {
		hsha1.Write(slice)
	}
	return hsha1.Sum(nil)
}

// md5SHA1Hash implements TLS 1.0's hybrid hash function which consists of the
// concatenation of an MD5 and SHA1 hash.
func md5SHA1Hash(slices [][]byte) []byte {
	md5sha1 := make([]byte, md5.Size+sha1.Size)
	hmd5 := md5.New()
	for _, slice := range slices {
		hmd5.Write(slice)
	}
	copy(md5sha1, hmd5.Sum(nil))
	copy(md5sha1[md5.Size:], sha1Hash(slices))
	return md5sha1
}

// hashForServerKeyExchange hashes the given slices and returns their digest
// and the identifier of the hash function used. The hashFunc argument is only
// used for >= TLS 1.2 and precisely identifies the hash function to use.
func hashForServerKeyExchange(sigType, hashFunc uint8, version uint16, slices ...[]byte) ([]byte, crypto.Hash, error) {
	if version >= VersionTLS12 {
		hash, err := lookupTLSHash(hashFunc)
		if err != nil {
			return nil, 0, err
		}
		h := hash.New()
		for _, slice := range slices {
			h.Write(slice)
		}
		return h.Sum(nil), hash, nil
	}
	if sigType == signatureECDSA {
		return sha1Hash(slices), crypto.SHA1, nil
	}
	return md5SHA1Hash(slices), crypto.MD5SHA1, nil
}

// pickTLS12HashForSignature returns a TLS 1.2 hash identifier for signing a
// ServerKeyExchange given the signature type being used and the client's
// advertized list of supported signature and hash combinations.
func pickTLS12HashForSignature(sigType uint8, clientList, serverList []signatureAndHash) (uint8, error) {
	if len(clientList) == 0 {
		// If the client didn't specify any signature_algorithms
		// extension then we can assume that it supports SHA1. See
		// http://tools.ietf.org/html/rfc5246#section-7.4.1.4.1
		return hashSHA1, nil
	}

	for _, sigAndHash := range clientList {
		if sigAndHash.signature != sigType {
			continue
		}
		if isSupportedSignatureAndHash(sigAndHash, serverList) {
			return sigAndHash.hash, nil
		}
	}

	return 0, errors.New("tls: client doesn't support any common hash functions")
}

func curveForCurveID(id CurveID) (elliptic.Curve, bool) {
	switch id {
	case CurveP224:
		return elliptic.P224(), true
	case CurveP256:
		return elliptic.P256(), true
	case CurveP384:
		return elliptic.P384(), true
	case CurveP521:
		return elliptic.P521(), true
	default:
		return nil, false
	}

}

// keyAgreementAuthentication is a helper interface that specifies how
// to authenticate the ServerKeyExchange parameters.
type keyAgreementAuthentication interface {
	signParameters(config *Config, cert *Certificate, clientHello *clientHelloMsg, hello *serverHelloMsg, params []byte) (*serverKeyExchangeMsg, error)
	verifyParameters(config *Config, clientHello *clientHelloMsg, serverHello *serverHelloMsg, cert *x509.Certificate, params []byte, sig []byte) error
}

// nilKeyAgreementAuthentication does not authenticate the key
// agreement parameters.
type nilKeyAgreementAuthentication struct{}

func (ka *nilKeyAgreementAuthentication) signParameters(config *Config, cert *Certificate, clientHello *clientHelloMsg, hello *serverHelloMsg, params []byte) (*serverKeyExchangeMsg, error) {
	skx := new(serverKeyExchangeMsg)
	skx.key = params
	return skx, nil
}

func (ka *nilKeyAgreementAuthentication) verifyParameters(config *Config, clientHello *clientHelloMsg, serverHello *serverHelloMsg, cert *x509.Certificate, params []byte, sig []byte) error {
	return nil
}

// signedKeyAgreement signs the ServerKeyExchange parameters with the
// server's private key.
type signedKeyAgreement struct {
	version uint16
	sigType uint8
}

func (ka *signedKeyAgreement) signParameters(config *Config, cert *Certificate, clientHello *clientHelloMsg, hello *serverHelloMsg, params []byte) (*serverKeyExchangeMsg, error) {
	var tls12HashId uint8
	var err error
	if ka.version >= VersionTLS12 {
		if tls12HashId, err = pickTLS12HashForSignature(ka.sigType, clientHello.signatureAndHashes, config.signatureAndHashesForServer()); err != nil {
			return nil, err
		}
	}

	digest, hashFunc, err := hashForServerKeyExchange(ka.sigType, tls12HashId, ka.version, clientHello.random, hello.random, params)
	if err != nil {
		return nil, err
	}

	if config.Bugs.InvalidSKXSignature {
		digest[0] ^= 0x80
	}

	var sig []byte
	switch ka.sigType {
	case signatureECDSA:
		privKey, ok := cert.PrivateKey.(*ecdsa.PrivateKey)
		if !ok {
			return nil, errors.New("ECDHE ECDSA requires an ECDSA server private key")
		}
		r, s, err := ecdsa.Sign(config.rand(), privKey, digest)
		if err != nil {
			return nil, errors.New("failed to sign ECDHE parameters: " + err.Error())
		}
		order := privKey.Curve.Params().N
		r = maybeCorruptECDSAValue(r, config.Bugs.BadECDSAR, order)
		s = maybeCorruptECDSAValue(s, config.Bugs.BadECDSAS, order)
		sig, err = asn1.Marshal(ecdsaSignature{r, s})
	case signatureRSA:
		privKey, ok := cert.PrivateKey.(*rsa.PrivateKey)
		if !ok {
			return nil, errors.New("ECDHE RSA requires a RSA server private key")
		}
		sig, err = rsa.SignPKCS1v15(config.rand(), privKey, hashFunc, digest)
		if err != nil {
			return nil, errors.New("failed to sign ECDHE parameters: " + err.Error())
		}
	default:
		return nil, errors.New("unknown ECDHE signature algorithm")
	}

	skx := new(serverKeyExchangeMsg)
	if config.Bugs.UnauthenticatedECDH {
		skx.key = params
	} else {
		sigAndHashLen := 0
		if ka.version >= VersionTLS12 {
			sigAndHashLen = 2
		}
		skx.key = make([]byte, len(params)+sigAndHashLen+2+len(sig))
		copy(skx.key, params)
		k := skx.key[len(params):]
		if ka.version >= VersionTLS12 {
			k[0] = tls12HashId
			k[1] = ka.sigType
			k = k[2:]
		}
		k[0] = byte(len(sig) >> 8)
		k[1] = byte(len(sig))
		copy(k[2:], sig)
	}

	return skx, nil
}

func (ka *signedKeyAgreement) verifyParameters(config *Config, clientHello *clientHelloMsg, serverHello *serverHelloMsg, cert *x509.Certificate, params []byte, sig []byte) error {
	if len(sig) < 2 {
		return errServerKeyExchange
	}

	var tls12HashId uint8
	if ka.version >= VersionTLS12 {
		// handle SignatureAndHashAlgorithm
		var sigAndHash []uint8
		sigAndHash, sig = sig[:2], sig[2:]
		if sigAndHash[1] != ka.sigType {
			return errServerKeyExchange
		}
		tls12HashId = sigAndHash[0]
		if len(sig) < 2 {
			return errServerKeyExchange
		}

		if !isSupportedSignatureAndHash(signatureAndHash{ka.sigType, tls12HashId}, config.signatureAndHashesForClient()) {
			return errors.New("tls: unsupported hash function for ServerKeyExchange")
		}
	}
	sigLen := int(sig[0])<<8 | int(sig[1])
	if sigLen+2 != len(sig) {
		return errServerKeyExchange
	}
	sig = sig[2:]

	digest, hashFunc, err := hashForServerKeyExchange(ka.sigType, tls12HashId, ka.version, clientHello.random, serverHello.random, params)
	if err != nil {
		return err
	}
	switch ka.sigType {
	case signatureECDSA:
		pubKey, ok := cert.PublicKey.(*ecdsa.PublicKey)
		if !ok {
			return errors.New("ECDHE ECDSA requires a ECDSA server public key")
		}
		ecdsaSig := new(ecdsaSignature)
		if _, err := asn1.Unmarshal(sig, ecdsaSig); err != nil {
			return err
		}
		if ecdsaSig.R.Sign() <= 0 || ecdsaSig.S.Sign() <= 0 {
			return errors.New("ECDSA signature contained zero or negative values")
		}
		if !ecdsa.Verify(pubKey, digest, ecdsaSig.R, ecdsaSig.S) {
			return errors.New("ECDSA verification failure")
		}
	case signatureRSA:
		pubKey, ok := cert.PublicKey.(*rsa.PublicKey)
		if !ok {
			return errors.New("ECDHE RSA requires a RSA server public key")
		}
		if err := rsa.VerifyPKCS1v15(pubKey, hashFunc, digest, sig); err != nil {
			return err
		}
	default:
		return errors.New("unknown ECDHE signature algorithm")
	}

	return nil
}

// ecdheRSAKeyAgreement implements a TLS key agreement where the server
// generates a ephemeral EC public/private key pair and signs it. The
// pre-master secret is then calculated using ECDH. The signature may
// either be ECDSA or RSA.
type ecdheKeyAgreement struct {
	auth       keyAgreementAuthentication
	privateKey []byte
	curve      elliptic.Curve
	x, y       *big.Int
}

func maybeCorruptECDSAValue(n *big.Int, typeOfCorruption BadValue, limit *big.Int) *big.Int {
	switch typeOfCorruption {
	case BadValueNone:
		return n
	case BadValueNegative:
		return new(big.Int).Neg(n)
	case BadValueZero:
		return big.NewInt(0)
	case BadValueLimit:
		return limit
	case BadValueLarge:
		bad := new(big.Int).Set(limit)
		return bad.Lsh(bad, 20)
	default:
		panic("unknown BadValue type")
	}
}

func (ka *ecdheKeyAgreement) generateServerKeyExchange(config *Config, cert *Certificate, clientHello *clientHelloMsg, hello *serverHelloMsg) (*serverKeyExchangeMsg, error) {
	var curveid CurveID
	preferredCurves := config.curvePreferences()

NextCandidate:
	for _, candidate := range preferredCurves {
		for _, c := range clientHello.supportedCurves {
			if candidate == c {
				curveid = c
				break NextCandidate
			}
		}
	}

	if curveid == 0 {
		return nil, errors.New("tls: no supported elliptic curves offered")
	}

	var ok bool
	if ka.curve, ok = curveForCurveID(curveid); !ok {
		return nil, errors.New("tls: preferredCurves includes unsupported curve")
	}

	var x, y *big.Int
	var err error
	ka.privateKey, x, y, err = elliptic.GenerateKey(ka.curve, config.rand())
	if err != nil {
		return nil, err
	}
	ecdhePublic := elliptic.Marshal(ka.curve, x, y)

	// http://tools.ietf.org/html/rfc4492#section-5.4
	serverECDHParams := make([]byte, 1+2+1+len(ecdhePublic))
	serverECDHParams[0] = 3 // named curve
	serverECDHParams[1] = byte(curveid >> 8)
	serverECDHParams[2] = byte(curveid)
	if config.Bugs.InvalidSKXCurve {
		serverECDHParams[2] ^= 0xff
	}
	serverECDHParams[3] = byte(len(ecdhePublic))
	copy(serverECDHParams[4:], ecdhePublic)

	return ka.auth.signParameters(config, cert, clientHello, hello, serverECDHParams)
}

func (ka *ecdheKeyAgreement) processClientKeyExchange(config *Config, cert *Certificate, ckx *clientKeyExchangeMsg, version uint16) ([]byte, error) {
	if len(ckx.ciphertext) == 0 || int(ckx.ciphertext[0]) != len(ckx.ciphertext)-1 {
		return nil, errClientKeyExchange
	}
	x, y := elliptic.Unmarshal(ka.curve, ckx.ciphertext[1:])
	if x == nil {
		return nil, errClientKeyExchange
	}
	x, _ = ka.curve.ScalarMult(x, y, ka.privateKey)
	preMasterSecret := make([]byte, (ka.curve.Params().BitSize+7)>>3)
	xBytes := x.Bytes()
	copy(preMasterSecret[len(preMasterSecret)-len(xBytes):], xBytes)

	return preMasterSecret, nil
}

func (ka *ecdheKeyAgreement) processServerKeyExchange(config *Config, clientHello *clientHelloMsg, serverHello *serverHelloMsg, cert *x509.Certificate, skx *serverKeyExchangeMsg) error {
	if len(skx.key) < 4 {
		return errServerKeyExchange
	}
	if skx.key[0] != 3 { // named curve
		return errors.New("tls: server selected unsupported curve")
	}
	curveid := CurveID(skx.key[1])<<8 | CurveID(skx.key[2])

	var ok bool
	if ka.curve, ok = curveForCurveID(curveid); !ok {
		return errors.New("tls: server selected unsupported curve")
	}

	publicLen := int(skx.key[3])
	if publicLen+4 > len(skx.key) {
		return errServerKeyExchange
	}
	ka.x, ka.y = elliptic.Unmarshal(ka.curve, skx.key[4:4+publicLen])
	if ka.x == nil {
		return errServerKeyExchange
	}
	serverECDHParams := skx.key[:4+publicLen]
	sig := skx.key[4+publicLen:]

	return ka.auth.verifyParameters(config, clientHello, serverHello, cert, serverECDHParams, sig)
}

func (ka *ecdheKeyAgreement) generateClientKeyExchange(config *Config, clientHello *clientHelloMsg, cert *x509.Certificate) ([]byte, *clientKeyExchangeMsg, error) {
	if ka.curve == nil {
		return nil, nil, errors.New("missing ServerKeyExchange message")
	}
	priv, mx, my, err := elliptic.GenerateKey(ka.curve, config.rand())
	if err != nil {
		return nil, nil, err
	}
	x, _ := ka.curve.ScalarMult(ka.x, ka.y, priv)
	preMasterSecret := make([]byte, (ka.curve.Params().BitSize+7)>>3)
	xBytes := x.Bytes()
	copy(preMasterSecret[len(preMasterSecret)-len(xBytes):], xBytes)

	serialized := elliptic.Marshal(ka.curve, mx, my)

	ckx := new(clientKeyExchangeMsg)
	ckx.ciphertext = make([]byte, 1+len(serialized))
	ckx.ciphertext[0] = byte(len(serialized))
	copy(ckx.ciphertext[1:], serialized)

	return preMasterSecret, ckx, nil
}

// dheRSAKeyAgreement implements a TLS key agreement where the server generates
// an ephemeral Diffie-Hellman public/private key pair and signs it. The
// pre-master secret is then calculated using Diffie-Hellman.
type dheKeyAgreement struct {
	auth    keyAgreementAuthentication
	p, g    *big.Int
	yTheirs *big.Int
	xOurs   *big.Int
}

func (ka *dheKeyAgreement) generateServerKeyExchange(config *Config, cert *Certificate, clientHello *clientHelloMsg, hello *serverHelloMsg) (*serverKeyExchangeMsg, error) {
	var q *big.Int
	if p := config.Bugs.DHGroupPrime; p != nil {
		ka.p = p
		ka.g = big.NewInt(2)
		q = p
	} else {
		// 2048-bit MODP Group with 256-bit Prime Order Subgroup (RFC
		// 5114, Section 2.3)
		ka.p, _ = new(big.Int).SetString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
		ka.g, _ = new(big.Int).SetString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
		q, _ = new(big.Int).SetString("8CF83642A709A097B447997640129DA299B1A47D1EB3750BA308B0FE64F5FBD3", 16)
	}

	var err error
	ka.xOurs, err = rand.Int(config.rand(), q)
	if err != nil {
		return nil, err
	}
	yOurs := new(big.Int).Exp(ka.g, ka.xOurs, ka.p)

	// http://tools.ietf.org/html/rfc5246#section-7.4.3
	pBytes := ka.p.Bytes()
	gBytes := ka.g.Bytes()
	yBytes := yOurs.Bytes()
	serverDHParams := make([]byte, 0, 2+len(pBytes)+2+len(gBytes)+2+len(yBytes))
	serverDHParams = append(serverDHParams, byte(len(pBytes)>>8), byte(len(pBytes)))
	serverDHParams = append(serverDHParams, pBytes...)
	serverDHParams = append(serverDHParams, byte(len(gBytes)>>8), byte(len(gBytes)))
	serverDHParams = append(serverDHParams, gBytes...)
	serverDHParams = append(serverDHParams, byte(len(yBytes)>>8), byte(len(yBytes)))
	serverDHParams = append(serverDHParams, yBytes...)

	return ka.auth.signParameters(config, cert, clientHello, hello, serverDHParams)
}

func (ka *dheKeyAgreement) processClientKeyExchange(config *Config, cert *Certificate, ckx *clientKeyExchangeMsg, version uint16) ([]byte, error) {
	if len(ckx.ciphertext) < 2 {
		return nil, errClientKeyExchange
	}
	yLen := (int(ckx.ciphertext[0]) << 8) | int(ckx.ciphertext[1])
	if yLen != len(ckx.ciphertext)-2 {
		return nil, errClientKeyExchange
	}
	yTheirs := new(big.Int).SetBytes(ckx.ciphertext[2:])
	if yTheirs.Sign() <= 0 || yTheirs.Cmp(ka.p) >= 0 {
		return nil, errClientKeyExchange
	}
	return new(big.Int).Exp(yTheirs, ka.xOurs, ka.p).Bytes(), nil
}

func (ka *dheKeyAgreement) processServerKeyExchange(config *Config, clientHello *clientHelloMsg, serverHello *serverHelloMsg, cert *x509.Certificate, skx *serverKeyExchangeMsg) error {
	// Read dh_p
	k := skx.key
	if len(k) < 2 {
		return errServerKeyExchange
	}
	pLen := (int(k[0]) << 8) | int(k[1])
	k = k[2:]
	if len(k) < pLen {
		return errServerKeyExchange
	}
	ka.p = new(big.Int).SetBytes(k[:pLen])
	k = k[pLen:]

	// Read dh_g
	if len(k) < 2 {
		return errServerKeyExchange
	}
	gLen := (int(k[0]) << 8) | int(k[1])
	k = k[2:]
	if len(k) < gLen {
		return errServerKeyExchange
	}
	ka.g = new(big.Int).SetBytes(k[:gLen])
	k = k[gLen:]

	// Read dh_Ys
	if len(k) < 2 {
		return errServerKeyExchange
	}
	yLen := (int(k[0]) << 8) | int(k[1])
	k = k[2:]
	if len(k) < yLen {
		return errServerKeyExchange
	}
	ka.yTheirs = new(big.Int).SetBytes(k[:yLen])
	k = k[yLen:]
	if ka.yTheirs.Sign() <= 0 || ka.yTheirs.Cmp(ka.p) >= 0 {
		return errServerKeyExchange
	}

	if l := config.Bugs.RequireDHPublicValueLen; l != 0 && l != yLen {
		return fmt.Errorf("RequireDHPublicValueLen set to %d, but server's public value was %d bytes on the wire and %d bytes if minimal", l, yLen, (ka.yTheirs.BitLen()+7)/8)
	}

	sig := k
	serverDHParams := skx.key[:len(skx.key)-len(sig)]

	return ka.auth.verifyParameters(config, clientHello, serverHello, cert, serverDHParams, sig)
}

func (ka *dheKeyAgreement) generateClientKeyExchange(config *Config, clientHello *clientHelloMsg, cert *x509.Certificate) ([]byte, *clientKeyExchangeMsg, error) {
	if ka.p == nil || ka.g == nil || ka.yTheirs == nil {
		return nil, nil, errors.New("missing ServerKeyExchange message")
	}

	xOurs, err := rand.Int(config.rand(), ka.p)
	if err != nil {
		return nil, nil, err
	}
	preMasterSecret := new(big.Int).Exp(ka.yTheirs, xOurs, ka.p).Bytes()

	yOurs := new(big.Int).Exp(ka.g, xOurs, ka.p)
	yBytes := yOurs.Bytes()
	ckx := new(clientKeyExchangeMsg)
	ckx.ciphertext = make([]byte, 2+len(yBytes))
	ckx.ciphertext[0] = byte(len(yBytes) >> 8)
	ckx.ciphertext[1] = byte(len(yBytes))
	copy(ckx.ciphertext[2:], yBytes)

	return preMasterSecret, ckx, nil
}

// nilKeyAgreement is a fake key agreement used to implement the plain PSK key
// exchange.
type nilKeyAgreement struct{}

func (ka *nilKeyAgreement) generateServerKeyExchange(config *Config, cert *Certificate, clientHello *clientHelloMsg, hello *serverHelloMsg) (*serverKeyExchangeMsg, error) {
	return nil, nil
}

func (ka *nilKeyAgreement) processClientKeyExchange(config *Config, cert *Certificate, ckx *clientKeyExchangeMsg, version uint16) ([]byte, error) {
	if len(ckx.ciphertext) != 0 {
		return nil, errClientKeyExchange
	}

	// Although in plain PSK, otherSecret is all zeros, the base key
	// agreement does not access to the length of the pre-shared
	// key. pskKeyAgreement instead interprets nil to mean to use all zeros
	// of the appropriate length.
	return nil, nil
}

func (ka *nilKeyAgreement) processServerKeyExchange(config *Config, clientHello *clientHelloMsg, serverHello *serverHelloMsg, cert *x509.Certificate, skx *serverKeyExchangeMsg) error {
	if len(skx.key) != 0 {
		return errServerKeyExchange
	}
	return nil
}

func (ka *nilKeyAgreement) generateClientKeyExchange(config *Config, clientHello *clientHelloMsg, cert *x509.Certificate) ([]byte, *clientKeyExchangeMsg, error) {
	// Although in plain PSK, otherSecret is all zeros, the base key
	// agreement does not access to the length of the pre-shared
	// key. pskKeyAgreement instead interprets nil to mean to use all zeros
	// of the appropriate length.
	return nil, &clientKeyExchangeMsg{}, nil
}

// makePSKPremaster formats a PSK pre-master secret based on otherSecret from
// the base key exchange and psk.
func makePSKPremaster(otherSecret, psk []byte) []byte {
	out := make([]byte, 0, 2+len(otherSecret)+2+len(psk))
	out = append(out, byte(len(otherSecret)>>8), byte(len(otherSecret)))
	out = append(out, otherSecret...)
	out = append(out, byte(len(psk)>>8), byte(len(psk)))
	out = append(out, psk...)
	return out
}

// pskKeyAgreement implements the PSK key agreement.
type pskKeyAgreement struct {
	base         keyAgreement
	identityHint string
}

func (ka *pskKeyAgreement) generateServerKeyExchange(config *Config, cert *Certificate, clientHello *clientHelloMsg, hello *serverHelloMsg) (*serverKeyExchangeMsg, error) {
	// Assemble the identity hint.
	bytes := make([]byte, 2+len(config.PreSharedKeyIdentity))
	bytes[0] = byte(len(config.PreSharedKeyIdentity) >> 8)
	bytes[1] = byte(len(config.PreSharedKeyIdentity))
	copy(bytes[2:], []byte(config.PreSharedKeyIdentity))

	// If there is one, append the base key agreement's
	// ServerKeyExchange.
	baseSkx, err := ka.base.generateServerKeyExchange(config, cert, clientHello, hello)
	if err != nil {
		return nil, err
	}

	if baseSkx != nil {
		bytes = append(bytes, baseSkx.key...)
	} else if config.PreSharedKeyIdentity == "" {
		// ServerKeyExchange is optional if the identity hint is empty
		// and there would otherwise be no ServerKeyExchange.
		return nil, nil
	}

	skx := new(serverKeyExchangeMsg)
	skx.key = bytes
	return skx, nil
}

func (ka *pskKeyAgreement) processClientKeyExchange(config *Config, cert *Certificate, ckx *clientKeyExchangeMsg, version uint16) ([]byte, error) {
	// First, process the PSK identity.
	if len(ckx.ciphertext) < 2 {
		return nil, errClientKeyExchange
	}
	identityLen := (int(ckx.ciphertext[0]) << 8) | int(ckx.ciphertext[1])
	if 2+identityLen > len(ckx.ciphertext) {
		return nil, errClientKeyExchange
	}
	identity := string(ckx.ciphertext[2 : 2+identityLen])

	if identity != config.PreSharedKeyIdentity {
		return nil, errors.New("tls: unexpected identity")
	}

	if config.PreSharedKey == nil {
		return nil, errors.New("tls: pre-shared key not configured")
	}

	// Process the remainder of the ClientKeyExchange to compute the base
	// pre-master secret.
	newCkx := new(clientKeyExchangeMsg)
	newCkx.ciphertext = ckx.ciphertext[2+identityLen:]
	otherSecret, err := ka.base.processClientKeyExchange(config, cert, newCkx, version)
	if err != nil {
		return nil, err
	}

	if otherSecret == nil {
		// Special-case for the plain PSK key exchanges.
		otherSecret = make([]byte, len(config.PreSharedKey))
	}
	return makePSKPremaster(otherSecret, config.PreSharedKey), nil
}

func (ka *pskKeyAgreement) processServerKeyExchange(config *Config, clientHello *clientHelloMsg, serverHello *serverHelloMsg, cert *x509.Certificate, skx *serverKeyExchangeMsg) error {
	if len(skx.key) < 2 {
		return errServerKeyExchange
	}
	identityLen := (int(skx.key[0]) << 8) | int(skx.key[1])
	if 2+identityLen > len(skx.key) {
		return errServerKeyExchange
	}
	ka.identityHint = string(skx.key[2 : 2+identityLen])

	// Process the remainder of the ServerKeyExchange.
	newSkx := new(serverKeyExchangeMsg)
	newSkx.key = skx.key[2+identityLen:]
	return ka.base.processServerKeyExchange(config, clientHello, serverHello, cert, newSkx)
}

func (ka *pskKeyAgreement) generateClientKeyExchange(config *Config, clientHello *clientHelloMsg, cert *x509.Certificate) ([]byte, *clientKeyExchangeMsg, error) {
	// The server only sends an identity hint but, for purposes of
	// test code, the server always sends the hint and it is
	// required to match.
	if ka.identityHint != config.PreSharedKeyIdentity {
		return nil, nil, errors.New("tls: unexpected identity")
	}

	// Serialize the identity.
	bytes := make([]byte, 2+len(config.PreSharedKeyIdentity))
	bytes[0] = byte(len(config.PreSharedKeyIdentity) >> 8)
	bytes[1] = byte(len(config.PreSharedKeyIdentity))
	copy(bytes[2:], []byte(config.PreSharedKeyIdentity))

	// Append the base key exchange's ClientKeyExchange.
	otherSecret, baseCkx, err := ka.base.generateClientKeyExchange(config, clientHello, cert)
	if err != nil {
		return nil, nil, err
	}
	ckx := new(clientKeyExchangeMsg)
	ckx.ciphertext = append(bytes, baseCkx.ciphertext...)

	if config.PreSharedKey == nil {
		return nil, nil, errors.New("tls: pre-shared key not configured")
	}
	if otherSecret == nil {
		otherSecret = make([]byte, len(config.PreSharedKey))
	}
	return makePSKPremaster(otherSecret, config.PreSharedKey), ckx, nil
}