func benchScalarMult(curve elliptic.Curve, k []byte, n int) {
x := curve.Params().Gx
y := curve.Params().Gy
for i := 0; i < n; i++ {
curve.ScalarMult(x, y, k)
}
}
func DecryptMark(c elliptic.Curve, m *Mark, priv []byte) (int, error) {
tx, ty := c.ScalarMult(m.ax, m.ay, priv)
tm := big.NewInt(0)
tm.Sub(c.Params().P, ty)
tm.Mod(tm, c.Params().P)
px, py := c.Add(m.bx, m.by, tx, tm)
return DiscreteLog(px, py, c, 1<<10)
}
func VoteOne(c elliptic.Curve, px *big.Int, py *big.Int) *Checkbox {
var err error
h := new(Checkbox)
h.s, err = rand.Int(rand.Reader, c.Params().N)
if err != nil {
panic("this shouldn't happen")
}
h.ax, h.ay = c.ScalarBaseMult(h.s.Bytes())
tx, ty := c.ScalarMult(px, py, h.s.Bytes())
h.bx, h.by = c.Add(tx, ty, c.Params().Gx, c.Params().Gy)
//TODO: refactor: lots of similar logic here but parts very
//c2, r2 fake, c1 r1 genuine
//Form the faked challenge
h.c2, err = rand.Int(rand.Reader, c.Params().N)
if err != nil {
panic("this shouldn't happen")
}
h.r2, err = rand.Int(rand.Reader, c.Params().N)
if err != nil {
panic("this shouldn't happen")
}
//Compute the commitments v3, v4 as the verifier will
v3x, v3y := doublescalarmult(c, c.Params().Gx, c.Params().Gy, h.r2.Bytes(),
h.ax, h.ay, h.c2.Bytes())
v4x, v4y := doublescalarmult(c, px, py, h.r2.Bytes(),
h.bx, h.by, h.c2.Bytes())
//Commit to other side
s1, err := rand.Int(rand.Reader, c.Params().N)
if err != nil {
panic("something deeply wrong")
}
v1x, v1y := c.ScalarBaseMult(s1.Bytes())
v2x, v2y := c.ScalarMult(px, py, s1.Bytes())
//Compute the total challenge
var entries [6][]byte
entries[0] = elliptic.Marshal(c, h.ax, h.ay)
entries[1] = elliptic.Marshal(c, h.bx, h.by)
entries[2] = elliptic.Marshal(c, v1x, v1y)
entries[3] = elliptic.Marshal(c, v2x, v2y)
entries[4] = elliptic.Marshal(c, v3x, v3y)
entries[5] = elliptic.Marshal(c, v4x, v4y)
challenge := sha256.Sum256(bytes.Join(entries[:], []byte{}))
ctot := big.NewInt(0)
ctot.SetBytes(challenge[:])
ctot.Mod(ctot, c.Params().N)
h.c1 = big.NewInt(0)
h.c1.Sub(ctot, h.c2)
h.c1.Mod(h.c1, c.Params().N)
//r=s1-c1*h.s
t := big.NewInt(0)
t.Mul(h.c1, h.s)
t.Mod(t, c.Params().N)
t.Sub(s1, t)
t.Mod(t, c.Params().N)
h.r1 = t
return h
}
// kexECDH performs Elliptic Curve Diffie-Hellman key exchange as
// described in RFC 5656, section 4.
func (c *ClientConn) kexECDH(curve elliptic.Curve, magics *handshakeMagics, hostKeyAlgo string) (*kexResult, error) {
ephKey, err := ecdsa.GenerateKey(curve, c.config.rand())
if err != nil {
return nil, err
}
kexInit := kexECDHInitMsg{
ClientPubKey: elliptic.Marshal(curve, ephKey.PublicKey.X, ephKey.PublicKey.Y),
}
serialized := marshal(msgKexECDHInit, kexInit)
if err := c.writePacket(serialized); err != nil {
return nil, err
}
packet, err := c.readPacket()
if err != nil {
return nil, err
}
var reply kexECDHReplyMsg
if err = unmarshal(&reply, packet, msgKexECDHReply); err != nil {
return nil, err
}
x, y := elliptic.Unmarshal(curve, reply.EphemeralPubKey)
if x == nil {
return nil, errors.New("ssh: elliptic.Unmarshal failure")
}
if !validateECPublicKey(curve, x, y) {
return nil, errors.New("ssh: ephemeral server key not on curve")
}
// generate shared secret
secret, _ := curve.ScalarMult(x, y, ephKey.D.Bytes())
hashFunc := ecHash(curve)
h := hashFunc.New()
writeString(h, magics.clientVersion)
writeString(h, magics.serverVersion)
writeString(h, magics.clientKexInit)
writeString(h, magics.serverKexInit)
writeString(h, reply.HostKey)
writeString(h, kexInit.ClientPubKey)
writeString(h, reply.EphemeralPubKey)
K := make([]byte, intLength(secret))
marshalInt(K, secret)
h.Write(K)
return &kexResult{
H: h.Sum(nil),
K: K,
HostKey: reply.HostKey,
Signature: reply.Signature,
Hash: hashFunc,
}, nil
}
// Generates an ephemeral public key and returns a function that will compute
// the shared secret key. Used in the identify module.
//
// Focuses only on ECDH now, but can be made more general in the future.
func GenerateEKeyPair(curveName string) ([]byte, GenSharedKey, error) {
var curve elliptic.Curve
switch curveName {
case "P-224":
curve = elliptic.P224()
case "P-256":
curve = elliptic.P256()
case "P-384":
curve = elliptic.P384()
case "P-521":
curve = elliptic.P521()
}
priv, x, y, err := elliptic.GenerateKey(curve, rand.Reader)
if err != nil {
return nil, nil, err
}
var pubKey bytes.Buffer
pubKey.Write(x.Bytes())
pubKey.Write(y.Bytes())
done := func(theirPub []byte) ([]byte, error) {
// Verify and unpack node's public key.
curveSize := curve.Params().BitSize
if len(theirPub) != (curveSize / 4) {
return nil, errors.New("Malformed public key.")
}
bound := (curveSize / 8)
x := big.NewInt(0)
y := big.NewInt(0)
x.SetBytes(theirPub[0:bound])
y.SetBytes(theirPub[bound : bound*2])
if !curve.IsOnCurve(x, y) {
return nil, errors.New("Invalid public key.")
}
// Generate shared secret.
secret, _ := curve.ScalarMult(x, y, priv)
return secret.Bytes(), nil
}
return pubKey.Bytes(), done, nil
}
func FillBallot(c elliptic.Curve, px *big.Int, py *big.Int, entry int,
size int) *Ballot {
b := new(Ballot)
b.boxes = make([]*Checkbox, size, size)
for i := 0; i < size; i++ {
if i == entry {
b.boxes[i] = VoteOne(c, px, py)
} else {
b.boxes[i] = VoteZero(c, px, py)
}
}
//TODO: add validation
//Let A be the sum of all the A, B the sum of all the B
//Then we want log_g(A)=log_h(B-g)
ax := big.NewInt(0)
ay := big.NewInt(0)
bx := big.NewInt(0)
by := big.NewInt(0)
s := big.NewInt(0)
for i := 0; i < size; i++ {
ax, ay = c.Add(ax, ay, b.boxes[i].ax, b.boxes[i].ay)
bx, by = c.Add(bx, by, b.boxes[i].bx, b.boxes[i].by)
s.Add(s, b.boxes[i].s)
}
s.Mod(s, c.Params().N)
k, err := rand.Int(rand.Reader, c.Params().N)
if err != nil {
panic("Not here, not now")
}
v1x, v1y := c.ScalarBaseMult(k.Bytes())
v2x, v2y := c.ScalarMult(px, py, k.Bytes())
var commit [4][]byte
commit[0] = elliptic.Marshal(c, ax, ay)
commit[1] = elliptic.Marshal(c, bx, by)
commit[2] = elliptic.Marshal(c, v1x, v1y)
commit[3] = elliptic.Marshal(c, v2x, v2y)
cb := bytes.Join(commit[:], []byte{})
cbytes := sha256.Sum256(cb[:])
b.c = big.NewInt(0)
b.c.SetBytes(cbytes[:])
b.c.Mod(b.c, c.Params().N)
b.r = big.NewInt(0)
//r=k-c*s
b.r.Mul(b.c, s)
b.r.Sub(k, b.r)
b.r.Mod(b.r, c.Params().N)
return b
}
// Generates an ephemeral public key and returns a function that will compute
// the shared secret key. Used in the identify module.
//
// Focuses only on ECDH now, but can be made more general in the future.
func GenerateEKeyPair(curveName string) ([]byte, GenSharedKey, error) {
var curve elliptic.Curve
switch curveName {
case "P-224":
curve = elliptic.P224()
case "P-256":
curve = elliptic.P256()
case "P-384":
curve = elliptic.P384()
case "P-521":
curve = elliptic.P521()
}
priv, x, y, err := elliptic.GenerateKey(curve, rand.Reader)
if err != nil {
return nil, nil, err
}
pubKey := elliptic.Marshal(curve, x, y)
// log.Debug("GenerateEKeyPair %d", len(pubKey))
done := func(theirPub []byte) ([]byte, error) {
// Verify and unpack node's public key.
x, y := elliptic.Unmarshal(curve, theirPub)
if x == nil {
return nil, fmt.Errorf("Malformed public key: %d %v", len(theirPub), theirPub)
}
if !curve.IsOnCurve(x, y) {
return nil, errors.New("Invalid public key.")
}
// Generate shared secret.
secret, _ := curve.ScalarMult(x, y, priv)
return secret.Bytes(), nil
}
return pubKey, done, nil
}
func doublescalarmult(c elliptic.Curve, ax *big.Int, ay *big.Int, s1 []byte,
bx *big.Int, by *big.Int, s2 []byte) (*big.Int, *big.Int) {
t1x, t1y := c.ScalarMult(ax, ay, s1)
t2x, t2y := c.ScalarMult(bx, by, s2)
return c.Add(t1x, t1y, t2x, t2y)
}
func VoteZero(c elliptic.Curve, px *big.Int, py *big.Int) *Checkbox {
var err error
h := new(Checkbox)
h.s, err = rand.Int(rand.Reader, c.Params().N)
if err != nil {
panic("this shouldn't happen")
}
h.ax, h.ay = c.ScalarBaseMult(h.s.Bytes())
h.bx, h.by = c.ScalarMult(px, py, h.s.Bytes())
//TODO: get the proof generated
//c1, r1 fake, c2, r2 genuine
//First compute the missing B-g
tx := big.NewInt(0)
tx.Set(c.Params().Gx)
ty := big.NewInt(0)
ty.Set(c.Params().Gy)
ty.Neg(ty)
ty.Mod(ty, c.Params().P)
bgx, bgy := c.Add(tx, ty, h.bx, h.by)
//Now fake the challenge
h.c1, err = rand.Int(rand.Reader, c.Params().N)
if err != nil {
panic("this shouldn't happen")
}
h.r1, err = rand.Int(rand.Reader, c.Params().N)
if err != nil {
panic("this shouldn't happen")
}
//Compute v1, v2 as verifier will
v1x, v1y := doublescalarmult(c, c.Params().Gx, c.Params().Gy,
h.r1.Bytes(), h.ax, h.ay, h.c1.Bytes())
v2x, v2y := doublescalarmult(c, px, py, h.r1.Bytes(),
bgx, bgy, h.c1.Bytes())
//Other part of commitment
s1, err := rand.Int(rand.Reader, c.Params().N)
if err != nil {
panic("something is deeply wrong")
}
v3x, v3y := c.ScalarBaseMult(s1.Bytes())
v4x, v4y := c.ScalarMult(px, py, s1.Bytes())
//Compute total challenge
var entries [6][]byte
entries[0] = elliptic.Marshal(c, h.ax, h.ay)
entries[1] = elliptic.Marshal(c, h.bx, h.by)
entries[2] = elliptic.Marshal(c, v1x, v1y)
entries[3] = elliptic.Marshal(c, v2x, v2y)
entries[4] = elliptic.Marshal(c, v3x, v3y)
entries[5] = elliptic.Marshal(c, v4x, v4y)
challenge := sha256.Sum256(bytes.Join(entries[:], []byte{}))
ctot := big.NewInt(0)
ctot.SetBytes(challenge[:])
ctot.Mod(ctot, c.Params().N)
h.c2 = big.NewInt(0)
h.c2.Sub(ctot, h.c1)
h.c2.Mod(h.c2, c.Params().N)
//r2=s1-c2*s
h.r2 = big.NewInt(0)
h.r2.Mul(h.c2, h.s)
h.r2.Sub(s1, h.r2)
h.r2.Mod(h.r2, c.Params().N)
return h
}
// kexECDH performs Elliptic Curve Diffie-Hellman key agreement on a
// ServerConnection, as documented in RFC 5656, section 4.
func (s *ServerConn) kexECDH(curve elliptic.Curve, magics *handshakeMagics, priv Signer) (result *kexResult, err error) {
packet, err := s.readPacket()
if err != nil {
return
}
var kexECDHInit kexECDHInitMsg
if err = unmarshal(&kexECDHInit, packet, msgKexECDHInit); err != nil {
return
}
clientX, clientY := elliptic.Unmarshal(curve, kexECDHInit.ClientPubKey)
if clientX == nil {
return nil, errors.New("ssh: elliptic.Unmarshal failure")
}
if !validateECPublicKey(curve, clientX, clientY) {
return nil, errors.New("ssh: not a valid EC public key")
}
// We could cache this key across multiple users/multiple
// connection attempts, but the benefit is small. OpenSSH
// generates a new key for each incoming connection.
ephKey, err := ecdsa.GenerateKey(curve, s.config.rand())
if err != nil {
return nil, err
}
hostKeyBytes := MarshalPublicKey(priv.PublicKey())
serializedEphKey := elliptic.Marshal(curve, ephKey.PublicKey.X, ephKey.PublicKey.Y)
// generate shared secret
secret, _ := curve.ScalarMult(clientX, clientY, ephKey.D.Bytes())
hashFunc := ecHash(curve)
h := hashFunc.New()
writeString(h, magics.clientVersion)
writeString(h, magics.serverVersion)
writeString(h, magics.clientKexInit)
writeString(h, magics.serverKexInit)
writeString(h, hostKeyBytes)
writeString(h, kexECDHInit.ClientPubKey)
writeString(h, serializedEphKey)
K := make([]byte, intLength(secret))
marshalInt(K, secret)
h.Write(K)
H := h.Sum(nil)
// H is already a hash, but the hostkey signing will apply its
// own key specific hash algorithm.
sig, err := signAndMarshal(priv, s.config.rand(), H)
if err != nil {
return nil, err
}
reply := kexECDHReplyMsg{
EphemeralPubKey: serializedEphKey,
HostKey: hostKeyBytes,
Signature: sig,
}
serialized := marshal(msgKexECDHReply, reply)
if err := s.writePacket(serialized); err != nil {
return nil, err
}
return &kexResult{
H: H,
K: K,
HostKey: reply.HostKey,
Hash: hashFunc,
}, nil
}
// ComputeShared computes the shared key for the private key material priv and
// the x and y public coordinates
func ComputeShared(curve elliptic.Curve, x, y *big.Int, priv []byte) []byte {
x, _ = curve.ScalarMult(x, y, priv)
return x.Bytes()
}
func testScalarMult(curve elliptic.Curve, x1, y1, k, ex, ey *big.Int) bool {
x, y := curve.ScalarMult(x1, y1, k.Bytes())
return x.Cmp(ex) == 0 && y.Cmp(ey) == 0
}
