func benchDouble(curve elliptic.Curve, n int) {
x := curve.Params().Gx
y := curve.Params().Gy
for i := 0; i < n; i++ {
curve.Double(x, y)
}
}
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 benchAdd(curve elliptic.Curve, n int) {
x := curve.Params().Gx
y := curve.Params().Gy
for i := 0; i < n; i++ {
curve.Add(x, y, x, y)
}
}
// parseECPrivateKey parses an ASN.1 Elliptic Curve Private Key Structure.
// The OID for the named curve may be provided from another source (such as
// the PKCS8 container) - if it is provided then use this instead of the OID
// that may exist in the EC private key structure.
func parseECPrivateKey(namedCurveOID *asn1.ObjectIdentifier, der []byte) (key *ecdsa.PrivateKey, err error) {
var privKey ecPrivateKey
if _, err := asn1.Unmarshal(der, &privKey); err != nil {
return nil, errors.New("x509: failed to parse EC private key: " + err.Error())
}
if privKey.Version != ecPrivKeyVersion {
return nil, fmt.Errorf("x509: unknown EC private key version %d", privKey.Version)
}
var curve elliptic.Curve
if namedCurveOID != nil {
curve = namedCurveFromOID(*namedCurveOID)
} else {
curve = namedCurveFromOID(privKey.NamedCurveOID)
}
if curve == nil {
return nil, errors.New("x509: unknown elliptic curve")
}
k := new(big.Int).SetBytes(privKey.PrivateKey)
if k.Cmp(curve.Params().N) >= 0 {
return nil, errors.New("x509: invalid elliptic curve private key value")
}
priv := new(ecdsa.PrivateKey)
priv.Curve = curve
priv.D = k
priv.X, priv.Y = curve.ScalarBaseMult(privKey.PrivateKey)
return priv, nil
}
// getSuitableAlgFromCurve inspects the key length in curve, and determines the
// corresponding jwt.Algorithm.
func getSuitableAlgFromCurve(curve elliptic.Curve) (jwt.Algorithm, error) {
curveBitSize := curve.Params().BitSize
// compute curve key len
keyLen := curveBitSize / 8
if curveBitSize%8 > 0 {
keyLen++
}
// determine alg
var alg jwt.Algorithm
switch 2 * keyLen {
case 64:
alg = jwt.ES256
case 96:
alg = jwt.ES384
case 132:
alg = jwt.ES512
default:
return jwt.NONE, fmt.Errorf("invalid key length %d", keyLen)
}
return alg, nil
}
func UnmarshalBallot(c elliptic.Curve, bytes []byte) (*Ballot, error) {
if len(bytes) < 4 {
return nil, errors.New("Not long enough!")
}
numballots := int(bytes[0])<<24 + int(bytes[1])<<16 +
int(bytes[2])<<8 + int(bytes[3])
ret := new(Ballot)
ret.boxes = make([]*Checkbox, numballots, numballots)
bytesize := (c.Params().BitSize + 7) >> 3
ballotlen := 2 + 8*bytesize
if len(bytes) != 4+numballots*ballotlen+2*bytesize {
return nil, errors.New("Wrong length!")
}
for i := 0; i < numballots; i++ {
ret.boxes[i] = UnmarshalCheckbox(c, bytes[i*ballotlen+4:(i+1)*ballotlen+4])
if ret.boxes[i] == nil {
return nil, errors.New("Incorrect serialization")
}
}
ret.c = new(big.Int)
ret.c.SetBytes(bytes[numballots*ballotlen+4 : numballots*ballotlen+
4+bytesize])
ret.r = new(big.Int)
ret.r.SetBytes(bytes[numballots*ballotlen+4+bytesize : numballots*ballotlen+4+2*bytesize])
return ret, nil
}
// validateECPublicKey checks that the point is a valid public key for
// the given curve. See [SEC1], 3.2.2
func validateECPublicKey(curve elliptic.Curve, x, y *big.Int) bool {
if x.Sign() == 0 && y.Sign() == 0 {
return false
}
if x.Cmp(curve.Params().P) >= 0 {
return false
}
if y.Cmp(curve.Params().P) >= 0 {
return false
}
if !curve.IsOnCurve(x, y) {
return false
}
// We don't check if N * PubKey == 0, since
//
// - the NIST curves have cofactor = 1, so this is implicit.
// (We don't foresee an implementation that supports non NIST
// curves)
//
// - for ephemeral keys, we don't need to worry about small
// subgroup attacks.
return true
}
// https://tools.ietf.org/html/rfc6979#section-2.3.4
func bits2octets(in []byte, curve elliptic.Curve, rolen int) []byte {
z1 := hashToInt(in, curve)
z2 := new(big.Int).Sub(z1, curve.Params().N)
if z2.Sign() < 0 {
return int2octets(z1, rolen)
}
return int2octets(z2, rolen)
}
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)
}
// ecHash returns the hash to match the given elliptic curve, see RFC
// 5656, section 6.2.1
func ecHash(curve elliptic.Curve) crypto.Hash {
bitSize := curve.Params().BitSize
switch {
case bitSize <= 256:
return crypto.SHA256
case bitSize <= 384:
return crypto.SHA384
}
return crypto.SHA512
}
func UnmarshalMark(c elliptic.Curve, bytes []byte) *Mark {
bytelen := (c.Params().BitSize + 7) >> 3
pointlen := 1 + 2*bytelen
if len(bytes) != 2*pointlen {
return nil
}
ret := new(Mark)
ret.ax, ret.ay = elliptic.Unmarshal(c, bytes[:pointlen])
ret.bx, ret.by = elliptic.Unmarshal(c, bytes[pointlen:2*pointlen])
return ret
}
func MarshalMark(c elliptic.Curve, m *Mark) []byte {
bytelen := (c.Params().BitSize + 7) >> 3
pointlen := 1 + 2*bytelen
outlen := 2 * pointlen
ret := make([]byte, outlen, outlen)
abytes := elliptic.Marshal(c, m.ax, m.ay)
copy(ret, abytes)
bbytes := elliptic.Marshal(c, m.bx, m.by)
copy(ret[pointlen:], bbytes)
return ret
}
// Marshal encodes a ECC Point into it's compressed representation
func Marshal(curve elliptic.Curve, x, y *big.Int) []byte {
byteLen := (curve.Params().BitSize + 7) >> 3
ret := make([]byte, 1+byteLen)
ret[0] = 2 + byte(y.Bit(0))
xBytes := x.Bytes()
copy(ret[1+byteLen-len(xBytes):], xBytes)
return ret
}
// Get size of curve in bytes
func curveSize(crv elliptic.Curve) int {
bits := crv.Params().BitSize
div := bits / 8
mod := bits % 8
if mod == 0 {
return div
}
return div + 1
}
// GoodCurve determines if an elliptic curve meets our requirements.
func (policy *KeyPolicy) goodCurve(c elliptic.Curve) (err error) {
// Simply use a whitelist for now.
params := c.Params()
switch {
case policy.AllowECDSANISTP256 && params == elliptic.P256().Params():
return nil
case policy.AllowECDSANISTP384 && params == elliptic.P384().Params():
return nil
default:
return core.MalformedRequestError(fmt.Sprintf("ECDSA curve %v not allowed", params.Name))
}
}
// Unmarshal converts a point, serialized by Marshal, into an x, y pair.
// It is an error if the point is not on the curve. On error, x = nil.
func Unmarshal(curve elliptic.Curve, data []byte) (x, y *big.Int) {
byteLen := (curve.Params().BitSize + 7) >> 3
if len(data) != 1+2*byteLen {
return
}
if data[0] != 4 { // uncompressed form
return
}
x = new(big.Int).SetBytes(data[1 : 1+byteLen])
y = new(big.Int).SetBytes(data[1+byteLen:])
return
}
func parseECCoordinate(cB64Url string, curve elliptic.Curve) (*big.Int, error) {
curveByteLen := (curve.Params().BitSize + 7) >> 3
cBytes, err := joseBase64UrlDecode(cB64Url)
if err != nil {
return nil, fmt.Errorf("invalid base64 URL encoding: %s", err)
}
cByteLength := len(cBytes)
if cByteLength != curveByteLen {
return nil, fmt.Errorf("invalid number of octets: got %d, should be %d", cByteLength, curveByteLen)
}
return new(big.Int).SetBytes(cBytes), nil
}
// hashToInt converts a hash value to an integer. There is some disagreement
// about how this is done. [NSA] suggests that this is done in the obvious
// manner, but [SECG] truncates the hash to the bit-length of the curve order
// first. We follow [SECG] because that's what OpenSSL does. Additionally,
// OpenSSL right shifts excess bits from the number if the hash is too large
// and we mirror that too.
func hashToInt(hash []byte, c elliptic.Curve) *big.Int {
orderBits := c.Params().N.BitLen()
orderBytes := (orderBits + 7) / 8
if len(hash) > orderBytes {
hash = hash[:orderBytes]
}
ret := new(big.Int).SetBytes(hash)
excess := len(hash)*8 - orderBits
if excess > 0 {
ret.Rsh(ret, uint(excess))
}
return ret
}
// randFieldElement returns a random element of the field underlying the given
// curve using the procedure given in [NSA] A.2.1.
func randFieldElement(c elliptic.Curve, rand io.Reader) (k *big.Int, err error) {
params := c.Params()
b := make([]byte, params.BitSize/8+8)
_, err = io.ReadFull(rand, b)
if err != nil {
return
}
k = new(big.Int).SetBytes(b)
n := new(big.Int).Sub(params.N, one)
k.Mod(k, n)
k.Add(k, one)
return
}
// 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
}
// NewEllipticSigner creates an Elliptic Curve Signer for the specified curve.
func NewEllipticSigner(alg Algorithm, curve elliptic.Curve) func(pemutil.Store, crypto.Hash) (Signer, error) {
curveBitSize := curve.Params().BitSize
// precompute curve key len
keyLen := curveBitSize / 8
if curveBitSize%8 > 0 {
keyLen++
}
return func(store pemutil.Store, hash crypto.Hash) (Signer, error) {
var ok bool
var privRaw, pubRaw interface{}
var priv *ecdsa.PrivateKey
var pub *ecdsa.PublicKey
// check private key
if privRaw, ok = store[pemutil.ECPrivateKey]; ok {
if priv, ok = privRaw.(*ecdsa.PrivateKey); !ok {
return nil, errors.New("NewEllipticSigner: private key must be a *ecdsa.PrivateKey")
}
// check curve type matches private key curve type
if curveBitSize != priv.Curve.Params().BitSize {
return nil, fmt.Errorf("NewEllipticSigner: private key have bit size %d", curve.Params().BitSize)
}
}
// check public key
if pubRaw, ok = store[pemutil.PublicKey]; ok {
if pub, ok = pubRaw.(*ecdsa.PublicKey); !ok {
return nil, errors.New("NewEllipticSigner: public key must be a *ecdsa.PublicKey")
}
}
// check that either a private or public key has been provided
if priv == nil && pub == nil {
return nil, errors.New("NewEllipticSigner: either a private key or a public key must be provided")
}
return &eccSigner{
alg: alg,
curve: curve,
hash: hash,
priv: priv,
pub: pub,
keyLen: keyLen,
}, nil
}
}
func MarshalReckoning(c elliptic.Curve, r *Reckoning) []byte {
num := len(r.marks)
bytesize := (c.Params().BitSize + 7) >> 3
marklen := 2 + 4*bytesize
totsize := 4 + marklen*num
ret := make([]byte, totsize, totsize)
ret[0] = byte((num >> 24) & 0xff)
ret[1] = byte((num >> 16) & 0xff)
ret[2] = byte((num >> 8) & 0xff)
ret[3] = byte((num) & 0xff)
for i := 0; i < num; i++ {
copy(ret[i*marklen+4:(i+1)*marklen+4], MarshalMark(c, r.marks[i]))
}
return ret
}
// parseECPrivateKey parses an ASN.1 Elliptic Curve Private Key Structure.
// The OID for the named curve may be provided from another source (such as
// the PKCS8 container) - if it is provided then use this instead of the OID
// that may exist in the EC private key structure.
func parseECPrivateKey(namedCurveOID *asn1.ObjectIdentifier, der []byte) (key *ecdsa.PrivateKey, err error) {
var privKey ecPrivateKey
if _, err := asn1.Unmarshal(der, &privKey); err != nil {
return nil, errors.New("x509: failed to parse EC private key: " + err.Error())
}
if privKey.Version != ecPrivKeyVersion {
return nil, fmt.Errorf("x509: unknown EC private key version %d", privKey.Version)
}
var curve elliptic.Curve
if namedCurveOID != nil {
curve = namedCurveFromOID(*namedCurveOID)
} else {
curve = namedCurveFromOID(privKey.NamedCurveOID)
}
if curve == nil {
return nil, errors.New("x509: unknown elliptic curve")
}
k := new(big.Int).SetBytes(privKey.PrivateKey)
curveOrder := curve.Params().N
if k.Cmp(curveOrder) >= 0 {
return nil, errors.New("x509: invalid elliptic curve private key value")
}
priv := new(ecdsa.PrivateKey)
priv.Curve = curve
priv.D = k
privateKey := make([]byte, (curveOrder.BitLen()+7)/8)
// Some private keys have leading zero padding. This is invalid
// according to [SEC1], but this code will ignore it.
for len(privKey.PrivateKey) > len(privateKey) {
if privKey.PrivateKey[0] != 0 {
return nil, errors.New("x509: invalid private key length")
}
privKey.PrivateKey = privKey.PrivateKey[1:]
}
// Some private keys remove all leading zeros, this is also invalid
// according to [SEC1] but since OpenSSL used to do this, we ignore
// this too.
copy(privateKey[len(privateKey)-len(privKey.PrivateKey):], privKey.PrivateKey)
priv.X, priv.Y = curve.ScalarBaseMult(privateKey)
return priv, nil
}
func UnmarshalReckoning(c elliptic.Curve, bytes []byte) (*Reckoning, error) {
if len(bytes) < 4 {
return nil, errors.New("Insufficient length")
}
num := int(bytes[0])<<24 + int(bytes[1])<<16 + int(bytes[2])<<8 + int(bytes[3])
bytesize := (c.Params().BitSize + 7) >> 3
marklen := 2 + 4*bytesize
if len(bytes) != marklen*num+4 {
return nil, errors.New("Incorrect length")
}
ret := new(Reckoning)
ret.marks = make([]*Mark, num, num)
for i := 0; i < num; i++ {
ret.marks[i] = UnmarshalMark(c, bytes[i*marklen+4:(i+1)*marklen+4])
}
return ret, nil
}
func MarshalCheckbox(c elliptic.Curve, b *Checkbox) []byte {
bytelen := (c.Params().BitSize + 7) >> 3
pointlen := 1 + 2*bytelen
scalarlen := bytelen
outlen := 2*pointlen + 4*scalarlen
ret := make([]byte, outlen, outlen)
abytes := elliptic.Marshal(c, b.ax, b.ay)
copy(ret, abytes)
bbytes := elliptic.Marshal(c, b.bx, b.by)
copy(ret[pointlen:], bbytes)
c1bytes := b.c1.Bytes()
copy(ret[2*pointlen+scalarlen-len(c1bytes):], c1bytes)
c2bytes := b.c2.Bytes()
copy(ret[2*pointlen+2*scalarlen-len(c2bytes):], c2bytes)
r1bytes := b.r1.Bytes()
copy(ret[2*pointlen+3*scalarlen-len(r1bytes):], r1bytes)
r2bytes := b.r2.Bytes()
copy(ret[2*pointlen+4*scalarlen-len(r2bytes):], r2bytes)
return ret
}
func UnmarshalCheckbox(c elliptic.Curve, bytes []byte) *Checkbox {
bytelen := (c.Params().BitSize + 7) >> 3
pointlen := 1 + 2*bytelen
scalarlen := bytelen
if len(bytes) != 2*pointlen+4*scalarlen {
return nil
}
ret := new(Checkbox)
ret.ax, ret.ay = elliptic.Unmarshal(c, bytes[:pointlen])
ret.bx, ret.by = elliptic.Unmarshal(c, bytes[pointlen:2*pointlen])
ret.c1 = new(big.Int)
ret.c2 = new(big.Int)
ret.r1 = new(big.Int)
ret.r2 = new(big.Int)
ret.c1.SetBytes(bytes[2*pointlen : 2*pointlen+scalarlen])
ret.c2.SetBytes(bytes[2*pointlen+scalarlen : 2*pointlen+2*scalarlen])
ret.r1.SetBytes(bytes[2*pointlen+2*scalarlen : 2*pointlen+3*scalarlen])
ret.r2.SetBytes(bytes[2*pointlen+3*scalarlen : 2*pointlen+4*scalarlen])
return ret
}
func newrcurve(twisted elliptic.Curve, gx, gy, z *big.Int) *rcurve {
var curve rcurve
curve.twisted = twisted
curve.params = *twisted.Params()
curve.params.B = nil // FIXME: crypto/elliptic assumes A=-3
curve.params.Gx = gx
curve.params.Gy = gy
two := big.NewInt(2)
three := big.NewInt(3)
curve.z = z
curve.zinv = new(big.Int).ModInverse(z, curve.params.P)
curve.z2 = new(big.Int).Exp(curve.z, two, curve.params.P)
curve.z3 = new(big.Int).Exp(curve.z, three, curve.params.P)
curve.zinv2 = new(big.Int).Exp(curve.zinv, two, curve.params.P)
curve.zinv3 = new(big.Int).Exp(curve.zinv, three, curve.params.P)
return &curve
}
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
}
func MarshalBallot(c elliptic.Curve, b *Ballot) []byte {
/* The format is very simple: first 4 bytes are length of ballot
Then that many serialized checkboxes, one after the other
lastly, (c, r) */
numballots := len(b.boxes)
bytelen := (c.Params().BitSize + 7) >> 3
ballotlen := 2 + 8*bytelen //Result of not compressing
size := 4 + numballots*ballotlen + 2*bytelen
ret := make([]byte, size, size)
ret[0] = byte((numballots >> 24) & 0xff)
ret[1] = byte((numballots >> 16) & 0xff)
ret[2] = byte((numballots >> 8) & 0xff)
ret[3] = byte(numballots & 0xff)
for i := 0; i < numballots; i++ {
copy(ret[i*ballotlen+4:(i+1)*ballotlen+4],
MarshalCheckbox(c, b.boxes[i]))
}
cbytes := b.c.Bytes()
copy(ret[numballots*ballotlen+4+bytelen-len(cbytes):], cbytes)
rbytes := b.r.Bytes()
copy(ret[numballots*ballotlen+4+2*bytelen-len(rbytes):], rbytes)
return ret
}
func parseECPrivateParam(dB64Url string, curve elliptic.Curve) (*big.Int, error) {
dBytes, err := joseBase64UrlDecode(dB64Url)
if err != nil {
return nil, fmt.Errorf("invalid base64 URL encoding: %s", err)
}
// 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 := curve.Params().N
octetLength := (new(big.Int).Sub(n, big.NewInt(1)).BitLen() + 7) >> 3
dByteLength := len(dBytes)
if dByteLength != octetLength {
return nil, fmt.Errorf("invalid number of octets: got %d, should be %d", dByteLength, octetLength)
}
return new(big.Int).SetBytes(dBytes), nil
}