// 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
}
func hashG(c elliptic.Curve, m []byte) (hx, hy *big.Int) {
h := sha256.New()
h.Write(m)
d := h.Sum(nil)
hx, hy = c.ScalarBaseMult(d) // g^H'()
return
}
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
}
// GenerateKey generates a public and private key pair.
func GenerateKey(c elliptic.Curve, rand io.Reader) (priv *PrivateKey, err error) {
k, err := randFieldElement(c, rand)
if err != nil {
return
}
priv = new(PrivateKey)
priv.PublicKey.Curve = c
priv.D = k
priv.PublicKey.X, priv.PublicKey.Y = c.ScalarBaseMult(k.Bytes())
return
}
func DiscreteLog(x *big.Int, y *big.Int, c elliptic.Curve, bound int) (int, error) {
var xprime *big.Int
var yprime *big.Int
if x.Cmp(big.NewInt(0)) == 0 && y.Cmp(big.NewInt(0)) == 0 {
return 0, nil
}
for i := 0; i < bound; i++ {
xprime, yprime = c.ScalarBaseMult(big.NewInt(int64(i)).Bytes())
if xprime.Cmp(x) == 0 && yprime.Cmp(y) == 0 {
return i, nil
}
}
return -1, errors.New("log not found")
}
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
}
// PrivKeyFromBytes returns a private and public key for `curve' based on the
// private key passed as an argument as a byte slice.
func PrivKeyFromBytes(curve elliptic.Curve, pk []byte) (*PrivateKey,
*PublicKey) {
x, y := curve.ScalarBaseMult(pk)
priv := &ecdsa.PrivateKey{
PublicKey: ecdsa.PublicKey{
Curve: curve,
X: x,
Y: y,
},
D: new(big.Int).SetBytes(pk),
}
return (*PrivateKey)(priv), (*PublicKey)(&priv.PublicKey)
}
// 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 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
}
func testScalarBaseMult(curve elliptic.Curve, k, ex, ey *big.Int) bool {
x, y := curve.ScalarBaseMult(k.Bytes())
return x.Cmp(ex) == 0 && y.Cmp(ey) == 0
}