// Vrati cisla n, e, d, p, q takova ze, pro nahodne vygenerovana ln-bitova
// prvocisla p, q plati, ze e*d + (p-1)(q-1)*X = 1 (mod (p-1)(q-1)) a n = p*q.
func GenerateKeys(ln int) (n, e, d, p, q *big.Int) {
e = big.NewInt(17) // mělo by stačit
n = new(big.Int)
m := new(big.Int)
t := new(big.Int) // tmp
var r *big.Int
for {
p = NewPrime(ln)
q = NewPrime(ln)
if p.Cmp(q) == 0 {
continue
}
n.Mul(p, q) // n = p*q
m.Mul(t.Sub(p, big1), m.Sub(q, big1)) // m = (p-1)*(q-1)
_, d, r = Euklid(m, e, m)
if r.Cmp(big1) != 0 {
continue
} // je GCD(e,m) = 1 ?
break
}
return
}
// GenerateMultiPrimeKey generates a multi-prime RSA keypair of the given bit
// size, as suggested in [1]. Although the public keys are compatible
// (actually, indistinguishable) from the 2-prime case, the private keys are
// not. Thus it may not be possible to export multi-prime private keys in
// certain formats or to subsequently import them into other code.
//
// Table 1 in [2] suggests maximum numbers of primes for a given size.
//
// [1] US patent 4405829 (1972, expired)
// [2] http://www.cacr.math.uwaterloo.ca/techreports/2006/cacr2006-16.pdf
func GenerateMultiPrimeKey(random io.Reader, nprimes int, bits int) (priv *PrivateKey, err error) {
priv = new(PrivateKey)
priv.E = 65537
if nprimes < 2 {
return nil, errors.New("rsa.GenerateMultiPrimeKey: nprimes must be >= 2")
}
primes := make([]*big.Int, nprimes)
NextSetOfPrimes:
for {
todo := bits
for i := 0; i < nprimes; i++ {
primes[i], err = rand.Prime(random, todo/(nprimes-i))
if err != nil {
return nil, err
}
todo -= primes[i].BitLen()
}
// Make sure that primes is pairwise unequal.
for i, prime := range primes {
for j := 0; j < i; j++ {
if prime.Cmp(primes[j]) == 0 {
continue NextSetOfPrimes
}
}
}
n := new(big.Int).Set(bigOne)
totient := new(big.Int).Set(bigOne)
pminus1 := new(big.Int)
for _, prime := range primes {
n.Mul(n, prime)
pminus1.Sub(prime, bigOne)
totient.Mul(totient, pminus1)
}
g := new(big.Int)
priv.D = new(big.Int)
y := new(big.Int)
e := big.NewInt(int64(priv.E))
big.GcdInt(g, priv.D, y, e, totient)
if g.Cmp(bigOne) == 0 {
priv.D.Add(priv.D, totient)
priv.Primes = primes
priv.N = n
break
}
}
priv.Precompute()
return
}
// GenerateKeyPair generates an RSA keypair of the given bit size.
func GenerateKey(rand io.Reader, bits int) (priv *PrivateKey, err os.Error) {
priv = new(PrivateKey)
// Smaller public exponents lead to faster public key
// operations. Since the exponent must be coprime to
// (p-1)(q-1), the smallest possible value is 3. Some have
// suggested that a larger exponent (often 2**16+1) be used
// since previous implementation bugs[1] were avoided when this
// was the case. However, there are no current reasons not to use
// small exponents.
// [1] http://marc.info/?l=cryptography&m=115694833312008&w=2
priv.E = 3
pminus1 := new(big.Int)
qminus1 := new(big.Int)
totient := new(big.Int)
for {
p, err := randomPrime(rand, bits/2)
if err != nil {
return nil, err
}
q, err := randomPrime(rand, bits/2)
if err != nil {
return nil, err
}
if p.Cmp(q) == 0 {
continue
}
n := new(big.Int).Mul(p, q)
pminus1.Sub(p, bigOne)
qminus1.Sub(q, bigOne)
totient.Mul(pminus1, qminus1)
g := new(big.Int)
priv.D = new(big.Int)
y := new(big.Int)
e := big.NewInt(int64(priv.E))
big.GcdInt(g, priv.D, y, e, totient)
if g.Cmp(bigOne) == 0 {
priv.D.Add(priv.D, totient)
priv.P = p
priv.Q = q
priv.N = n
break
}
}
return
}
/**
* Store the solution in the Calculator output lines.
*/
func (calc *Calculator) setSolutionLine() {
var solution big.Int
if calc.operator == '+' {
solution.Add(&calc.operands[0], &calc.operands[1])
} else if calc.operator == '-' {
solution.Sub(&calc.operands[0], &calc.operands[1])
} else {
solution.Mul(&calc.operands[0], &calc.operands[1])
}
calc.lines[len(calc.lines)-1] = solution.String()
}
func marshalInt(to []byte, n *big.Int) []byte {
lengthBytes := to
to = to[4:]
length := 0
if n.Sign() < 0 {
// A negative number has to be converted to two's-complement
// form. So we'll subtract 1 and invert. If the
// most-significant-bit isn't set then we'll need to pad the
// beginning with 0xff in order to keep the number negative.
nMinus1 := new(big.Int).Neg(n)
nMinus1.Sub(nMinus1, bigOne)
bytes := nMinus1.Bytes()
for i := range bytes {
bytes[i] ^= 0xff
}
if len(bytes) == 0 || bytes[0]&0x80 == 0 {
to[0] = 0xff
to = to[1:]
length++
}
nBytes := copy(to, bytes)
to = to[nBytes:]
length += nBytes
} else if n.Sign() == 0 {
// A zero is the zero length string
} else {
bytes := n.Bytes()
if len(bytes) > 0 && bytes[0]&0x80 != 0 {
// We'll have to pad this with a 0x00 in order to
// stop it looking like a negative number.
to[0] = 0
to = to[1:]
length++
}
nBytes := copy(to, bytes)
to = to[nBytes:]
length += nBytes
}
lengthBytes[0] = byte(length >> 24)
lengthBytes[1] = byte(length >> 16)
lengthBytes[2] = byte(length >> 8)
lengthBytes[3] = byte(length)
return to
}
// IsOnCurve returns true if the given (x,y) lies on the curve.
func (curve *Curve) IsOnCurve(x, y *big.Int) bool {
// y² = x³ - 3x + b
y2 := new(big.Int).Mul(y, y)
y2.Mod(y2, curve.P)
x3 := new(big.Int).Mul(x, x)
x3.Mul(x3, x)
threeX := new(big.Int).Lsh(x, 1)
threeX.Add(threeX, x)
x3.Sub(x3, threeX)
x3.Add(x3, curve.B)
x3.Mod(x3, curve.P)
return x3.Cmp(y2) == 0
}
func binaryIntOp(x *big.Int, op token.Token, y *big.Int) interface{} {
var z big.Int
switch op {
case token.ADD:
return z.Add(x, y)
case token.SUB:
return z.Sub(x, y)
case token.MUL:
return z.Mul(x, y)
case token.QUO:
return z.Quo(x, y)
case token.REM:
return z.Rem(x, y)
case token.AND:
return z.And(x, y)
case token.OR:
return z.Or(x, y)
case token.XOR:
return z.Xor(x, y)
case token.AND_NOT:
return z.AndNot(x, y)
case token.SHL:
panic("unimplemented")
case token.SHR:
panic("unimplemented")
case token.EQL:
return x.Cmp(y) == 0
case token.NEQ:
return x.Cmp(y) != 0
case token.LSS:
return x.Cmp(y) < 0
case token.LEQ:
return x.Cmp(y) <= 0
case token.GTR:
return x.Cmp(y) > 0
case token.GEQ:
return x.Cmp(y) >= 0
}
panic("unreachable")
}
// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
// returns its double, also in Jacobian form.
func (BitCurve *BitCurve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l
a := new(big.Int).Mul(x, x) //X1²
b := new(big.Int).Mul(y, y) //Y1²
c := new(big.Int).Mul(b, b) //B²
d := new(big.Int).Add(x, b) //X1+B
d.Mul(d, d) //(X1+B)²
d.Sub(d, a) //(X1+B)²-A
d.Sub(d, c) //(X1+B)²-A-C
d.Mul(d, big.NewInt(2)) //2*((X1+B)²-A-C)
e := new(big.Int).Mul(big.NewInt(3), a) //3*A
f := new(big.Int).Mul(e, e) //E²
x3 := new(big.Int).Mul(big.NewInt(2), d) //2*D
x3.Sub(f, x3) //F-2*D
x3.Mod(x3, BitCurve.P)
y3 := new(big.Int).Sub(d, x3) //D-X3
y3.Mul(e, y3) //E*(D-X3)
y3.Sub(y3, new(big.Int).Mul(big.NewInt(8), c)) //E*(D-X3)-8*C
y3.Mod(y3, BitCurve.P)
z3 := new(big.Int).Mul(y, z) //Y1*Z1
z3.Mul(big.NewInt(2), z3) //3*Y1*Z1
z3.Mod(z3, BitCurve.P)
return x3, y3, z3
}
// Generate3PrimeKey generates a 3-prime RSA keypair of the given bit size, as
// suggested in [1]. Although the public keys are compatible (actually,
// indistinguishable) from the 2-prime case, the private keys are not. Thus it
// may not be possible to export 3-prime private keys in certain formats or to
// subsequently import them into other code.
//
// Table 1 in [2] suggests that size should be >= 1024 when using 3 primes.
//
// [1] US patent 4405829 (1972, expired)
// [2] http://www.cacr.math.uwaterloo.ca/techreports/2006/cacr2006-16.pdf
func Generate3PrimeKey(rand io.Reader, bits int) (priv *PrivateKey, err os.Error) {
priv = new(PrivateKey)
priv.E = 3
pminus1 := new(big.Int)
qminus1 := new(big.Int)
rminus1 := new(big.Int)
totient := new(big.Int)
for {
p, err := randomPrime(rand, bits/3)
if err != nil {
return nil, err
}
todo := bits - p.BitLen()
q, err := randomPrime(rand, todo/2)
if err != nil {
return nil, err
}
todo -= q.BitLen()
r, err := randomPrime(rand, todo)
if err != nil {
return nil, err
}
if p.Cmp(q) == 0 ||
q.Cmp(r) == 0 ||
r.Cmp(p) == 0 {
continue
}
n := new(big.Int).Mul(p, q)
n.Mul(n, r)
pminus1.Sub(p, bigOne)
qminus1.Sub(q, bigOne)
rminus1.Sub(r, bigOne)
totient.Mul(pminus1, qminus1)
totient.Mul(totient, rminus1)
g := new(big.Int)
priv.D = new(big.Int)
y := new(big.Int)
e := big.NewInt(int64(priv.E))
big.GcdInt(g, priv.D, y, e, totient)
if g.Cmp(bigOne) == 0 {
priv.D.Add(priv.D, totient)
priv.P = p
priv.Q = q
priv.R = r
priv.N = n
break
}
}
return
}
func number_subtract(x, y Obj) Obj {
xfx := (uintptr(unsafe.Pointer(x)) & fixnum_mask) == fixnum_tag
yfx := (uintptr(unsafe.Pointer(y)) & fixnum_mask) == fixnum_tag
if xfx && yfx {
i1 := uintptr(unsafe.Pointer(x))
i2 := uintptr(unsafe.Pointer(y))
r := (int(i1) >> fixnum_shift) - (int(i2) >> fixnum_shift)
if r >= fixnum_min && r <= fixnum_max {
return Make_fixnum(r)
} else {
return wrap(big.NewInt(int64(r)))
}
}
if (!xfx && (uintptr(unsafe.Pointer(x))&heap_mask) != heap_tag) ||
(!yfx && (uintptr(unsafe.Pointer(y))&heap_mask) != heap_tag) {
panic("bad type")
}
if xfx {
x = wrap(big.NewInt(int64(fixnum_to_int(x))))
}
if yfx {
y = wrap(big.NewInt(int64(fixnum_to_int(y))))
}
switch vx := (*x).(type) {
case *big.Int:
var z *big.Int = big.NewInt(0)
switch vy := (*y).(type) {
case *big.Int:
return simpBig(z.Sub(vx, vy))
default:
panic("bad type")
}
}
panic("bad type")
}
// doubleJacobian takes a point in Jacobian coordinates, (x, y, z), and
// returns its double, also in Jacobian form.
func (curve *Curve) doubleJacobian(x, y, z *big.Int) (*big.Int, *big.Int, *big.Int) {
// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
delta := new(big.Int).Mul(z, z)
delta.Mod(delta, curve.P)
gamma := new(big.Int).Mul(y, y)
gamma.Mod(gamma, curve.P)
alpha := new(big.Int).Sub(x, delta)
if alpha.Sign() == -1 {
alpha.Add(alpha, curve.P)
}
alpha2 := new(big.Int).Add(x, delta)
alpha.Mul(alpha, alpha2)
alpha2.Set(alpha)
alpha.Lsh(alpha, 1)
alpha.Add(alpha, alpha2)
beta := alpha2.Mul(x, gamma)
x3 := new(big.Int).Mul(alpha, alpha)
beta8 := new(big.Int).Lsh(beta, 3)
x3.Sub(x3, beta8)
for x3.Sign() == -1 {
x3.Add(x3, curve.P)
}
x3.Mod(x3, curve.P)
z3 := new(big.Int).Add(y, z)
z3.Mul(z3, z3)
z3.Sub(z3, gamma)
if z3.Sign() == -1 {
z3.Add(z3, curve.P)
}
z3.Sub(z3, delta)
if z3.Sign() == -1 {
z3.Add(z3, curve.P)
}
z3.Mod(z3, curve.P)
beta.Lsh(beta, 2)
beta.Sub(beta, x3)
if beta.Sign() == -1 {
beta.Add(beta, curve.P)
}
y3 := alpha.Mul(alpha, beta)
gamma.Mul(gamma, gamma)
gamma.Lsh(gamma, 3)
gamma.Mod(gamma, curve.P)
y3.Sub(y3, gamma)
if y3.Sign() == -1 {
y3.Add(y3, curve.P)
}
y3.Mod(y3, curve.P)
return x3, y3, z3
}
func marshalBigInt(out *forkableWriter, n *big.Int) (err os.Error) {
if n.Sign() < 0 {
// A negative number has to be converted to two's-complement
// form. So we'll subtract 1 and invert. If the
// most-significant-bit isn't set then we'll need to pad the
// beginning with 0xff in order to keep the number negative.
nMinus1 := new(big.Int).Neg(n)
nMinus1.Sub(nMinus1, bigOne)
bytes := nMinus1.Bytes()
for i := range bytes {
bytes[i] ^= 0xff
}
if len(bytes) == 0 || bytes[0]&0x80 == 0 {
err = out.WriteByte(0xff)
if err != nil {
return
}
}
_, err = out.Write(bytes)
} else if n.Sign() == 0 {
// Zero is written as a single 0 zero rather than no bytes.
err = out.WriteByte(0x00)
} else {
bytes := n.Bytes()
if len(bytes) > 0 && bytes[0]&0x80 != 0 {
// We'll have to pad this with 0x00 in order to stop it
// looking like a negative number.
err = out.WriteByte(0)
if err != nil {
return
}
}
_, err = out.Write(bytes)
}
return
}
func intLength(n *big.Int) int {
length := 4 /* length bytes */
if n.Sign() < 0 {
nMinus1 := new(big.Int).Neg(n)
nMinus1.Sub(nMinus1, bigOne)
bitLen := nMinus1.BitLen()
if bitLen%8 == 0 {
// The number will need 0xff padding
length++
}
length += (bitLen + 7) / 8
} else if n.Sign() == 0 {
// A zero is the zero length string
} else {
bitLen := n.BitLen()
if bitLen%8 == 0 {
// The number will need 0x00 padding
length++
}
length += (bitLen + 7) / 8
}
return length
}
func (curve *Curve) Add(p1, p2 *Point) *Point {
fmt.Printf("a")
if p1 == nil {
return p2
}
if p2 == nil {
return p1
}
lambda_numerator := new(big.Int)
lambda_denominator := new(big.Int)
lambda := new(big.Int)
lambda_numerator.Sub(p2.Y, p1.Y)
lambda_denominator.Sub(p2.X, p1.X)
if lambda_denominator.Cmp(BigZero) == -1 { //if Y is negative
lambda_denominator.Neg(lambda_denominator)
lambda_denominator.Sub(curve.P, lambda_denominator)
}
lambda_denominator, ok := modInverse(lambda_denominator, curve.P)
if !ok {
fmt.Printf("Add : Not ok\n")
return nil
}
lambda.Mul(lambda_numerator, lambda_denominator)
lambda = lambda.Mod(lambda, curve.P)
p3 := NewPoint()
p3.X.Exp(lambda, BigTwo, curve.P)
p3.X.Sub(p3.X, p1.X)
p3.X.Sub(p3.X, p2.X)
p3.X = p3.X.Mod(p3.X, curve.P)
p3.Y.Sub(p1.X, p3.X)
p3.Y.Mul(lambda, p3.Y)
p3.Y.Sub(p3.Y, p1.Y)
p3.Y = p3.Y.Mod(p3.Y, curve.P)
if p3.X.Cmp(BigZero) == -1 { //if X is negative
p3.X.Neg(p3.X)
p3.X.Sub(curve.P, p3.X)
}
if p3.Y.Cmp(BigZero) == -1 { //if Y is negative
p3.Y.Neg(p3.Y)
p3.Y.Sub(curve.P, p3.Y)
}
return p3
}
// GenerateParameters puts a random, valid set of DSA parameters into params.
// This function takes many seconds, even on fast machines.
func GenerateParameters(params *Parameters, rand io.Reader, sizes ParameterSizes) (err os.Error) {
// This function doesn't follow FIPS 186-3 exactly in that it doesn't
// use a verification seed to generate the primes. The verification
// seed doesn't appear to be exported or used by other code and
// omitting it makes the code cleaner.
var L, N int
switch sizes {
case L1024N160:
L = 1024
N = 160
case L2048N224:
L = 2048
N = 224
case L2048N256:
L = 2048
N = 256
case L3072N256:
L = 3072
N = 256
default:
return os.ErrorString("crypto/dsa: invalid ParameterSizes")
}
qBytes := make([]byte, N/8)
pBytes := make([]byte, L/8)
q := new(big.Int)
p := new(big.Int)
rem := new(big.Int)
one := new(big.Int)
one.SetInt64(1)
GeneratePrimes:
for {
_, err = io.ReadFull(rand, qBytes)
if err != nil {
return
}
qBytes[len(qBytes)-1] |= 1
qBytes[0] |= 0x80
q.SetBytes(qBytes)
if !big.ProbablyPrime(q, numMRTests) {
continue
}
for i := 0; i < 4*L; i++ {
_, err = io.ReadFull(rand, pBytes)
if err != nil {
return
}
pBytes[len(pBytes)-1] |= 1
pBytes[0] |= 0x80
p.SetBytes(pBytes)
rem.Mod(p, q)
rem.Sub(rem, one)
p.Sub(p, rem)
if p.BitLen() < L {
continue
}
if !big.ProbablyPrime(p, numMRTests) {
continue
}
params.P = p
params.Q = q
break GeneratePrimes
}
}
h := new(big.Int)
h.SetInt64(2)
g := new(big.Int)
pm1 := new(big.Int).Sub(p, one)
e := new(big.Int).Div(pm1, q)
for {
g.Exp(h, e, p)
if g.Cmp(one) == 0 {
h.Add(h, one)
continue
}
params.G = g
return
}
panic("unreachable")
}
// decrypt performs an RSA decryption, resulting in a plaintext integer. If a
// random source is given, RSA blinding is used.
func decrypt(random io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err os.Error) {
// TODO(agl): can we get away with reusing blinds?
if c.Cmp(priv.N) > 0 {
err = DecryptionError{}
return
}
var ir *big.Int
if random != nil {
// Blinding enabled. Blinding involves multiplying c by r^e.
// Then the decryption operation performs (m^e * r^e)^d mod n
// which equals mr mod n. The factor of r can then be removed
// by multiplying by the multiplicative inverse of r.
var r *big.Int
for {
r, err = rand.Int(random, priv.N)
if err != nil {
return
}
if r.Cmp(bigZero) == 0 {
r = bigOne
}
var ok bool
ir, ok = modInverse(r, priv.N)
if ok {
break
}
}
bigE := big.NewInt(int64(priv.E))
rpowe := new(big.Int).Exp(r, bigE, priv.N)
cCopy := new(big.Int).Set(c)
cCopy.Mul(cCopy, rpowe)
cCopy.Mod(cCopy, priv.N)
c = cCopy
}
if priv.Precomputed.Dp == nil {
m = new(big.Int).Exp(c, priv.D, priv.N)
} else {
// We have the precalculated values needed for the CRT.
m = new(big.Int).Exp(c, priv.Precomputed.Dp, priv.Primes[0])
m2 := new(big.Int).Exp(c, priv.Precomputed.Dq, priv.Primes[1])
m.Sub(m, m2)
if m.Sign() < 0 {
m.Add(m, priv.Primes[0])
}
m.Mul(m, priv.Precomputed.Qinv)
m.Mod(m, priv.Primes[0])
m.Mul(m, priv.Primes[1])
m.Add(m, m2)
for i, values := range priv.Precomputed.CRTValues {
prime := priv.Primes[2+i]
m2.Exp(c, values.Exp, prime)
m2.Sub(m2, m)
m2.Mul(m2, values.Coeff)
m2.Mod(m2, prime)
if m2.Sign() < 0 {
m2.Add(m2, prime)
}
m2.Mul(m2, values.R)
m.Add(m, m2)
}
}
if ir != nil {
// Unblind.
m.Mul(m, ir)
m.Mod(m, priv.N)
}
return
}
// GenerateMultiPrimeKey generates a multi-prime RSA keypair of the given bit
// size, as suggested in [1]. Although the public keys are compatible
// (actually, indistinguishable) from the 2-prime case, the private keys are
// not. Thus it may not be possible to export multi-prime private keys in
// certain formats or to subsequently import them into other code.
//
// Table 1 in [2] suggests maximum numbers of primes for a given size.
//
// [1] US patent 4405829 (1972, expired)
// [2] http://www.cacr.math.uwaterloo.ca/techreports/2006/cacr2006-16.pdf
func GenerateMultiPrimeKey(random io.Reader, nprimes int, bits int) (priv *PrivateKey, err os.Error) {
priv = new(PrivateKey)
// Smaller public exponents lead to faster public key
// operations. Since the exponent must be coprime to
// (p-1)(q-1), the smallest possible value is 3. Some have
// suggested that a larger exponent (often 2**16+1) be used
// since previous implementation bugs[1] were avoided when this
// was the case. However, there are no current reasons not to use
// small exponents.
// [1] http://marc.info/?l=cryptography&m=115694833312008&w=2
priv.E = 3
if nprimes < 2 {
return nil, os.ErrorString("rsa.GenerateMultiPrimeKey: nprimes must be >= 2")
}
primes := make([]*big.Int, nprimes)
NextSetOfPrimes:
for {
todo := bits
for i := 0; i < nprimes; i++ {
primes[i], err = rand.Prime(random, todo/(nprimes-i))
if err != nil {
return nil, err
}
todo -= primes[i].BitLen()
}
// Make sure that primes is pairwise unequal.
for i, prime := range primes {
for j := 0; j < i; j++ {
if prime.Cmp(primes[j]) == 0 {
continue NextSetOfPrimes
}
}
}
n := new(big.Int).Set(bigOne)
totient := new(big.Int).Set(bigOne)
pminus1 := new(big.Int)
for _, prime := range primes {
n.Mul(n, prime)
pminus1.Sub(prime, bigOne)
totient.Mul(totient, pminus1)
}
g := new(big.Int)
priv.D = new(big.Int)
y := new(big.Int)
e := big.NewInt(int64(priv.E))
big.GcdInt(g, priv.D, y, e, totient)
if g.Cmp(bigOne) == 0 {
priv.D.Add(priv.D, totient)
priv.Primes = primes
priv.N = n
break
}
}
priv.Precompute()
return
}
// decrypt performs an RSA decryption, resulting in a plaintext integer. If a
// random source is given, RSA blinding is used.
func decrypt(rand io.Reader, priv *PrivateKey, c *big.Int) (m *big.Int, err os.Error) {
// TODO(agl): can we get away with reusing blinds?
if c.Cmp(priv.N) > 0 {
err = DecryptionError{}
return
}
var ir *big.Int
if rand != nil {
// Blinding enabled. Blinding involves multiplying c by r^e.
// Then the decryption operation performs (m^e * r^e)^d mod n
// which equals mr mod n. The factor of r can then be removed
// by multipling by the multiplicative inverse of r.
var r *big.Int
for {
r, err = randomNumber(rand, priv.N)
if err != nil {
return
}
if r.Cmp(bigZero) == 0 {
r = bigOne
}
var ok bool
ir, ok = modInverse(r, priv.N)
if ok {
break
}
}
bigE := big.NewInt(int64(priv.E))
rpowe := new(big.Int).Exp(r, bigE, priv.N)
c.Mul(c, rpowe)
c.Mod(c, priv.N)
}
priv.rwMutex.RLock()
if priv.dP == nil && priv.P != nil {
priv.rwMutex.RUnlock()
priv.rwMutex.Lock()
if priv.dP == nil && priv.P != nil {
priv.precompute()
}
priv.rwMutex.Unlock()
priv.rwMutex.RLock()
}
if priv.dP == nil {
m = new(big.Int).Exp(c, priv.D, priv.N)
} else {
// We have the precalculated values needed for the CRT.
m = new(big.Int).Exp(c, priv.dP, priv.P)
m2 := new(big.Int).Exp(c, priv.dQ, priv.Q)
m.Sub(m, m2)
if m.Sign() < 0 {
m.Add(m, priv.P)
}
m.Mul(m, priv.qInv)
m.Mod(m, priv.P)
m.Mul(m, priv.Q)
m.Add(m, m2)
if priv.dR != nil {
// 3-prime CRT.
m2.Exp(c, priv.dR, priv.R)
m2.Sub(m2, m)
m2.Mul(m2, priv.tr)
m2.Mod(m2, priv.R)
if m2.Sign() < 0 {
m2.Add(m2, priv.R)
}
m2.Mul(m2, priv.pq)
m.Add(m, m2)
}
}
priv.rwMutex.RUnlock()
if ir != nil {
// Unblind.
m.Mul(m, ir)
m.Mod(m, priv.N)
}
return
}
// addJacobian takes two points in Jacobian coordinates, (x1, y1, z1) and
// (x2, y2, z2) and returns their sum, also in Jacobian form.
func (curve *Curve) addJacobian(x1, y1, z1, x2, y2, z2 *big.Int) (*big.Int, *big.Int, *big.Int) {
// See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl
z1z1 := new(big.Int).Mul(z1, z1)
z1z1.Mod(z1z1, curve.P)
z2z2 := new(big.Int).Mul(z2, z2)
z2z2.Mod(z2z2, curve.P)
u1 := new(big.Int).Mul(x1, z2z2)
u1.Mod(u1, curve.P)
u2 := new(big.Int).Mul(x2, z1z1)
u2.Mod(u2, curve.P)
h := new(big.Int).Sub(u2, u1)
if h.Sign() == -1 {
h.Add(h, curve.P)
}
i := new(big.Int).Lsh(h, 1)
i.Mul(i, i)
j := new(big.Int).Mul(h, i)
s1 := new(big.Int).Mul(y1, z2)
s1.Mul(s1, z2z2)
s1.Mod(s1, curve.P)
s2 := new(big.Int).Mul(y2, z1)
s2.Mul(s2, z1z1)
s2.Mod(s2, curve.P)
r := new(big.Int).Sub(s2, s1)
if r.Sign() == -1 {
r.Add(r, curve.P)
}
r.Lsh(r, 1)
v := new(big.Int).Mul(u1, i)
x3 := new(big.Int).Set(r)
x3.Mul(x3, x3)
x3.Sub(x3, j)
x3.Sub(x3, v)
x3.Sub(x3, v)
x3.Mod(x3, curve.P)
y3 := new(big.Int).Set(r)
v.Sub(v, x3)
y3.Mul(y3, v)
s1.Mul(s1, j)
s1.Lsh(s1, 1)
y3.Sub(y3, s1)
y3.Mod(y3, curve.P)
z3 := new(big.Int).Add(z1, z2)
z3.Mul(z3, z3)
z3.Sub(z3, z1z1)
if z3.Sign() == -1 {
z3.Add(z3, curve.P)
}
z3.Sub(z3, z2z2)
if z3.Sign() == -1 {
z3.Add(z3, curve.P)
}
z3.Mul(z3, h)
z3.Mod(z3, curve.P)
return x3, y3, z3
}
func factcalc(f *big.Int) *big.Int {
if f.Cmp(1) != 0 {
return big.Mul(f, factcalc(f.Sub(f, 1)))
}
return big.NewInt(1)
}
