public void TestMultBook()
{
EllipticCurve curve = new EllipticCurve(a: -1, b: 3231, modulus: 661643);
Point q = (87, 2);
q = curve.Multiply(BigInteger.Pow(2, 9), q);
bool success = q.Equals((Point)(196083, 134895));
q = curve.Multiply(BigInteger.Pow(3, 6), q);
success = success && q.Equals((Point)(470021, 282574));
Assert.IsTrue(success);
}
public EllipticDiffieHellman(EllipticCurve curve, Point generator, BigInteger order, byte[] priv = null)
{
this.curve = curve;
this.generator = generator;
// Generate private key
if (priv == null)
{
byte[] max = order.ToByteArray();
do
{
byte[] p1 = new byte[5 /*rand.Next(max.Length) + 1*/];
rand.NextBytes(p1);
if (p1.Length == max.Length)
{
p1[p1.Length - 1] %= max[max.Length - 1];
}
else
{
p1[p1.Length - 1] &= 127;
}
this.priv = new BigInteger(p1);
} while (this.priv < 2);
}
else
{
this.priv = new BigInteger(priv);
}
// Generate public key
pub = curve.Multiply(generator, this.priv);
}
public static Point HashToPoint(byte[] toHash, EllipticCurve ec, BigInt cofactor)
{
Point P = HashToPoint(toHash, ec);
P = ec.Multiply(P, cofactor);
return(P);
}
public void Multiply()
{
int n = Form.NumericUpDownNValue;
ECPoint s = (ECPoint)Form.ComboBoxS.SelectedItem;
multiplicationResult = ellipticCurve.Multiply(n, s);
Form.TextBoxMultiplicationResult.Text = multiplicationResult.ToString();
Form.MultiplicationLogButtonEnabled = true;
DrawCurve();
}
public byte[] GetSharedSecret(byte[] pK)
{
BitReader reader = new BitReader(pK);
byte[] x = reader.ReadByteArray();
Point remotePublic = new Point(
new BigInteger(x),
new BigInteger(reader.ReadByteArray(pK.Length - BinaryHelpers.VarIntSize(x.Length) - x.Length))
);
return(curve.Multiply(remotePublic, priv).X.ToByteArray()); // Use the x-coordinate as the shared secret
}
public void MultiplyTest()
{
BigInt xA = new BigInt("489a03c58dcf7fcfc97e99ffef0bb4634", 16);
BigInt yA = new BigInt("510c6972d795ec0c2b081b81de767f808", 16);
BigInt l = new BigInt("b8bbbc0089098f2769b32373ade8f0daf", 16);
BigInt xE = new BigInt("073734b32a882cc97956b9f7e54a2d326", 16);
BigInt yE = new BigInt("9c4b891aab199741a44a5b6b632b949f7", 16);
Point e = new Point(xE, yE);
Point a = new Point(xA, yA);
Assert.AreEqual(e, curve.Multiply(a, l));
}
public byte[] GetSharedSecretRaw(byte[] pK)
{
byte[] p1 = new byte[pK[0] | (pK[1] << 8) | (pK[2] << 16) | (pK[3] << 24)]; // Reconstruct x-axis size
byte[] p2 = new byte[pK.Length - p1.Length - 4];
Array.Copy(pK, 4, p1, 0, p1.Length);
Array.Copy(pK, 4 + p1.Length, p2, 0, p2.Length);
CurvePoint remotePublic = new CurvePoint(new BigInteger(p1), new BigInteger(p2));
byte[] secret = curve.Multiply(remotePublic, priv).X.GetBytes(); // Use the x-coordinate as the shared secret
return(secret);
}
public void BillinearTest()
{
//using a predefined pairing
Pairing e = Predefined.nssTate();
//get P, which is a random point in group G1
BigInt xP = new BigInt("6489939838247988945871981900040296813593014269345452667904622838482534881503698483366430292883248221510827517646942621360563883893977498988822397615847035", 10);
BigInt yP = new BigInt("4183869719038127850866054323652097154062917818644838834002147757841525900395398794914246812190615424669832349278263049648914095684913634131502517423626958", 10);
Point P = new Point(xP, yP);
//get Q, which is a random point in group G2
BigInt xQ = new BigInt("2954273822533893703877488768696651085799471510788466547935020721095428933759242911655447662730930250257332528194261492443088328780492269310876627460775540", 10);
BigInt yQ = new BigInt("5618108911398484778214611016375606480759218944436047801309324726445485710683489022960503194997792712985027904009701406998265308597942813750269945637462064", 10);
Point Q = new Point(xQ, yQ);
//compute e(P,Q)
FieldElement epq = e.Compute(P, Q);
//the curve on which G1 is defined
EllipticCurve g1 = e.Curve;
//a is a 160-bit random integer
BigInt a = new BigInt(160, new Random());
//Point aP is computed over G1
Point aP = g1.Multiply(P, a);
//The curve on which G2 is defined
EllipticCurve g2 = e.Curve2;
//b is a 160-bit random integer
BigInt b = new BigInt(160, new Random());
//bQ is computed over G2
Point bQ = g2.Multiply(Q, b);
//compute e(aP,bQ)
FieldElement res = e.Compute(aP, bQ);
//compute e(P,Q)^ab, this is done in group Gt
BigInt ab = a.Multiply(b);
//get the field on which Gt is defined
Field gt = e.Gt;
FieldElement res2 = gt.Pow(epq, ab);
//compare these two
Assert.AreEqual(res, res2);
}
public ECDiffieHellman(EllipticCurve curve, CurvePoint generator, BigInteger order, byte[] priv = null)
{
this.curve = curve;
this.generator = generator;
// Generate private key
if (priv == null)
{
this.priv = new BigInteger();
this.priv.GenRandomBits(order.DataLength, rand);
}
else
{
this.priv = new BigInteger(priv);
}
// Generate public key
pub = curve.Multiply(generator, this.priv);
}
public void TestMult()
{
EllipticCurve curve = new EllipticCurve(a: 1, b: 1, modulus: 23);
Point[] expected = new Point[] {
(0, 1), (6, 19), (3, 13), (13, 16), (18, 3), (7, 11),
(11, 3), (5, 19), (19, 18), (12, 4), (1, 16), (17, 20),
(9, 16), (4, 0), (9, 7), (17, 3), (1, 7), (12, 19),
(19, 5), (5, 4), (11, 20), (7, 12), (18, 20), (13, 7),
(3, 10), (6, 4), (0, 22), null
};
Point p = (0, 1);
Point[] actual = new Point[expected.Length];
for (int i = 0; i < expected.Length; i++)
{
actual[i] = curve.Multiply(i + 1, p);
}
CollectionAssert.AreEqual(expected, actual);
}
