public Cypher GetCypher(string message)
{
BigInteger x = GeneralFunctions.H1hash(ID, prim);
BigInteger y = x.Pow(3).Add(new BigInteger("7", 10)).Pow(2).ModInverse(prim);
FpFieldElement x_Qid = new FpFieldElement(E.Q, x);
FpFieldElement y_Qid = new FpFieldElement(E.Q, y);
FpPoint Qid = new FpPoint(E, x_Qid, y_Qid);
int r = 0;
do
{
Random rnd = new Random();
r = rnd.Next(1, int.MaxValue - 1);
} while (r == 0);
FpPoint rP = (FpPoint)P.Multiply(new BigInteger(r.ToString(), 10));
BigInteger gid = GeneralFunctions.Pair(Qid, Ppub, k, prim);
gid = gid.ModPow(new BigInteger(r.ToString(), 10), prim);
char[] M = message.ToCharArray();
char[] cArray = new char[M.Length];
char[] hash = GeneralFunctions.H2hash(gid, prim).ToCharArray();
for (int i = 0; i < message.Length; i++)
{
cArray[i] = (char)(M[i] ^ hash[i % hash.Length]);
}
string c = new String(cArray);
return new Cypher { U = rP, V = c };
}
public virtual bool Equals(FpFieldElement other)
{
if (q.Equals(other.q))
{
return(base.Equals(other));
}
return(false);
}
/**
* Decode a point on this curve from its ASN.1 encoding. The different
* encodings are taken account of, including point compression for
* <code>F<sub>p</sub><code> (X9.62 s 4.2.1 pg 17).
* @return The decoded point.
*/
public override ECPoint DecodePoint(
byte[] encoded)
{
ECPoint p = null;
switch (encoded[0])
{
// compressed
case 0x02:
case 0x03:
int ytilde = encoded[0] & 1;
byte[] i = new byte[encoded.Length - 1];
Array.Copy(encoded, 1, i, 0, i.Length);
ECFieldElement x = new FpFieldElement(this.q, new BigInteger(1, i));
ECFieldElement alpha = x.Multiply(x.Square()).Add(x.Multiply(a).Add(b));
ECFieldElement beta = alpha.Sqrt();
//
// if we can't find a sqrt we haven't got a point on the
// curve - run!
//
if (beta == null)
{
throw new ArithmeticException("Invalid point compression");
}
BigInteger betaValue = beta.ToBigInteger();
int bit0 = betaValue.TestBit(0) ? 1 : 0;
if (bit0 != ytilde)
{
// Use the other root
beta = new FpFieldElement(q, q.Subtract(betaValue));
}
p = new FpPoint(this, x, beta, true);
break;
case 0x04:
byte[] xEnc = new byte[(encoded.Length - 1) / 2];
byte[] yEnc = new byte[(encoded.Length - 1) / 2];
Array.Copy(encoded, 1, xEnc, 0, xEnc.Length);
Array.Copy(encoded, xEnc.Length + 1, yEnc, 0, yEnc.Length);
p = new FpPoint(this,
new FpFieldElement(this.q, new BigInteger(1, xEnc)),
new FpFieldElement(this.q, new BigInteger(1, yEnc)));
break;
default:
throw new FormatException("Invalid point encoding " + encoded[0]);
}
return(p);
}
public override bool Equals(object obj)
{
if (obj == this)
{
return(true);
}
FpFieldElement fpFieldElement = obj as FpFieldElement;
return(fpFieldElement != null && this.Equals(fpFieldElement));
}
public FpCurve(BigInteger q, BigInteger a, BigInteger b, BigInteger order, BigInteger cofactor) : base(q)
{
this.m_q = q;
this.m_r = FpFieldElement.CalculateResidue(q);
this.m_infinity = new FpPoint(this, null, null);
base.m_a = this.FromBigInteger(a);
base.m_b = this.FromBigInteger(b);
base.m_order = order;
base.m_cofactor = cofactor;
base.m_coord = 4;
}
/**
* Creates the points on the curve with literature values.
*/
internal static void createPoints()
{
for (int i = 0; i < pointSource.Length / 2; i++)
{
FpFieldElement x = new FpFieldElement(q, new BigInteger(
pointSource[2 * i].ToString()));
FpFieldElement y = new FpFieldElement(q, new BigInteger(
pointSource[2 * i + 1].ToString()));
p[i] = new FpPoint(curve, x, y);
}
}
public FpCurve(BigInteger q, BigInteger a, BigInteger b, BigInteger order, BigInteger cofactor)
: base(FiniteFields.GetPrimeField(q))
{
this.m_q = q;
this.m_r = FpFieldElement.CalculateResidue(q);
this.m_infinity = new FpPoint(this, null, null);
this.m_a = FromBigInteger(a);
this.m_b = FromBigInteger(b);
this.m_order = order;
this.m_cofactor = cofactor;
this.m_coord = FP_DEFAULT_COORDS;
}
public override bool Equals(object obj)
{
if (obj == this)
{
return(true);
}
FpFieldElement fpFieldElement = obj as FpFieldElement;
if (fpFieldElement == null)
{
return(false);
}
return(Equals(fpFieldElement));
}
public override bool Equals(object obj)
{
if (obj == this)
{
return(true);
}
FpFieldElement other = obj as FpFieldElement;
if (other == null)
{
return(false);
}
return(this.Equals(other));
}
/**
* Decode a point on this curve from its ASN.1 encoding. The different
* encodings are taken account of, including point compression for
* <code>F<sub>p</sub></code> (X9.62 s 4.2.1 pg 17).
* @return The decoded point.
*/
public override ECPoint DecodePoint(
byte[] encoded)
{
ECPoint p = null;
switch (encoded[0])
{
// compressed
case 0x02:
case 0x03:
int ytilde = encoded[0] & 1;
byte[] i = new byte[encoded.Length - 1];
Array.Copy(encoded, 1, i, 0, i.Length);
ECFieldElement x = new FpFieldElement(this.q, new BigInteger(1, i));
ECFieldElement alpha = x.Multiply(x.Square()).Add(x.Multiply(a).Add(b));
ECFieldElement beta = alpha.Sqrt();
//
// if we can't find a sqrt we haven't got a point on the
// curve - run!
//
if (beta == null)
throw new ArithmeticException("Invalid point compression");
BigInteger betaValue = beta.ToBigInteger();
int bit0 = betaValue.TestBit(0) ? 1 : 0;
if (bit0 != ytilde)
{
// Use the other root
beta = new FpFieldElement(q, q.Subtract(betaValue));
}
p = new FpPoint(this, x, beta, true);
break;
case 0x04:
byte[] xEnc = new byte[(encoded.Length - 1) / 2];
byte[] yEnc = new byte[(encoded.Length - 1) / 2];
Array.Copy(encoded, 1, xEnc, 0, xEnc.Length);
Array.Copy(encoded, xEnc.Length + 1, yEnc, 0, yEnc.Length);
p = new FpPoint(this,
new FpFieldElement(this.q, new BigInteger(1, xEnc)),
new FpFieldElement(this.q, new BigInteger(1, yEnc)));
break;
default:
throw new FormatException("Invalid point encoding " + encoded[0]);
}
return p;
}
protected bool Equals(
FpFieldElement other)
{
return(q.Equals(other.q) && base.Equals(other));
}
// D.1.4 91
/**
* return a sqrt root - the routine verifies that the calculation
* returns the right value - if none exists it returns null.
*/
public override ECFieldElement Sqrt()
{
if (!q.TestBit(0))
{
throw Platform.CreateNotImplementedException("even value of q");
}
// p mod 4 == 3
if (q.TestBit(1))
{
// TODO Can this be optimised (inline the Square?)
// z = g^(u+1) + p, p = 4u + 3
ECFieldElement z = new FpFieldElement(q, x.ModPow(q.ShiftRight(2).Add(BigInteger.One), q));
return(z.Square().Equals(this) ? z : null);
}
// p mod 4 == 1
BigInteger qMinusOne = q.Subtract(BigInteger.One);
BigInteger legendreExponent = qMinusOne.ShiftRight(1);
if (!(x.ModPow(legendreExponent, q).Equals(BigInteger.One)))
{
return(null);
}
BigInteger u = qMinusOne.ShiftRight(2);
BigInteger k = u.ShiftLeft(1).Add(BigInteger.One);
BigInteger Q = this.x;
BigInteger fourQ = Q.ShiftLeft(2).Mod(q);
BigInteger U, V;
do
{
Random rand = new Random();
BigInteger P;
do
{
P = new BigInteger(q.BitLength, rand);
}while (P.CompareTo(q) >= 0 ||
!(P.Multiply(P).Subtract(fourQ).ModPow(legendreExponent, q).Equals(qMinusOne)));
BigInteger[] result = fastLucasSequence(q, P, Q, k);
U = result[0];
V = result[1];
if (V.Multiply(V).Mod(q).Equals(fourQ))
{
// Integer division by 2, mod q
if (V.TestBit(0))
{
V = V.Add(q);
}
V = V.ShiftRight(1);
Debug.Assert(V.Multiply(V).Mod(q).Equals(x));
return(new FpFieldElement(q, V));
}
}while (U.Equals(BigInteger.One) || U.Equals(qMinusOne));
return(null);
// BigInteger qMinusOne = q.Subtract(BigInteger.One);
//
// BigInteger legendreExponent = qMinusOne.ShiftRight(1);
// if (!(x.ModPow(legendreExponent, q).Equals(BigInteger.One)))
// return null;
//
// Random rand = new Random();
// BigInteger fourX = x.ShiftLeft(2);
//
// BigInteger r;
// do
// {
// r = new BigInteger(q.BitLength, rand);
// }
// while (r.CompareTo(q) >= 0
// || !(r.Multiply(r).Subtract(fourX).ModPow(legendreExponent, q).Equals(qMinusOne)));
//
// BigInteger n1 = qMinusOne.ShiftRight(2);
// BigInteger n2 = n1.Add(BigInteger.One);
//
// BigInteger wOne = WOne(r, x, q);
// BigInteger wSum = W(n1, wOne, q).Add(W(n2, wOne, q)).Mod(q);
// BigInteger twoR = r.ShiftLeft(1);
//
// BigInteger root = twoR.ModPow(q.Subtract(BigInteger.Two), q)
// .Multiply(x).Mod(q)
// .Multiply(wSum).Mod(q);
//
// return new FpFieldElement(q, root);
}
public FpFieldElement(BigInteger q, BigInteger x) : this(q, FpFieldElement.CalculateResidue(q), x)
{
}
private FiniteFieldElement(FpFieldElement innerField)
{
_field = innerField;
}
public virtual bool Equals(
FpFieldElement other)
{
return q.Equals(other.q) && base.Equals(other);
}
// D.1.4 91
/**
* return a sqrt root - the routine verifies that the calculation
* returns the right value - if none exists it returns null.
*/
public override ECFieldElement Sqrt()
{
if (!q.TestBit(0))
throw Platform.CreateNotImplementedException("even value of q");
// p mod 4 == 3
if (q.TestBit(1))
{
// TODO Can this be optimised (inline the Square?)
// z = g^(u+1) + p, p = 4u + 3
ECFieldElement z = new FpFieldElement(q, x.ModPow(q.ShiftRight(2).Add(BigInteger.One), q));
return this.Equals(z.Square()) ? z : null;
}
// p mod 4 == 1
BigInteger qMinusOne = q.Subtract(BigInteger.One);
BigInteger legendreExponent = qMinusOne.ShiftRight(1);
if (!(x.ModPow(legendreExponent, q).Equals(BigInteger.One)))
return null;
BigInteger u = qMinusOne.ShiftRight(2);
BigInteger k = u.ShiftLeft(1).Add(BigInteger.One);
BigInteger Q = this.x;
BigInteger fourQ = Q.ShiftLeft(2).Mod(q);
BigInteger U, V;
do
{
Random rand = new Random();
BigInteger P;
do
{
P = new BigInteger(q.BitLength, rand);
}
while (P.CompareTo(q) >= 0
|| !(P.Multiply(P).Subtract(fourQ).ModPow(legendreExponent, q).Equals(qMinusOne)));
BigInteger[] result = fastLucasSequence(q, P, Q, k);
U = result[0];
V = result[1];
if (V.Multiply(V).Mod(q).Equals(fourQ))
{
// Integer division by 2, mod q
if (V.TestBit(0))
{
V = V.Add(q);
}
V = V.ShiftRight(1);
Debug.Assert(V.Multiply(V).Mod(q).Equals(x));
return new FpFieldElement(q, V);
}
}
while (U.Equals(BigInteger.One) || U.Equals(qMinusOne));
return null;
// BigInteger qMinusOne = q.Subtract(BigInteger.One);
//
// BigInteger legendreExponent = qMinusOne.ShiftRight(1);
// if (!(x.ModPow(legendreExponent, q).Equals(BigInteger.One)))
// return null;
//
// Random rand = new Random();
// BigInteger fourX = x.ShiftLeft(2);
//
// BigInteger r;
// do
// {
// r = new BigInteger(q.BitLength, rand);
// }
// while (r.CompareTo(q) >= 0
// || !(r.Multiply(r).Subtract(fourX).ModPow(legendreExponent, q).Equals(qMinusOne)));
//
// BigInteger n1 = qMinusOne.ShiftRight(2);
// BigInteger n2 = n1.Add(BigInteger.One);
//
// BigInteger wOne = WOne(r, x, q);
// BigInteger wSum = W(n1, wOne, q).Add(W(n2, wOne, q)).Mod(q);
// BigInteger twoR = r.ShiftLeft(1);
//
// BigInteger root = twoR.ModPow(q.Subtract(BigInteger.Two), q)
// .Multiply(x).Mod(q)
// .Multiply(wSum).Mod(q);
//
// return new FpFieldElement(q, root);
}
protected override X9ECParameters CreateParameters()
{
// p = 2^224 - 2^96 + 1
BigInteger secp224r1P = new BigInteger(
"26959946667150639794667015087019630673557916260026308143510066298881");
// a = -3, b = b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4
ECCurve secp224r1Curve = new FpCurve(secp224r1P,
new BigInteger("26959946667150639794667015087019630673557916260026308143510066298878"),
new BigInteger("b4050a850c04b3abf54132565044b0b7d7bfd8ba270b39432355ffb4", 16));
// x = b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21
ECFieldElement secp224r1x = new FpFieldElement(
secp224r1P,
new BigInteger("b70e0cbd6bb4bf7f321390b94a03c1d356c21122343280d6115c1d21", 16));
// y = bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34
ECFieldElement secp224r1y = new FpFieldElement(
secp224r1P,
new BigInteger("bd376388b5f723fb4c22dfe6cd4375a05a07476444d5819985007e34", 16));
ECPoint secp224r1BasePoint = new FpPoint(
secp224r1Curve, secp224r1x, secp224r1y, false);
BigInteger secp224r1n = new BigInteger("26959946667150639794667015087019625940457807714424391721682722368061");
BigInteger secp224r1h = new BigInteger("1");
//static readonly byte[] secp224r1Seed = (Hex.decode("bd71344799d5c7fcdc45b59fa3b9ab8f6a948bc5"));
byte[] secp224r1Seed = null;
return new X9ECParameters(
secp224r1Curve,
secp224r1BasePoint,
secp224r1n,
secp224r1h,
secp224r1Seed);
}
public virtual bool Equals(FpFieldElement other) => (this.q.Equals(other.q) && base.Equals((ECFieldElement)other));
public FiniteFieldElement Multiply(BigInteger x)
{
var xInnerField = new FpFieldElement(this._field.Q, x.ToBouncyCastleBigInteger());
var xAsFiniteFieldElement = new FiniteFieldElement(xInnerField);
return Multiply(xAsFiniteFieldElement);
}
public FpPoint Exctract(string ID, bool decrypt = false)
{
if (decrypt)
{
string sStr = File.ReadAllText("mk");
s = int.Parse(sStr);
}
// y^2 = x^3 + 117050x^2 + x
BigInteger x = GeneralFunctions.H1hash(ID, p);
BigInteger y = x.Pow(3).Add(x.Pow(2).Multiply(new BigInteger("117050", 10))).Add(x).Pow(2).ModInverse(p);
FpFieldElement x_Qid = new FpFieldElement(q, x);
FpFieldElement y_Qid = new FpFieldElement(q, y);
FpPoint Qid = new FpPoint(E, x_Qid, y_Qid);
FpPoint d_id = (FpPoint)Qid.Multiply(new BigInteger(s.ToString(), 10));
// privatni ključ
return d_id;
}
protected override X9ECParameters CreateParameters()
{
// p = 2^256 - 2^224 + 2^192 + 2^96 - 1
BigInteger secp256r1P = new BigInteger(
"115792089210356248762697446949407573530086143415290314195533631308867097853951");
// a = -3, b = 5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b
ECCurve secp256r1Curve = new FpCurve(secp256r1P,
new BigInteger("115792089210356248762697446949407573530086143415290314195533631308867097853948"),
new BigInteger("5ac635d8aa3a93e7b3ebbd55769886bc651d06b0cc53b0f63bce3c3e27d2604b", 16));
// x = 6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296
ECFieldElement secp256r1x = new FpFieldElement(
secp256r1P,
new BigInteger("6b17d1f2e12c4247f8bce6e563a440f277037d812deb33a0f4a13945d898c296", 16));
// y = 4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5
ECFieldElement secp256r1y = new FpFieldElement(
secp256r1P,
new BigInteger("4fe342e2fe1a7f9b8ee7eb4a7c0f9e162bce33576b315ececbb6406837bf51f5", 16));
ECPoint secp256r1BasePoint = new FpPoint(
secp256r1Curve, secp256r1x, secp256r1y, false);
BigInteger secp256r1n = new BigInteger("115792089210356248762697446949407573529996955224135760342422259061068512044369");
BigInteger secp256r1h = new BigInteger("1");
//static readonly byte[] secp256r1Seed = (Hex.decode("c49d360886e704936a6678e1139d26b7819f7e90"));
byte[] secp256r1Seed = null;
return new X9ECParameters(
secp256r1Curve,
secp256r1BasePoint,
secp256r1n,
secp256r1h,
secp256r1Seed);
}
public FiniteFieldElement(BigInteger value, BigInteger prime)
{
Org.BouncyCastle.Math.BigInteger bouncy_q = prime.ToBouncyCastleBigInteger();
Org.BouncyCastle.Math.BigInteger bouncy_x = value.ToBouncyCastleBigInteger();
_field = new FpFieldElement(bouncy_q, bouncy_x);
}
protected bool Equals(
FpFieldElement other)
{
return q.Equals(other.q) && base.Equals(other);
}
protected override X9ECParameters CreateParameters()
{
// p = 2^384 - 2^128 - 2^96 + 2^32 - 1
BigInteger secp384r1P = new BigInteger(
"FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF", 16);
// a, b
ECCurve secp384r1Curve = new FpCurve(secp384r1P,
new BigInteger("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC", 16),
new BigInteger("B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF", 16));
// x
ECFieldElement secp384r1x = new FpFieldElement(
secp384r1P,
new BigInteger("AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7", 16));
// y
ECFieldElement secp384r1y = new FpFieldElement(
secp384r1P,
new BigInteger("3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F", 16));
ECPoint secp384r1BasePoint = new FpPoint(
secp384r1Curve, secp384r1x, secp384r1y, false);
BigInteger secp384r1n = new BigInteger("FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973", 16);
BigInteger secp384r1h = BigInteger.One;
//static readonly byte[] secp384r1Seed = (Hex.decode("A335926AA319A27A1D00896A6773A4827ACDAC73"));
byte[] secp384r1Seed = null;
return new X9ECParameters(
secp384r1Curve,
secp384r1BasePoint,
secp384r1n,
secp384r1h,
secp384r1Seed);
}
public virtual bool Equals(
FpFieldElement other)
{
return(q.Equals(other.q) && base.Equals(other));
}
protected override X9ECParameters CreateParameters()
{
// p = 2^521 - 1
BigInteger secp521r1P = new BigInteger(
"6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057151");
// a = -3, b = 051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00
ECCurve secp521r1Curve = new FpCurve(secp521r1P,
new BigInteger("6864797660130609714981900799081393217269435300143305409394463459185543183397656052122559640661454554977296311391480858037121987999716643812574028291115057148"),
new BigInteger("051953eb9618e1c9a1f929a21a0b68540eea2da725b99b315f3b8b489918ef109e156193951ec7e937b1652c0bd3bb1bf073573df883d2c34f1ef451fd46b503f00", 16));
// x = c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66
ECFieldElement secp521r1x = new FpFieldElement(
secp521r1P,
new BigInteger("c6858e06b70404e9cd9e3ecb662395b4429c648139053fb521f828af606b4d3dbaa14b5e77efe75928fe1dc127a2ffa8de3348b3c1856a429bf97e7e31c2e5bd66", 16));
// y = 11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650
ECFieldElement secp521r1y = new FpFieldElement(
secp521r1P,
new BigInteger("11839296a789a3bc0045c8a5fb42c7d1bd998f54449579b446817afbd17273e662c97ee72995ef42640c550b9013fad0761353c7086a272c24088be94769fd16650", 16));
ECPoint secp521r1BasePoint = new FpPoint(
secp521r1Curve, secp521r1x, secp521r1y, false);
BigInteger secp521r1n = new BigInteger("6864797660130609714981900799081393217269435300143305409394463459185543183397655394245057746333217197532963996371363321113864768612440380340372808892707005449");
BigInteger secp521r1h = new BigInteger("1");
//static readonly byte[] secp521r1Seed = (Hex.decode("d09e8800291cb85396cc6717393284aaa0da64ba"));
byte[] secp521r1Seed = null;
return new X9ECParameters(
secp521r1Curve,
secp521r1BasePoint,
secp521r1n,
secp521r1h,
secp521r1Seed);
}
