/// <summary>
/// Returns the final point via summation. This method is very slow. Do not use big value for Sk.
/// </summary>
/// <param name="A"></param>
/// <param name="B"></param>
/// <param name="G"></param>
/// <param name="Sk"></param>
/// <returns></returns>
public static EcModPoint EcSlowKeyPairGeneratorByClassicPointSum(BigInteger P, BigInteger A, BigInteger B, EcModPoint G, int Sk)
{
var delta = 4 * A * A * A + 27 * B * B;
if (0 == delta)
{
throw new Exception("Delta cannot be zero.");
}
int cnt = 2;
bool inf = false;
EcModPoint qMod = null;
while (cnt <= Sk && !inf)
{
qMod = computePointSum(A, G, qMod, P);
inf = G.x == qMod.x;
if (inf)
{
qMod.IsInf = true;
qMod.OrderN = cnt;
}
++cnt;
}
return(qMod);
}
private static EcModPoint pointAdd(EcModPoint pointP, EcModPoint pointQ, BigInteger p)
{
// compute m = (y1 - y0) / (x1 - x0) (mod p)
var x0 = pointP.x;
var y0 = pointP.y;
var x1 = pointQ.x;
var y1 = pointQ.y;
// compute m mod p
BigInteger dy = (y1 - y0) % p;
BigInteger dx = (x1 - x0) % p;
dy = (dy + p) % p;
dx = (dx + p) % p;
BigInteger inv_dx = dx.ModInv(p);
BigInteger m = BigInteger.Multiply(dy, inv_dx) % p;
m = (m + p) % p;
var x = (m * m - x0 - x1) % p;
x = (x + p) % p;
var y = (m * (x0 - x) - y0) % p; //(-m * m * m + 3 * m * x0 - y0) % p;
y = (y + p) % p;
EcModPoint ret = new EcModPoint {
x = x, y = y
};
return(ret);
}
/// <summary>
/// Encrypt text on elliptic curve and return a list of points on the elliptic curve in Json format (string)
/// </summary>
/// <param name="Text"></param>
/// <param name="PubKey"></param>
/// <returns></returns>
public static string EcEncryptJson(string Text, EcModPoint PubKey, EllipticCurveType EcType)
{
var lstEncr = EcEncrypt(Text, PubKey, EcType);
var json = JsonConvert.SerializeObject(lstEncr);
return(json);
}
/// <summary>
/// Returns the list of points by addition (P + Q). This method is very slow. Do not use big value for Sk.
/// </summary>
/// <param name="P"></param>
/// <param name="A"></param>
/// <param name="B></param>
/// <param name="G"></param>
/// <param name="Sk"></param>
/// <returns></returns>
public static List <EcModPoint> EcSlowPointListByAddition(BigInteger P, BigInteger A, BigInteger B, EcModPoint G, int Sk)
{
var delta = 4 * A * A * A + 27 * B * B;
if (0 == delta)
{
throw new Exception("Delta cannot be zero.");
}
var ret = new List <EcModPoint>();
ret.Add(G);
int cnt = 2;
bool inf = false;
EcModPoint qMod = null;
while (cnt <= Sk && !inf)
{
qMod = computePointSum(A, G, qMod, P);
inf = G.x == qMod.x;
if (inf)
{
qMod.IsInf = true;
qMod.OrderN = cnt;
}
ret.Add(qMod);
++cnt;
}
return(ret);
}
private static EcModPoint pointDouble(EcModPoint point, BigInteger a, BigInteger p)
{
// compute m = dy/dx = dy * dx^-1 (mod p)
var x0 = point.x;
var y0 = point.y;
BigInteger dy = (3 * x0 * x0 + a) % p;
BigInteger dx = (2 * y0) % p;
dy = (dy + p) % p;
dx = (dx + p) % p;
// compute inverse of dx mod p
BigInteger inv_dx = dx.ModInv(p);
// compute m mod p
BigInteger m = BigInteger.Multiply(dy, inv_dx) % p;
m = (m + p) % p;
var x = (m * m - 2 * x0) % p;
x = (x + p) % p;
var y = (m * (x0 - x) - y0) % p; //(-m * m * m + 3 * m * x0 - y0) % p;
y = (y + p) % p;
EcModPoint ret = new EcModPoint {
x = x, y = y
};
return(ret);
}
/// <summary>
/// Returns the final point via summation. This method is very slow. Do not use big value for Sk.
/// </summary>
/// <param name="A"></param>
/// <param name="G"></param>
/// <param name="Sk"></param>
/// <returns></returns>
public static EcModPoint EcSlowKeyPairGeneratorByClassicPointSum(BigInteger P, BigInteger A, EcModPoint G, int Sk)
{
int cnt = 2;
bool inf = false;
EcModPoint qMod = null;
while (cnt <= Sk && !inf)
{
qMod = computePointSum(A, G, qMod, P);
inf = G.x == qMod.x;
++cnt;
}
return(qMod);
}
private static EcModPoint computeECPointMultiply(BigInteger a, EcModPoint g, BigInteger p, BigInteger sk)
{
var bitString = sk.ToBinaryString();
EcModPoint q = g;
foreach (var bit in bitString)
{
q = pointDouble(q, a, p);
if (bit == '1')
{
q = pointAdd(q, g, p);
}
}
return(q);
}
private static EcModPoint computePointSum(BigInteger a, EcModPoint pointP, EcModPoint pointQ, BigInteger p)
{
BigInteger x2 = 0;
BigInteger y2 = 0;
BigInteger m = 0;
EcModPoint ret = null;
if (null == pointQ) // P1 = P0, P2 = P0 + P1 = 2P0
{
ret = pointDouble(pointP, a, p);
}
else // P2 = P0 + P1
{
ret = pointAdd(pointP, pointQ, p);
}
return(ret);
}
/// <summary>
/// Return point Q coords representing public key pair (see specs for secp256k1 parameters)
/// </summary>
/// <returns></returns>
public static EcModPoint SecP256k1KeyPairGenerator(BigInteger Sk)
{
// Big prime
var p = BigInteger.Parse("115792089237316195423570985008687907853269984665640564039457584007908834671663");
// Elliptic curve equation: y^2 = x^3 + a*x + b => y^2 = x^3 + 7
var a = 0;
var b = 7;
// Generator coordinates
EcModPoint G = new EcModPoint
{
x = BigInteger.Parse("55066263022277343669578718895168534326250603453777594175500187360389116729240"),
y = BigInteger.Parse("32670510020758816978083085130507043184471273380659243275938904335757337482424")
};
// Order of G
var ordG = BigInteger.Parse("115792089237316195423570985008687907852837564279074904382605163141518161494337");
return(ECKeyPairGenerator(p, a, b, G, ordG, Sk));
}
/// <summary>
/// Returns the list of points by addition (P + Q). This method is very slow. Do not use big value for Sk.
/// </summary>
/// <param name="P"></param>
/// <param name="A"></param>
/// <param name="G"></param>
/// <param name="Sk"></param>
/// <returns></returns>
public static List <EcModPoint> EcSlowPointListByAddition(BigInteger P, BigInteger A, EcModPoint G, int Sk)
{
var ret = new List <EcModPoint>();
ret.Add(G);
int cnt = 2;
bool inf = false;
EcModPoint qMod = null;
while (cnt <= Sk && !inf)
{
qMod = computePointSum(A, G, qMod, P);
inf = G.x == qMod.x;
ret.Add(qMod);
++cnt;
}
return(ret);
}
/// <summary>
/// Dencrypt text on elliptic curve and return the message
/// </summary>
/// <param name="LstEncr"></param>
/// <param name="SecretKey"></param>
/// <returns></returns>
public static string EcDecrypt(List <EcModPoint> LstEncr, BigInteger SecretKey, EllipticCurveType EcType)
{
BigInteger p;
BigInteger n;
BigInteger a;
BigInteger b;
// Set params
switch (EcType)
{
case EllipticCurveType.SEC256K1:
p = SEC256K1_P;
n = SEC256K1_N;
a = SEC256K1_A;
b = SEC256K1_B;
break;
case EllipticCurveType.M383:
p = M383_P;
n = M383_N;
a = M383_A;
b = M383_B;
break;
case EllipticCurveType.E521:
p = E521_P;
n = E521_N;
a = E521_A;
b = E521_B;
break;
default:
break;
}
// 1) get kG
var kG = LstEncr.First();
// 2) compute kPb = k(SkG) = Sk(kG)
var kPb = ECKeyPairGenerator(p, a, b, kG, n, SecretKey);
// set -kPb
var negkPb = new EcModPoint {
x = kPb.x, y = -kPb.y
};
// remove kG from the list
LstEncr.RemoveAt(0);
// 3) decrypt - compute Pc - kPb = Pm (plain message)
var strMsg = string.Empty;
foreach (var pnt in LstEncr)
{
var decPnt = pointAdd(pnt, negkPb, p);
// data from x coord
var arrUShort = Base65536Helper.ToArray(decPnt.x);
var bytes = arrUShort.ToByteArray();
var str = Encoding.Unicode.GetString(bytes);
strMsg = string.Concat(strMsg, str);
// data from y coord
arrUShort = Base65536Helper.ToArray(decPnt.y);
bytes = arrUShort.ToByteArray();
str = Encoding.Unicode.GetString(bytes);
strMsg = string.Concat(strMsg, str);
}
return(strMsg);
}
/// <summary>
/// Encrypt text on elliptic curve and return a list of points on the elliptic curve
/// </summary>
/// <param name="Text"></param>
/// <param name="PubKey"></param>
/// <returns></returns>
public static List <EcModPoint> EcEncrypt(string Text, EcModPoint PubKey, EllipticCurveType EcType)
{
BigInteger p;
BigInteger n;
BigInteger a;
BigInteger b;
// Set params
switch (EcType)
{
case EllipticCurveType.SEC256K1:
p = SEC256K1_P;
n = SEC256K1_N;
a = SEC256K1_A;
b = SEC256K1_B;
break;
case EllipticCurveType.M383:
p = M383_P;
n = M383_N;
a = M383_A;
b = M383_B;
break;
case EllipticCurveType.E521:
p = E521_P;
n = E521_N;
a = E521_A;
b = E521_B;
break;
default:
break;
}
// return the digits of P base 65536
ushort[] digits = Base65536Helper.ToArray(p);
var partitionLen = digits.Length - 1;
// return a string array with string spit in groups of digits
var partitionStrings = Text.SplitInGroup(partitionLen);
// 1) create a list of big integers out of partitioned message
List <BigInteger> lstBiMsg = new List <BigInteger>();
foreach (var partitionStr in partitionStrings)
{
// encode the partioned str in Unicode
var encUtf8 = Encoding.Unicode.GetBytes(partitionStr);
// convert to ushort array
var arrShort = encUtf8.ToUShortArray();
// convert to Base 65536 big integer
var bi65536 = Base65536Helper.FromArray(arrShort);
// add to the list
lstBiMsg.Add(bi65536);
}
// 2) pair with ascii 32 (space) if list count is odd
var lstCnt = lstBiMsg.Count;
if (0 != lstCnt % 2)
{
lstBiMsg.Add(32);
lstCnt++;
}
// 3) build the pairs
List <EcModPoint> lstPm = new List <EcModPoint>();
for (int i = 0; i < lstCnt; i += 2)
{
var pnt = new EcModPoint {
x = lstBiMsg[i], y = lstBiMsg[i + 1]
};
lstPm.Add(pnt);
}
// get a random big integer k
var k = BigIntegerExtensions.NextBigInteger(185, DateTime.Now.Millisecond);
// 4) compute k*G for the chosen curve
EcModPoint kG = null;
switch (EcType)
{
case EllipticCurveType.SEC256K1:
kG = SecP256k1KeyPairGenerator(k);
break;
case EllipticCurveType.M383:
kG = M383KeyPairGenerator(k);
break;
case EllipticCurveType.E521:
kG = E521KeyPairGenerator(k);
break;
default:
break;
}
// 5) compute kPb = k(SkG)
var kPb = ECKeyPairGenerator(p, a, b, PubKey, n, k);
// 6) compute Pm + kPb = Pc (encrypted data)
List <EcModPoint> lstEncr = new List <EcModPoint>();
// first row is kG
lstEncr.Add(kG);
foreach (var pnt in lstPm)
{
var pntAdded = pointAdd(pnt, kPb, p);
lstEncr.Add(pntAdded);
}
return(lstEncr);
}
/// <summary>
/// Returns the key pair
/// </summary>
/// <param name="P"></param>
/// <param name="A"></param>
/// <param name="B"></param>
/// <param name="G"></param>
/// <param name="N"></param>
/// <param name="SecretKey"></param>
/// <returns></returns>
public static EcModPoint ECKeyPairGenerator(BigInteger P, BigInteger A, BigInteger B, EcModPoint G, BigInteger N, BigInteger SecretKey)
{
// If private key Sk is not in the range 0 < Sk < N (order of G) then error
if (SecretKey < 1 || SecretKey >= N)
{
throw new Exception("Private key is not in the range.");
}
// Check the discriminant for the eliptic curve y^2 = x^3 + a*x + b: -16(4a^3 + 27b^2) != 0
var delta = 4 * A * A * A + 27 * B * B;
if (0 == delta)
{
throw new Exception("Delta cannot be zero.");
}
return(computeECPointMultiply(A, G, P, SecretKey));
}
