/// <summary>
/// Recreate a secret from the specified shares.
/// </summary>
/// <param name="Shares">The shares to be recombined.</param>
public Secret(KeyShare[] Shares) {
this.Key = Combine(Shares);
}
/// <summary>
/// Recreate a secret from shares specified as Base32 encoded strings.
/// </summary>
/// <param name="Shares">The shares to be recombined.</param>
public Secret (string[] Shares) {
var KeyShares = new KeyShare[Shares.Length];
int i = 0;
foreach (var Share in Shares) {
var Bytes = BaseConvert.FromBase32String(Share);
KeyShares[i++] = new KeyShare(Bytes);
}
this.Key = Combine(KeyShares);
}
static byte[] CombineNK(KeyShare[] Shares) {
var Threshold = Shares[0].Threshold;
if (Shares.Length < Threshold) throw new Throw("Not Enough Shares");
var Modulus = BigInteger.Pow(2, 129) - 25;
BigInteger Accum = 0;
//Console.WriteLine("Modulus = {0} ", Modulus);
for (var Formula = 0; Formula < Threshold; Formula++) {
var Value = Shares[Formula].Value;
//Console.WriteLine("Value = {0} ", Value);
BigInteger Numerator = 1, Denominator = 1;
for (var Count = 0; Count < Threshold; Count++) {
if (Formula == Count) continue; // If not the same value
var Start = Shares[Formula].Index;
var Next = Shares[Count].Index;
Numerator = (Numerator * -Next) % Modulus;
Denominator = (Denominator * (Start - Next)) % Modulus;
}
var InvDenominator = ModInverse(Denominator, Modulus);
//Console.WriteLine(" Numerator = {0}", Numerator);
//Console.WriteLine(" Denominator = {0}", Denominator);
//Console.WriteLine(" InvDenominator = {0}", InvDenominator);
Accum = (Modulus + Modulus + Accum + (Value * Numerator * InvDenominator)) % Modulus;
if (Accum < 0) {
//Console.WriteLine("Accum = {0}\n", Accum);
}
}
//Console.WriteLine("Accum = {0} ", Accum);
return GetBytes (Accum);
}
static byte[] CombineN(KeyShare[] Shares) {
var KeyBytes = Shares[0].Key.Length;
byte[] Result = new byte[KeyBytes - 1];
foreach (var Share in Shares) {
ArrayXOR1(Result, Share.Key);
}
return Result;
}
static byte[] Combine(KeyShare[] Shares) {
//var KeyBytes = 16; //Shares[0].Key.Length;
var Threshold = Shares[0].Threshold;
foreach (var Share in Shares) {
//if (Share.Key.Length != KeyBytes) {
// throw new Exception("Keys must be same length");
// }
if (Share.Threshold != Threshold) {
throw new Throw("Keys must have same threshold");
}
}
if (Shares[0].Index == 16) {
return CombineN(Shares);
}
else {
return CombineNK(Shares);
}
}
/// <summary>
/// Create a set of N key shares with a quorum of N.
/// </summary>
/// <returns>The key shares created.</returns>
public KeyShare[] Split(int N) {
var KeyShares = new KeyShare[N];
var Threshold = (16 * N) + 15;
var XOR = new byte[KeyBytes];
Array.Copy(Key, XOR, KeyBytes);
for (int i = 0; i < N - 1; i++) {
var Bytes = CryptoCatalog.GetBytes(KeyBytes);
KeyShares[i] = new KeyShare(Threshold, Bytes);
ArrayXOR(XOR, Bytes);
}
KeyShares[N - 1] = new KeyShare(Threshold, XOR);
return KeyShares;
}
/// <summary>
/// Create a set of N key shares with a quorum of K.
/// </summary>
/// <param name="N">Number of key shares to create (max is 32).</param>
/// <param name="K">Quorum of key shares required to reconstruct the secret.</param>
/// <returns>The key shares created.</returns>
public KeyShare[] Split(int N, int K) {
if (K > N) throw new Throw("Quorum can't exceed shares");
if (K < 2) throw new Throw("Quorum must be at least 2");
if (N < 2) throw new Throw("Shares must be at least 2");
if (N > 15) throw new Throw("Too many shares");
if (N == K) return Split(N);
if (K > 15) throw new Throw("Degree too high");
var PolyNomial = new BigInteger[K];
PolyNomial[0] = MakePositive(Key);
//Console.WriteLine("Key = {0} ", PolyNomial[0]);
for (int i = 1; i < K; i++) {
var Random = CryptoCatalog.GetBytes(KeyBytes);
PolyNomial[i] = MakePositive(Random);
}
if (KeyBits != 128) throw new Throw("Only 128 bit keys supported right now");
// 2^129-25 is a pseudo Mersene prime
var Modulus = BigInteger.Pow(2, 129) - 25;
//Console.WriteLine("Modulus = {0} ", Modulus);
var KeyShares = new KeyShare[N];
for (int i = 0; i < N; i++) {
var D = PolyMod(i + 1, PolyNomial, Modulus);
KeyShares[i] = new KeyShare((K * 16) + i, D);
//Console.WriteLine("Share {0} = {1}", i, D);
}
return KeyShares;
}