public FiniteFieldPolynomial(IrreduciblePolynomial primePolynomial, params int[] setCoefficients) {
_PrimePolynomial = primePolynomial;
_PolynomialSetCoefficients = BigInteger.Zero;
for (int i = 0; i < setCoefficients.Length; i++) {
_PolynomialSetCoefficients = _PolynomialSetCoefficients.SetBit(setCoefficients[i]);
}
}
private static IEnumerable<FiniteFieldPolynomial> GetRandomPolynomials(IrreduciblePolynomial irreduciblePolynomial, int total) {
var rng = RandomNumberGenerator.Create();
for (int i = 0; i < total; i++) {
var randomCoefficientBytes = new byte[irreduciblePolynomial.SizeInBytes];
rng.GetBytes(randomCoefficientBytes);
yield return new FiniteFieldPolynomial(irreduciblePolynomial, randomCoefficientBytes.ToBigIntegerFromLittleEndianUnsignedBytes());
}
}
public FiniteFieldPolynomial(IrreduciblePolynomial primePolynomial, params int[] setCoefficients)
{
_PrimePolynomial = primePolynomial;
_PolynomialSetCoefficients = BigInteger.Zero;
for (int i = 0; i < setCoefficients.Length; i++)
{
_PolynomialSetCoefficients = _PolynomialSetCoefficients.SetBit(setCoefficients[i]);
}
}
public void TestInverse() {
var rijndaelPoly = new IrreduciblePolynomial(8);
var a = new FiniteFieldPolynomial(rijndaelPoly, 6, 4, 1, 0);
var expectedInverse = new FiniteFieldPolynomial(rijndaelPoly, 7, 6, 3, 1);
var actualInverse = a.GetInverse();
Assert.AreEqual(expectedInverse.ToString(), actualInverse.ToString());
var productSanityCheck = a*actualInverse;
Assert.IsTrue(productSanityCheck.One.Equals(productSanityCheck));
}
internal static bool TryParse(Match match, out FiniteFieldPoint result)
{
if (!match.Success)
{
result = null;
return(false);
}
try {
var xString = match.Groups["x"].Value.ToLowerInvariant();
var yString = match.Groups["y"].Value.ToLowerInvariant();
// get rid of any initial 0's
while (xString.StartsWith("0", StringComparison.Ordinal))
{
xString = xString.Substring(1);
}
// Each hex letter makes up 4 bits, so to get the degree in bits
// we multiply by 4
int polynomialDegree = yString.Length * 4;
var irp = new IrreduciblePolynomial(polynomialDegree);
var x = new FiniteFieldPolynomial(irp, BigInteger.Parse(xString));
// get bytes
var bigEndianBytes = new byte[yString.Length / 2];
for (int i = 0; i < yString.Length; i += 2)
{
bigEndianBytes[i / 2] = Byte.Parse(yString.Substring(i, 2), NumberStyles.HexNumber);
}
var y = new FiniteFieldPolynomial(irp, bigEndianBytes.ToBigIntegerFromBigEndianUnsignedBytes());
result = new FiniteFieldPoint(x, y);
return(true);
}
catch (Exception exception) {
result = null;
return(false);
}
}
public void BasicTests() {
var rijndaelPoly = new IrreduciblePolynomial(8);
var a = new FiniteFieldPolynomial(rijndaelPoly, 6, 4, 1, 0);
var b = new FiniteFieldPolynomial(rijndaelPoly, 7, 6, 3, 1);
var product = a*b;
// "a" and "b" are inverses, so their product is 1
Assert.AreEqual(1, (int)product.PolynomialValue);
var g = new FiniteFieldPolynomial(rijndaelPoly, BigInteger.Parse("0e5", NumberStyles.HexNumber));
var p = new FiniteFieldPolynomial(rijndaelPoly, BigInteger.One);
// g is a generator, so we should generate all values except 0
var vals = new HashSet<BigInteger> {p.PolynomialValue};
for (int i = 0; i < 255; i++) {
p = p*g;
vals.Add(p.PolynomialValue);
}
Assert.AreEqual(255, vals.Count);
Assert.IsTrue(vals.Contains((p*g).PolynomialValue));
}
internal static bool TryParse(Match match, out FiniteFieldPoint result) {
if (!match.Success) {
result = null;
return false;
}
try {
var xString = match.Groups["x"].Value.ToLowerInvariant();
var yString = match.Groups["y"].Value.ToLowerInvariant();
// get rid of any initial 0's
while (xString.StartsWith("0", StringComparison.Ordinal)) {
xString = xString.Substring(1);
}
// Each hex letter makes up 4 bits, so to get the degree in bits
// we multiply by 4
int polynomialDegree = yString.Length*4;
var irp = new IrreduciblePolynomial(polynomialDegree);
var x = new FiniteFieldPolynomial(irp, BigInteger.Parse(xString));
// get bytes
var bigEndianBytes = new byte[yString.Length/2];
for (int i = 0; i < yString.Length; i += 2) {
bigEndianBytes[i/2] = Byte.Parse(yString.Substring(i, 2), NumberStyles.HexNumber);
}
var y = new FiniteFieldPolynomial(irp, bigEndianBytes.ToBigIntegerFromBigEndianUnsignedBytes());
result = new FiniteFieldPoint(x, y);
return true;
}
catch(Exception exception) {
result = null;
return false;
}
}
public FiniteFieldPolynomial(IrreduciblePolynomial primePolynomial, BigInteger polynomial) {
_PrimePolynomial = primePolynomial;
_PolynomialSetCoefficients = polynomial;
}
public FiniteFieldPolynomial(IrreduciblePolynomial primePolynomial, BigInteger polynomial)
{
_PrimePolynomial = primePolynomial;
_PolynomialSetCoefficients = polynomial;
}
public SplitSecret(SecretShareType shareType, int threshold, IrreduciblePolynomial irreduciblePolynomial, FiniteFieldPolynomial[] allCoefficients, SecureString passPhrase = null)
{
_ShareType = shareType;
Threshold = threshold;
_IrreduciblePolynomial = irreduciblePolynomial;
_AllCoefficients = allCoefficients;
_PassPhrase = passPhrase;
}
