/// <summary>
/// Generate an encryption Key pair
/// </summary>
///
/// <returns>A McElieceKeyPair containing public and private keys</returns>
public IAsymmetricKeyPair GenerateKeyPair()
{
// finite field GF(2^m)
GF2mField field = new GF2mField(_M, _fieldPoly);
// irreducible Goppa polynomial
PolynomialGF2mSmallM gp = new PolynomialGF2mSmallM(field, _T, PolynomialGF2mSmallM.RANDOM_IRREDUCIBLE_POLYNOMIAL, _rndEngine);
PolynomialRingGF2m ring = new PolynomialRingGF2m(field, gp);
// matrix for computing square roots in (GF(2^m))^t
PolynomialGF2mSmallM[] qInv = ring.SquareRootMatrix;
// generate canonical check matrix
GF2Matrix h = GoppaCode.CreateCanonicalCheckMatrix(field, gp);
// compute short systematic form of check matrix
GoppaCode.MaMaPe mmp = GoppaCode.ComputeSystematicForm(h, _rndEngine);
GF2Matrix shortH = mmp.SecondMatrix;
Permutation p = mmp.Permutation;
// compute short systematic form of generator matrix
GF2Matrix shortG = (GF2Matrix)shortH.ComputeTranspose();
// obtain number of rows of G (= dimension of the code)
int k = shortG.RowCount;
// generate keys
IAsymmetricKey pubKey = new MPKCPublicKey(_N, _T, shortG);
IAsymmetricKey privKey = new MPKCPrivateKey(_N, k, field, gp, p, h, qInv);
// return key pair
return(new MPKCKeyPair(pubKey, privKey));
}
/// <summary>
/// The McEliece decryption primitive
/// </summary>
///
/// <param name="PrivateKey">The private key</param>
/// <param name="C">The ciphertext vector <c>c = m*G + z</c></param>
///
/// <returns>The message vector <c>m</c> and the error vector <c>z</c></returns>
public static GF2Vector[] Decrypt(MPKCPrivateKey PrivateKey, GF2Vector C)
{
// obtain values from private key
int k = PrivateKey.K;
Permutation p = PrivateKey.P1;
GF2mField field = PrivateKey.GF;
PolynomialGF2mSmallM gp = PrivateKey.GP;
GF2Matrix h = PrivateKey.H;
PolynomialGF2mSmallM[] q = PrivateKey.QInv;
// compute inverse permutation P^-1
Permutation pInv = p.ComputeInverse();
// multiply c with permutation P^-1
GF2Vector cPInv = (GF2Vector)C.Multiply(pInv);
// compute syndrome of cP^-1
GF2Vector syndVec = (GF2Vector)h.RightMultiply(cPInv);
// decode syndrome
GF2Vector errors = GoppaCode.SyndromeDecode(syndVec, field, gp, q);
GF2Vector mG = (GF2Vector)cPInv.Add(errors);
// multiply codeword and error vector with P
mG = (GF2Vector)mG.Multiply(p);
errors = (GF2Vector)errors.Multiply(p);
// extract plaintext vector (last k columns of mG)
GF2Vector m = mG.ExtractRightVector(k);
// return vectors
return(new GF2Vector[] { m, errors });
}