/// <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 }); }