_ Git - BoarSSL/blob - Tests/TestEC.cs

   1 using System;
   2 using System.IO;
   3 using System.Text;
   4
   5 using Crypto;
   6
   7 internal class TestEC {
   8
   9         internal static void Main(string[] args)
  10         {
  11                 try {
  12                         TestECInt();
  13                 } catch (Exception e) {
  14                         Console.WriteLine(e.ToString());
  15                         Environment.Exit(1);
  16                 }
  17         }
  18
  19         internal static void TestECInt()
  20         {
  21                 TestCurve25519();
  22                 SpeedCurve(EC.Curve25519);
  23
  24                 TestCurve(NIST.P256, KAT_P256);
  25                 TestCurve(NIST.P384, KAT_P384);
  26                 TestCurve(NIST.P521, KAT_P521);
  27
  28                 SpeedCurve(NIST.P256);
  29                 SpeedCurve(NIST.P384);
  30                 SpeedCurve(NIST.P521);
  31         }
  32
  33         static void TestCurve25519()
  34         {
  35                 Console.Write("Test Curve25519: ");
  36
  37                 TestCurve25519KAT(
  38     "a546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4",
  39     "e6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c",
  40     "c3da55379de9c6908e94ea4df28d084f32eccf03491c71f754b4075577a28552");
  41                 TestCurve25519KAT(
  42     "4b66e9d4d1b4673c5ad22691957d6af5c11b6421e0ea01d42ca4169e7918ba0d",
  43     "e5210f12786811d3f4b7959d0538ae2c31dbe7106fc03c3efc4cd549c715a493",
  44     "95cbde9476e8907d7aade45cb4b873f88b595a68799fa152e6f8f7647aac7957");
  45
  46                 byte[] u = EC.Curve25519.GetGenerator(false);
  47                 byte[] k = new byte[u.Length];
  48                 Array.Copy(u, 0, k, 0, u.Length);
  49                 Byteswap(k);
  50                 byte[] nk = new byte[u.Length];
  51
  52                 for (int i = 1; i <= 1000; i ++) {
  53                         EC.Curve25519.Mul(u, k, nk, false);
  54                         Array.Copy(k, 0, u, 0, u.Length);
  55                         Byteswap(u);
  56                         Array.Copy(nk, 0, k, 0, u.Length);
  57                         Byteswap(k);
  58                         if (i == 1) {
  59                                 byte[] z = ToBin(C25519_MC_1);
  60                                 Byteswap(z);
  61                                 if (!Eq(k, z)) {
  62                                         throw new Exception(
  63                                                 "Curve25519 MC 1");
  64                                 }
  65                         } else if (i == 1000) {
  66                                 byte[] z = ToBin(C25519_MC_1000);
  67                                 Byteswap(z);
  68                                 if (!Eq(k, z)) {
  69                                         throw new Exception(
  70                                                 "Curve25519 MC 1000");
  71                                 }
  72                         }
  73                         if (i % 1000 == 0) {
  74                                 Console.Write(".");
  75                         }
  76                 }
  77
  78                 /*
  79                 Byteswap(k);
  80                 if (!Eq(k, ToBin(C25519_MC_1000000))) {
  81                         throw new Exception("Curve25519 MC 1000");
  82                 }
  83                 */
  84
  85                 Console.WriteLine(" done.");
  86         }
  87
  88         static string C25519_MC_1 = "422c8e7a6227d7bca1350b3e2bb7279f7897b87bb6854b783c60e80311ae3079";
  89         static string C25519_MC_1000 = "684cf59ba83309552800ef566f2f4d3c1c3887c49360e3875f2eb94d99532c51";
  90         /*
  91         static string C25519_MC_1000000 = "7c3911e0ab2586fd864497297e575e6f3bc601c0883c30df5f4dd2d24f665424";
  92         */
  93
  94         static void Byteswap(byte[] t)
  95         {
  96                 for (int i = 0; i < (t.Length >> 1); i ++) {
  97                         byte x = t[i];
  98                         t[i] = t[t.Length - 1 - i];
  99                         t[t.Length - 1 - i] = x;
 100                 }
 101         }
 102
 103         static void TestCurve25519KAT(string sscalar, string s_in, string s_out)
 104         {
 105                 byte[] tmp = ToBin(sscalar);
 106                 byte[] scalar = new byte[tmp.Length];
 107                 for (int i = 0; i < tmp.Length; i ++) {
 108                         scalar[i] = tmp[tmp.Length - 1 - i];
 109                 }
 110                 byte[] A = ToBin(s_in);
 111                 byte[] B = new byte[A.Length];
 112                 if (EC.Curve25519.Mul(A, scalar, B, false) != 0xFFFFFFFF) {
 113                         throw new Exception("Curve25519 multiplication failed");
 114                 }
 115                 byte[] C = ToBin(s_out);
 116                 if (!Eq(B, C)) {
 117                         throw new Exception("Curve25519 KAT failed");
 118                 }
 119                 Console.Write(".");
 120         }
 121
 122         static void TestCurve(ECCurve curve, string[] kat)
 123         {
 124                 Console.Write("Test {0}: ", curve.Name);
 125
 126                 // ====================================================
 127
 128                 /* obsolete -- DEBUG
 129                 Console.WriteLine();
 130                 ZInt p = ZInt.DecodeUnsignedBE(((ECCurvePrime)curve).mod);
 131                 ZInt a = ZInt.DecodeUnsignedBE(((ECCurvePrime)curve).a);
 132                 ZInt b = ZInt.DecodeUnsignedBE(((ECCurvePrime)curve).b);
 133                 Console.WriteLine("p  = {0}", p.ToHexString());
 134                 Console.WriteLine("a  = {0}", a.ToHexString());
 135                 Console.WriteLine("b  = {0}", b.ToHexString());
 136                 MutableECPoint F1 = curve.MakeGenerator();
 137                 byte[] enc = F1.Encode(false);
 138                 int flen = enc.Length >> 1;
 139                 for (int i = 0; i < enc.Length; i ++) {
 140                         if (i == 1 || i == 1 + (enc.Length >> 1)) {
 141                                 Console.Write(" ");
 142                         }
 143                         Console.Write("{0:X2}", enc[i]);
 144                 }
 145                 Console.WriteLine();
 146                 byte[] X = new byte[flen];
 147                 byte[] Y = new byte[flen];
 148                 Array.Copy(enc, 1, X, 0, flen);
 149                 Array.Copy(enc, 1 + flen, Y, 0, flen);
 150                 ZInt x1 = ZInt.DecodeUnsignedBE(X);
 151                 ZInt y1 = ZInt.DecodeUnsignedBE(Y);
 152                 Console.WriteLine("X1 = {0}", x1.ToHexString());
 153                 Console.WriteLine("Y1 = {0}", y1.ToHexString());
 154                 MutableECPoint F2 = F1.Dup();
 155                 F2.DoubleCT();
 156                 MutableECPoint F3 = F2.Dup();
 157                 MutableECPoint F4 = F2.Dup();
 158                 enc = F2.Encode(false);
 159                 for (int i = 0; i < enc.Length; i ++) {
 160                         if (i == 1 || i == 1 + (enc.Length >> 1)) {
 161                                 Console.Write(" ");
 162                         }
 163                         Console.Write("{0:X2}", enc[i]);
 164                 }
 165                 Console.WriteLine();
 166                 Array.Copy(enc, 1, X, 0, flen);
 167                 Array.Copy(enc, 1 + flen, Y, 0, flen);
 168                 ZInt x2 = ZInt.DecodeUnsignedBE(X);
 169                 ZInt y2 = ZInt.DecodeUnsignedBE(Y);
 170                 Console.WriteLine("X2 = {0}", x2.ToHexString());
 171                 Console.WriteLine("Y2 = {0}", y2.ToHexString());
 172                 if ((x1 * x1 * x1 + a * x1 + b - y1 * y1) % p != 0) {
 173                         throw new Exception("Generator not on curve");
 174                 }
 175                 if ((x2 * x2 * x2 + a * x2 + b - y2 * y2) % p != 0) {
 176                         throw new Exception("Double not on curve");
 177                 }
 178
 179                 if (F3.AddCT(F1) == 0) {
 180                         throw new Exception("Addition failed");
 181                 }
 182                 MutableECPoint F5 = F3.Dup();
 183                 enc = F3.Encode(false);
 184                 for (int i = 0; i < enc.Length; i ++) {
 185                         if (i == 1 || i == 1 + (enc.Length >> 1)) {
 186                                 Console.Write(" ");
 187                         }
 188                         Console.Write("{0:X2}", enc[i]);
 189                 }
 190                 Console.WriteLine();
 191                 Array.Copy(enc, 1, X, 0, flen);
 192                 Array.Copy(enc, 1 + flen, Y, 0, flen);
 193                 ZInt x3 = ZInt.DecodeUnsignedBE(X);
 194                 ZInt y3 = ZInt.DecodeUnsignedBE(Y);
 195                 Console.WriteLine("X3 = {0}", x3.ToHexString());
 196                 Console.WriteLine("Y3 = {0}", y3.ToHexString());
 197                 if ((x3 * x3 * x3 + a * x3 + b - y3 * y3) % p != 0) {
 198                         throw new Exception("Triple not on curve");
 199                 }
 200                 ZInt l3 = ((p + y2 - y1)
 201                         * ZInt.ModPow(p + x2 - x1, p - 2, p)) % p;
 202                 ZInt x3p = (l3 * l3 + p + p - x1 - x2) % p;
 203                 ZInt y3p = (l3 * (p + x1 - x3p) + p - y1) % p;
 204                 Console.WriteLine("X3p = {0}", x3p.ToHexString());
 205                 Console.WriteLine("Y3p = {0}", y3p.ToHexString());
 206                 Console.WriteLine("[X:{0}, Y:{1}]", x3 == x3p, y3 == y3p);
 207
 208                 if (F5.AddCT(F4) == 0) {
 209                         throw new Exception("Addition failed");
 210                 }
 211                 enc = F5.Encode(false);
 212                 for (int i = 0; i < enc.Length; i ++) {
 213                         if (i == 1 || i == 1 + (enc.Length >> 1)) {
 214                                 Console.Write(" ");
 215                         }
 216                         Console.Write("{0:X2}", enc[i]);
 217                 }
 218                 Console.WriteLine();
 219                 Array.Copy(enc, 1, X, 0, flen);
 220                 Array.Copy(enc, 1 + flen, Y, 0, flen);
 221                 ZInt x5 = ZInt.DecodeUnsignedBE(X);
 222                 ZInt y5 = ZInt.DecodeUnsignedBE(Y);
 223                 Console.WriteLine("X5 = {0}", x5.ToHexString());
 224                 Console.WriteLine("Y5 = {0}", y5.ToHexString());
 225                 if ((x5 * x5 * x5 + a * x5 + b - y5 * y5) % p != 0) {
 226                         throw new Exception("Quintuple not on curve");
 227                 }
 228                 ZInt l5 = ((p + y3 - y2)
 229                         * ZInt.ModPow(p + x3 - x2, p - 2, p)) % p;
 230                 ZInt x5p = (l5 * l5 + p + p - x2 - x3) % p;
 231                 ZInt y5p = (l5 * (p + x2 - x5p) + p - y2) % p;
 232                 Console.WriteLine("X5p = {0}", x5p.ToHexString());
 233                 Console.WriteLine("Y5p = {0}", y5p.ToHexString());
 234                 Console.WriteLine("[X:{0}, Y:{1}]", x5 == x5p, y5 == y5p);
 235
 236                 F1.Set(curve.MakeGenerator());
 237                 if (F1.MulSpecCT(new byte[] { 0x05 }) == 0) {
 238                         throw new Exception("Multiplication failed");
 239                 }
 240                 enc = F1.Encode(false);
 241                 for (int i = 0; i < enc.Length; i ++) {
 242                         if (i == 1 || i == 1 + (enc.Length >> 1)) {
 243                                 Console.Write(" ");
 244                         }
 245                         Console.Write("{0:X2}", enc[i]);
 246                 }
 247                 Console.WriteLine();
 248                 Array.Copy(enc, 1, X, 0, flen);
 249                 Array.Copy(enc, 1 + flen, Y, 0, flen);
 250                 ZInt x5t = ZInt.DecodeUnsignedBE(X);
 251                 ZInt y5t = ZInt.DecodeUnsignedBE(Y);
 252                 Console.WriteLine("X5t = {0}", x5t.ToHexString());
 253                 Console.WriteLine("Y5t = {0}", y5t.ToHexString());
 254                 if ((x5t * x5t * x5t + a * x5t + b - y5t * y5t) % p != 0) {
 255                         throw new Exception("Quintuple not on curve (2)");
 256                 }
 257                 Console.WriteLine("[X:{0}, Y:{1}]", x5t == x5p, y5t == y5p);
 258
 259                 F1.Set(F5);
 260                 F2.SetZero();
 261                 if (F1.AddCT(F2) == 0) {
 262                         throw new Exception("Addition failed (+0)");
 263                 }
 264                 enc = F1.Encode(false);
 265                 for (int i = 0; i < enc.Length; i ++) {
 266                         if (i == 1 || i == 1 + (enc.Length >> 1)) {
 267                                 Console.Write(" ");
 268                         }
 269                         Console.Write("{0:X2}", enc[i]);
 270                 }
 271                 Console.WriteLine();
 272                 Array.Copy(enc, 1, X, 0, flen);
 273                 Array.Copy(enc, 1 + flen, Y, 0, flen);
 274                 ZInt x5q = ZInt.DecodeUnsignedBE(X);
 275                 ZInt y5q = ZInt.DecodeUnsignedBE(Y);
 276                 Console.WriteLine("X5q = {0}", x5q.ToHexString());
 277                 Console.WriteLine("Y5q = {0}", y5q.ToHexString());
 278                 Console.WriteLine("[X:{0}, Y:{1}]", x5q == x5p, y5q == y5p);
 279
 280                 F2.SetZero();
 281                 if (F2.AddCT(F1) == 0) {
 282                         throw new Exception("Addition failed (0+)");
 283                 }
 284                 enc = F2.Encode(false);
 285                 for (int i = 0; i < enc.Length; i ++) {
 286                         if (i == 1 || i == 1 + (enc.Length >> 1)) {
 287                                 Console.Write(" ");
 288                         }
 289                         Console.Write("{0:X2}", enc[i]);
 290                 }
 291                 Console.WriteLine();
 292                 Array.Copy(enc, 1, X, 0, flen);
 293                 Array.Copy(enc, 1 + flen, Y, 0, flen);
 294                 ZInt x5r = ZInt.DecodeUnsignedBE(X);
 295                 ZInt y5r = ZInt.DecodeUnsignedBE(Y);
 296                 Console.WriteLine("X5r = {0}", x5r.ToHexString());
 297                 Console.WriteLine("Y5r = {0}", y5r.ToHexString());
 298                 Console.WriteLine("[X:{0}, Y:{1}]", x5r == x5p, y5r == y5p);
 299
 300                 EC rG = EC.Make(p.ToBytesUnsignedBE(),
 301                         a.ToBytesUnsignedBE(), b.ToBytesUnsignedBE());
 302                 rG.Set(x1.ToBytesUnsignedBE(), y1.ToBytesUnsignedBE());
 303                 for (int i = 1; i <= 30; i ++) {
 304                         Console.Write(".");
 305                         ZInt n = ZInt.MakeRand(i);
 306                         byte[] nb = n.ToBytesUnsignedBE();
 307                         F1 = curve.MakeGenerator();
 308                         if (F1.MulSpecCT(nb) == 0) {
 309                                 throw new Exception("Multiplication error");
 310                         }
 311                         enc = F1.Encode(false);
 312                         ZInt xp, yp;
 313                         if (enc.Length == 1) {
 314                                 xp = 0;
 315                                 yp = 0;
 316                         } else {
 317                                 Array.Copy(enc, 1, X, 0, flen);
 318                                 Array.Copy(enc, 1 + flen, Y, 0, flen);
 319                                 xp = ZInt.DecodeUnsignedBE(X);
 320                                 yp = ZInt.DecodeUnsignedBE(Y);
 321                         }
 322                         EC rH = rG.Dup();
 323                         rH.Mul(nb);
 324                         ZInt xh = ZInt.DecodeUnsignedBE(rH.X);
 325                         ZInt yh = ZInt.DecodeUnsignedBE(rH.Y);
 326                         if (xp != xh || yp != yh) {
 327                                 Console.WriteLine();
 328                                 Console.WriteLine("n = {0}", n);
 329                                 Console.WriteLine("xp = {0}", xp.ToHexString());
 330                                 Console.WriteLine("yp = {0}", yp.ToHexString());
 331                                 Console.WriteLine("xh = {0}", xh.ToHexString());
 332                                 Console.WriteLine("yh = {0}", yh.ToHexString());
 333                                 throw new Exception("Bad mult result");
 334                         }
 335                 }
 336                 Console.WriteLine();
 337                 */
 338
 339                 // ====================================================
 340
 341                 curve.CheckValid();
 342                 MutableECPoint G = curve.MakeGenerator();
 343                 if (G.IsInfinity) {
 344                         throw new Exception("Generator is infinity");
 345                 }
 346                 MutableECPoint P = G.Dup();
 347                 MutableECPoint Q = G.Dup();
 348                 MutableECPoint R = G.Dup();
 349                 MutableECPoint S = G.Dup();
 350                 MutableECPoint T = G.Dup();
 351
 352                 for (int i = 0; i < 10; i ++) {
 353                         Console.Write(".");
 354                         byte[] u, v, w;
 355                         u = MakeRandPoint(P);
 356                         do {
 357                                 v = MakeRandPoint(Q);
 358                         } while (BigInt.Compare(u, v) == 0);
 359                         // byte[] s = BigInt.Add(u, v);
 360                         byte[] t;
 361                         do {
 362                                 w = MakeRandPoint(R);
 363                                 t = BigInt.Add(v, w);
 364                         } while (BigInt.Compare(u, w) == 0
 365                                 || BigInt.Compare(v, w) == 0
 366                                 || BigInt.Compare(u, t) == 0);
 367                         if (P.Eq(Q) || P.Eq(R) || Q.Eq(R)) {
 368                                 throw new Exception("Equal points");
 369                         }
 370                         S.Set(P);
 371                         Add(S, Q);
 372                         Add(S, R);
 373                         T.Set(Q);
 374                         Add(T, R);
 375                         Add(T, P);
 376                         if (!S.Eq(T) || !T.Eq(S)) {
 377                                 throw new Exception("Associativity error");
 378                         }
 379                         S.Normalize();
 380                         if (!S.Eq(T) || !T.Eq(S)) {
 381                                 throw new Exception("Normalization error (1)");
 382                         }
 383                         T.Normalize();
 384                         if (!S.Eq(T) || !T.Eq(S)) {
 385                                 throw new Exception("Normalization error (2)");
 386                         }
 387
 388                         byte[] enc1 = P.Encode(false);
 389                         byte[] enc2 = P.Encode(true);
 390                         byte[] enc3 = new byte[enc1.Length];
 391                         Array.Copy(enc1, 1, enc3, 1, enc1.Length - 1);
 392                         enc3[0] = (byte)(enc2[0] | 0x04);
 393                         Q.Decode(enc1);
 394                         if (!P.Eq(Q) || !Q.Eq(P)) {
 395                                 throw new Exception("Encode/decode error 1");
 396                         }
 397                         Q.Decode(enc2);
 398                         if (!P.Eq(Q) || !Q.Eq(P)) {
 399                                 throw new Exception("Encode/decode error 2");
 400                         }
 401                         Q.Decode(enc3);
 402                         if (!P.Eq(Q) || !Q.Eq(P)) {
 403                                 throw new Exception("Encode/decode error 3");
 404                         }
 405                 }
 406
 407                 Console.Write(" ");
 408                 for (int i = 0; i < kat.Length; i += 2) {
 409                         P.Set(G);
 410                         byte[] n = ToBin(kat[i]);
 411                         if (P.MulSpecCT(n) == 0) {
 412                                 throw new Exception("Multiplication error");
 413                         }
 414                         byte[] er = ToBin(kat[i + 1]);
 415                         if (!Eq(er, P.Encode(false))) {
 416                                 throw new Exception("KAT failed");
 417                         }
 418                         byte[] eg = curve.GetGenerator(false);
 419                         byte[] ed = new byte[eg.Length];
 420                         curve.Mul(eg, n, ed, false);
 421                         if (!Eq(ed, er)) {
 422                                 throw new Exception("KAT failed (API 2)");
 423                         }
 424                         Console.Write(".");
 425                 }
 426
 427                 Console.WriteLine();
 428         }
 429
 430         static void SpeedCurve(ECCurve curve)
 431         {
 432                 byte[][] nn = new byte[100][];
 433                 for (int i = 0; i < nn.Length; i ++) {
 434                         nn[i] = BigInt.RandIntNZ(curve.SubgroupOrder);
 435                 }
 436                 MutableECPoint G = curve.MakeGenerator();
 437                 MutableECPoint P = G.Dup();
 438                 int num = 1;
 439                 for (;;) {
 440                         long orig = DateTime.Now.Ticks;
 441                         for (int i = 0, j = 0; i < num; i ++) {
 442                                 P.MulSpecCT(nn[j]);
 443                                 if (++ j == nn.Length) {
 444                                         j = 0;
 445                                 }
 446                         }
 447                         long end = DateTime.Now.Ticks;
 448                         double tt = (double)(end - orig) / 10000000.0;
 449                         if (tt < 2.0) {
 450                                 num <<= 1;
 451                                 continue;
 452                         }
 453                         double f = (double)num / tt;
 454                         Console.WriteLine("{0,10}  {1,9:f3} mul/s",
 455                                 curve.Name, f);
 456                         return;
 457                 }
 458         }
 459
 460         /*
 461          * Create a random non-infinity point by multiplying the
 462          * curve subgroup generator with a random non-zero integer
 463          * modulo the subgroup order. The multiplier is returned.
 464          */
 465         static byte[] MakeRandPoint(MutableECPoint P)
 466         {
 467                 ECCurve curve = P.Curve;
 468                 P.Set(curve.MakeGenerator());
 469                 byte[] n = BigInt.RandIntNZ(curve.SubgroupOrder);
 470                 if (P.MulSpecCT(n) == 0) {
 471                         throw new Exception("Multiplication failed");
 472                 }
 473                 return n;
 474         }
 475
 476         static void Add(MutableECPoint P, MutableECPoint Q)
 477         {
 478                 if (P.Eq(Q)) {
 479                         P.DoubleCT();
 480                 } else {
 481                         if (P.AddCT(Q) == 0) {
 482                                 throw new Exception("Addition failed");
 483                         }
 484                 }
 485         }
 486
 487         static bool Eq(byte[] a1, byte[] a2)
 488         {
 489                 if (a1 == a2) {
 490                         return true;
 491                 }
 492                 if (a1 == null || a2 == null) {
 493                         return false;
 494                 }
 495                 int n = a1.Length;
 496                 if (n != a2.Length) {
 497                         return false;
 498                 }
 499                 for (int i = 0; i < n; i ++) {
 500                         if (a1[i] != a2[i]) {
 501                                 return false;
 502                         }
 503                 }
 504                 return true;
 505         }
 506
 507         static byte[] ToBin(string str)
 508         {
 509                 MemoryStream ms = new MemoryStream();
 510                 bool z = true;
 511                 int acc = 0;
 512                 foreach (char c in str) {
 513                         int d;
 514                         if (c >= '0' && c <= '9') {
 515                                 d = c - '0';
 516                         } else if (c >= 'A' && c <= 'F') {
 517                                 d = c - ('A' - 10);
 518                         } else if (c >= 'a' && c <= 'f') {
 519                                 d = c - ('a' - 10);
 520                         } else if (c == ' ' || c == '\t' || c == ':') {
 521                                 continue;
 522                         } else {
 523                                 throw new ArgumentException(String.Format(
 524                                         "not hex: U+{0:X4}", (int)c));
 525                         }
 526                         if (z) {
 527                                 acc = d;
 528                         } else {
 529                                 ms.WriteByte((byte)((acc << 4) + d));
 530                         }
 531                         z = !z;
 532                 }
 533                 if (!z) {
 534                         throw new ArgumentException("final half byte");
 535                 }
 536                 return ms.ToArray();
 537         }
 538
 539         static string[] KAT_P256 = {
 540                 "C9AFA9D845BA75166B5C215767B1D6934E50C3DB36E89B127B8A622B120F6721",
 541                 "0460FED4BA255A9D31C961EB74C6356D68C049B8923B61FA6CE669622E60F29FB67903FE1008B8BC99A41AE9E95628BC64F2F1B20C2D7E9F5177A3C294D4462299"
 542         };
 543
 544         static string[] KAT_P384 = {
 545                 "6B9D3DAD2E1B8C1C05B19875B6659F4DE23C3B667BF297BA9AA47740787137D896D5724E4C70A825F872C9EA60D2EDF5",
 546                 "04EC3A4E415B4E19A4568618029F427FA5DA9A8BC4AE92E02E06AAE5286B300C64DEF8F0EA9055866064A254515480BC138015D9B72D7D57244EA8EF9AC0C621896708A59367F9DFB9F54CA84B3F1C9DB1288B231C3AE0D4FE7344FD2533264720"
 547         };
 548
 549         static string[] KAT_P521 = {
 550                 "00FAD06DAA62BA3B25D2FB40133DA757205DE67F5BB0018FEE8C86E1B68C7E75CAA896EB32F1F47C70855836A6D16FCC1466F6D8FBEC67DB89EC0C08B0E996B83538",
 551                 "0401894550D0785932E00EAA23B694F213F8C3121F86DC97A04E5A7167DB4E5BCD371123D46E45DB6B5D5370A7F20FB633155D38FFA16D2BD761DCAC474B9A2F5023A400493101C962CD4D2FDDF782285E64584139C2F91B47F87FF82354D6630F746A28A0DB25741B5B34A828008B22ACC23F924FAAFBD4D33F81EA66956DFEAA2BFDFCF5"
 552         };
 553 }