crypto: add simple P224 implementation.

This is intended to be the underlying group for an EKE implementation for
Remoting.

BUG=none
TEST=crypto_unittests

Review URL: http://codereview.chromium.org/8431007

git-svn-id: svn://svn.chromium.org/chrome/trunk/src@108866 0039d316-1c4b-4281-b951-d872f2087c98

4 files changed, 1519 insertions, 0 deletions

diff --git a/crypto/crypto.gyp b/crypto/crypto.gyp
index 7b031b2..906cbed 100644
--- a/crypto/crypto.gyp
+++ b/crypto/crypto.gyp
@@ -138,6 +138,8 @@
         'openpgp_symmetric_encryption.h',
         'openssl_util.cc',
         'openssl_util.h',
+        'p224.cc',
+        'p224.h',
         'rsa_private_key.cc',
         'rsa_private_key.h',
         'rsa_private_key_mac.cc',
@@ -184,6 +186,7 @@
         # Tests.
         'encryptor_unittest.cc',
         'hmac_unittest.cc',
+        'p224_unittest.cc',
         'rsa_private_key_unittest.cc',
         'rsa_private_key_nss_unittest.cc',
         'secure_hash_unittest.cc',
diff --git a/crypto/p224.cc b/crypto/p224.cc
new file mode 100644
index 0000000..0c87a5f
--- /dev/null
+++ b/crypto/p224.cc
@@ -0,0 +1,652 @@
+// Copyright (c) 2011 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+// This is an implementation of the P224 elliptic curve group. It's written to
+// be short and simple rather than fast, although it's still constant-time.
+//
+// See http://www.imperialviolet.org/2010/12/04/ecc.html ([1]) for background.
+
+#include "crypto/p224.h"
+
+#include <string.h>
+
+#include "build/build_config.h"
+
+// For htonl and ntohl.
+#if defined(OS_WIN)
+#include <winsock2.h>
+#else
+#include <arpa/inet.h>
+#endif
+
+namespace {
+
+// Field element functions.
+//
+// The field that we're dealing with is ℤ/pℤ where p = 2**224 - 2**96 + 1.
+//
+// Field elements are represented by a FieldElement, which is a typedef to an
+// array of 8 uint32's. The value of a FieldElement, a, is:
+//   a[0] + 2**28·a[1] + 2**56·a[1] + ... + 2**196·a[7]
+//
+// Using 28-bit limbs means that there's only 4 bits of headroom, which is less
+// than we would really like. But it has the useful feature that we hit 2**224
+// exactly, making the reflections during a reduce much nicer.
+
+using crypto::p224::FieldElement;
+
+// Add computes *out = a+b
+//
+// a[i] + b[i] < 2**32
+void Add(FieldElement* out, const FieldElement& a, const FieldElement& b) {
+  for (int i = 0; i < 8; i++) {
+    (*out)[i] = a[i] + b[i];
+  }
+}
+
+static const uint32 kTwo31p3 = (1u<<31) + (1u<<3);
+static const uint32 kTwo31m3 = (1u<<31) - (1u<<3);
+static const uint32 kTwo31m15m3 = (1u<<31) - (1u<<15) - (1u<<3);
+// kZero31ModP is 0 mod p where bit 31 is set in all limbs so that we can
+// subtract smaller amounts without underflow. See the section "Subtraction" in
+// [1] for why.
+static const FieldElement kZero31ModP = {
+  kTwo31p3, kTwo31m3, kTwo31m3, kTwo31m15m3,
+  kTwo31m3, kTwo31m3, kTwo31m3, kTwo31m3
+};
+
+// Subtract computes *out = a-b
+//
+// a[i], b[i] < 2**30
+// out[i] < 2**32
+void Subtract(FieldElement* out, const FieldElement& a, const FieldElement& b) {
+  for (int i = 0; i < 8; i++) {
+    // See the section on "Subtraction" in [1] for details.
+    (*out)[i] = a[i] + kZero31ModP[i] - b[i];
+  }
+}
+
+static const uint64 kTwo63p35 = (1ull<<63) + (1ull<<35);
+static const uint64 kTwo63m35 = (1ull<<63) - (1ull<<35);
+static const uint64 kTwo63m35m19 = (1ull<<63) - (1ull<<35) - (1ull<<19);
+// kZero63ModP is 0 mod p where bit 63 is set in all limbs. See the section
+// "Subtraction" in [1] for why.
+static const uint64 kZero63ModP[8] = {
+  kTwo63p35, kTwo63m35, kTwo63m35, kTwo63m35,
+  kTwo63m35m19, kTwo63m35, kTwo63m35, kTwo63m35,
+};
+
+static const uint32 kBottom28Bits = 0xfffffff;
+
+// LargeFieldElement also represents an element of the field. The limbs are
+// still spaced 28-bits apart and in little-endian order. So the limbs are at
+// 0, 28, 56, ..., 392 bits, each 64-bits wide.
+typedef uint64 LargeFieldElement[15];
+
+// ReduceLarge converts a LargeFieldElement to a FieldElement.
+//
+// in[i] < 2**62
+void ReduceLarge(FieldElement* out, LargeFieldElement* inptr) {
+  LargeFieldElement& in(*inptr);
+
+  for (int i = 0; i < 8; i++) {
+    in[i] += kZero63ModP[i];
+  }
+
+  // Eliminate the coefficients at 2**224 and greater while maintaining the
+  // same value mod p.
+  for (int i = 14; i >= 8; i--) {
+    in[i-8] -= in[i];  // reflection off the "+1" term of p.
+    in[i-5] += (in[i] & 0xffff) << 12;  // part of the "-2**96" reflection.
+    in[i-4] += in[i] >> 16;  // the rest of the "-2**96" reflection.
+  }
+  in[8] = 0;
+  // in[0..8] < 2**64
+
+  // As the values become small enough, we start to store them in |out| and use
+  // 32-bit operations.
+  for (int i = 1; i < 8; i++) {
+    in[i+1] += in[i] >> 28;
+    (*out)[i] = static_cast<uint32>(in[i] & kBottom28Bits);
+  }
+  // Eliminate the term at 2*224 that we introduced while keeping the same
+  // value mod p.
+  in[0] -= in[8];  // reflection off the "+1" term of p.
+  (*out)[3] += static_cast<uint32>(in[8] & 0xffff) << 12; // "-2**96" term
+  (*out)[4] += static_cast<uint32>(in[8] >> 16);  // rest of "-2**96" term
+  // in[0] < 2**64
+  // out[3] < 2**29
+  // out[4] < 2**29
+  // out[1,2,5..7] < 2**28
+
+  (*out)[0] = static_cast<uint32>(in[0] & kBottom28Bits);
+  (*out)[1] += static_cast<uint32>((in[0] >> 28) & kBottom28Bits);
+  (*out)[2] += static_cast<uint32>(in[0] >> 56);
+  // out[0] < 2**28
+  // out[1..4] < 2**29
+  // out[5..7] < 2**28
+}
+
+// Mul computes *out = a*b
+//
+// a[i] < 2**29, b[i] < 2**30 (or vice versa)
+// out[i] < 2**29
+void Mul(FieldElement* out, const FieldElement& a, const FieldElement& b) {
+  LargeFieldElement tmp;
+  memset(&tmp, 0, sizeof(tmp));
+
+  for (int i = 0; i < 8; i++) {
+    for (int j = 0; j < 8; j++) {
+      tmp[i+j] += static_cast<uint64>(a[i]) * static_cast<uint64>(b[j]);
+    }
+  }
+
+  ReduceLarge(out, &tmp);
+}
+
+// Square computes *out = a*a
+//
+// a[i] < 2**29
+// out[i] < 2**29
+void Square(FieldElement* out, const FieldElement& a) {
+  LargeFieldElement tmp;
+  memset(&tmp, 0, sizeof(tmp));
+
+  for (int i = 0; i < 8; i++) {
+    for (int j = 0; j <= i; j++) {
+      uint64 r = static_cast<uint64>(a[i]) * static_cast<uint64>(a[j]);
+      if (i == j) {
+        tmp[i+j] += r;
+      } else {
+        tmp[i+j] += r << 1;
+      }
+    }
+  }
+
+  ReduceLarge(out, &tmp);
+}
+
+// Reduce reduces the coefficients of in_out to smaller bounds.
+//
+// On entry: a[i] < 2**31 + 2**30
+// On exit: a[i] < 2**29
+void Reduce(FieldElement* in_out) {
+  FieldElement& a = *in_out;
+
+  for (int i = 0; i < 7; i++) {
+    a[i+1] += a[i] >> 28;
+    a[i] &= kBottom28Bits;
+  }
+  uint32 top = a[7] >> 28;
+  a[7] &= kBottom28Bits;
+
+  // top < 2**4
+  // Constant-time: mask = (top != 0) ? 0xffffffff : 0
+  uint32 mask = top;
+  mask |= mask >> 2;
+  mask |= mask >> 1;
+  mask <<= 31;
+  mask = static_cast<uint32>(static_cast<int32>(mask) >> 31);
+
+  // Eliminate top while maintaining the same value mod p.
+  a[0] -= top;
+  a[3] += top << 12;
+
+  // We may have just made a[0] negative but, if we did, then we must
+  // have added something to a[3], thus it's > 2**12. Therefore we can
+  // carry down to a[0].
+  a[3] -= 1 & mask;
+  a[2] += mask & ((1<<28) - 1);
+  a[1] += mask & ((1<<28) - 1);
+  a[0] += mask & (1<<28);
+}
+
+// Invert calcuates *out = in**-1 by computing in**(2**224 - 2**96 - 1), i.e.
+// Fermat's little theorem.
+void Invert(FieldElement* out, const FieldElement& in) {
+  FieldElement f1, f2, f3, f4;
+
+  Square(&f1, in);                        // 2
+  Mul(&f1, f1, in);                       // 2**2 - 1
+  Square(&f1, f1);                        // 2**3 - 2
+  Mul(&f1, f1, in);                       // 2**3 - 1
+  Square(&f2, f1);                        // 2**4 - 2
+  Square(&f2, f2);                        // 2**5 - 4
+  Square(&f2, f2);                        // 2**6 - 8
+  Mul(&f1, f1, f2);                       // 2**6 - 1
+  Square(&f2, f1);                        // 2**7 - 2
+  for (int i = 0; i < 5; i++) {           // 2**12 - 2**6
+    Square(&f2, f2);
+  }
+  Mul(&f2, f2, f1);                       // 2**12 - 1
+  Square(&f3, f2);                        // 2**13 - 2
+  for (int i = 0; i < 11; i++) {          // 2**24 - 2**12
+    Square(&f3, f3);
+  }
+  Mul(&f2, f3, f2);                       // 2**24 - 1
+  Square(&f3, f2);                        // 2**25 - 2
+  for (int i = 0; i < 23; i++) {          // 2**48 - 2**24
+    Square(&f3, f3);
+  }
+  Mul(&f3, f3, f2);                       // 2**48 - 1
+  Square(&f4, f3);                        // 2**49 - 2
+  for (int i = 0; i < 47; i++) {          // 2**96 - 2**48
+    Square(&f4, f4);
+  }
+  Mul(&f3, f3, f4);                       // 2**96 - 1
+  Square(&f4, f3);                        // 2**97 - 2
+  for (int i = 0; i < 23; i++) {          // 2**120 - 2**24
+    Square(&f4, f4);
+  }
+  Mul(&f2, f4, f2);                       // 2**120 - 1
+  for (int i = 0; i < 6; i++) {           // 2**126 - 2**6
+    Square(&f2, f2);
+  }
+  Mul(&f1, f1, f2);                       // 2**126 - 1
+  Square(&f1, f1);                        // 2**127 - 2
+  Mul(&f1, f1, in);                       // 2**127 - 1
+  for (int i = 0; i < 97; i++) {          // 2**224 - 2**97
+    Square(&f1, f1);
+  }
+  Mul(out, f1, f3);                       // 2**224 - 2**96 - 1
+}
+
+// Contract converts a FieldElement to its minimal, distinguished form.
+//
+// On entry, in[i] < 2**32
+// On exit, in[i] < 2**28
+void Contract(FieldElement* inout) {
+  FieldElement& out = *inout;
+
+  // Reduce the coefficients to < 2**28.
+  for (int i = 0; i < 7; i++) {
+    out[i+1] += out[i] >> 28;
+    out[i] &= kBottom28Bits;
+  }
+  uint32 top = out[7] >> 28;
+  out[7] &= kBottom28Bits;
+
+  // Eliminate top while maintaining the same value mod p.
+  out[0] -= top;
+  out[3] += top << 12;
+
+  // We may just have made out[0] negative. So we carry down. If we made
+  // out[0] negative then we know that out[3] is sufficiently positive
+  // because we just added to it.
+  for (int i = 0; i < 3; i++) {
+    uint32 mask = static_cast<uint32>(static_cast<int32>(out[i]) >> 31);
+    out[i] += (1 << 28) & mask;
+    out[i+1] -= 1 & mask;
+  }
+
+  // The value is < 2**224, but maybe greater than p. In order to reduce to a
+  // unique, minimal value we see if the value is >= p and, if so, subtract p.
+
+  // First we build a mask from the top four limbs, which must all be
+  // equal to bottom28Bits if the whole value is >= p. If top4AllOnes
+  // ends up with any zero bits in the bottom 28 bits, then this wasn't
+  // true.
+  uint32 top4AllOnes = 0xffffffffu;
+  for (int i = 4; i < 8; i++) {
+    top4AllOnes &= (out[i] & kBottom28Bits) - 1;
+  }
+  top4AllOnes |= 0xf0000000;
+  // Now we replicate any zero bits to all the bits in top4AllOnes.
+  top4AllOnes &= top4AllOnes >> 16;
+  top4AllOnes &= top4AllOnes >> 8;
+  top4AllOnes &= top4AllOnes >> 4;
+  top4AllOnes &= top4AllOnes >> 2;
+  top4AllOnes &= top4AllOnes >> 1;
+  top4AllOnes =
+      static_cast<uint32>(static_cast<int32>(top4AllOnes << 31) >> 31);
+
+  // Now we test whether the bottom three limbs are non-zero.
+  uint32 bottom3NonZero = out[0] | out[1] | out[2];
+  bottom3NonZero |= bottom3NonZero >> 16;
+  bottom3NonZero |= bottom3NonZero >> 8;
+  bottom3NonZero |= bottom3NonZero >> 4;
+  bottom3NonZero |= bottom3NonZero >> 2;
+  bottom3NonZero |= bottom3NonZero >> 1;
+  bottom3NonZero =
+      static_cast<uint32>(static_cast<int32>(bottom3NonZero << 31) >> 31);
+
+  // Everything depends on the value of out[3].
+  //    If it's > 0xffff000 and top4AllOnes != 0 then the whole value is >= p
+  //    If it's = 0xffff000 and top4AllOnes != 0 and bottom3NonZero != 0,
+  //      then the whole value is >= p
+  //    If it's < 0xffff000, then the whole value is < p
+  uint32 n = out[3] - 0xffff000;
+  uint32 out3Equal = n;
+  out3Equal |= out3Equal >> 16;
+  out3Equal |= out3Equal >> 8;
+  out3Equal |= out3Equal >> 4;
+  out3Equal |= out3Equal >> 2;
+  out3Equal |= out3Equal >> 1;
+  out3Equal =
+      ~static_cast<uint32>(static_cast<int32>(out3Equal << 31) >> 31);
+
+  // If out[3] > 0xffff000 then n's MSB will be zero.
+  uint32 out3GT = ~static_cast<uint32>(static_cast<int32>(n << 31) >> 31);
+
+  uint32 mask = top4AllOnes & ((out3Equal & bottom3NonZero) | out3GT);
+  out[0] -= 1 & mask;
+  out[3] -= 0xffff000 & mask;
+  out[4] -= 0xfffffff & mask;
+  out[5] -= 0xfffffff & mask;
+  out[6] -= 0xfffffff & mask;
+  out[7] -= 0xfffffff & mask;
+}
+
+
+// Group element functions.
+//
+// These functions deal with group elements. The group is an elliptic curve
+// group with a = -3 defined in FIPS 186-3, section D.2.2.
+
+using crypto::p224::Point;
+
+// kP is the P224 prime.
+const FieldElement kP = {
+  1, 0, 0, 268431360,
+  268435455, 268435455, 268435455, 268435455,
+};
+
+// kB is parameter of the elliptic curve.
+const FieldElement kB = {
+  55967668, 11768882, 265861671, 185302395,
+  39211076, 180311059, 84673715, 188764328,
+};
+
+// AddJacobian computes *out = a+b where a != b.
+void AddJacobian(Point *out,
+                 const Point& a,
+                 const Point& b) {
+  // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#addition-add-2007-bl
+  FieldElement z1z1, z2z2, u1, u2, s1, s2, h, i, j, r, v;
+
+  // Z1Z1 = Z1²
+  Square(&z1z1, a.z);
+
+  // Z2Z2 = Z2²
+  Square(&z2z2, b.z);
+
+  // U1 = X1*Z2Z2
+  Mul(&u1, a.x, z2z2);
+
+  // U2 = X2*Z1Z1
+  Mul(&u2, b.x, z1z1);
+
+  // S1 = Y1*Z2*Z2Z2
+  Mul(&s1, b.z, z2z2);
+  Mul(&s1, a.y, s1);
+
+  // S2 = Y2*Z1*Z1Z1
+  Mul(&s2, a.z, z1z1);
+  Mul(&s2, b.y, s2);
+
+  // H = U2-U1
+  Subtract(&h, u2, u1);
+  Reduce(&h);
+
+  // I = (2*H)²
+  for (int j = 0; j < 8; j++) {
+    i[j] = h[j] << 1;
+  }
+  Reduce(&i);
+  Square(&i, i);
+
+  // J = H*I
+  Mul(&j, h, i);
+  // r = 2*(S2-S1)
+  Subtract(&r, s2, s1);
+  Reduce(&r);
+  for (int i = 0; i < 8; i++) {
+    r[i] <<= 1;
+  }
+  Reduce(&r);
+
+  // V = U1*I
+  Mul(&v, u1, i);
+
+  // Z3 = ((Z1+Z2)²-Z1Z1-Z2Z2)*H
+  Add(&z1z1, z1z1, z2z2);
+  Add(&z2z2, a.z, b.z);
+  Reduce(&z2z2);
+  Square(&z2z2, z2z2);
+  Subtract(&out->z, z2z2, z1z1);
+  Reduce(&out->z);
+  Mul(&out->z, out->z, h);
+
+  // X3 = r²-J-2*V
+  for (int i = 0; i < 8; i++) {
+    z1z1[i] = v[i] << 1;
+  }
+  Add(&z1z1, j, z1z1);
+  Reduce(&z1z1);
+  Square(&out->x, r);
+  Subtract(&out->x, out->x, z1z1);
+  Reduce(&out->x);
+
+  // Y3 = r*(V-X3)-2*S1*J
+  for (int i = 0; i < 8; i++) {
+    s1[i] <<= 1;
+  }
+  Mul(&s1, s1, j);
+  Subtract(&z1z1, v, out->x);
+  Reduce(&z1z1);
+  Mul(&z1z1, z1z1, r);
+  Subtract(&out->y, z1z1, s1);
+  Reduce(&out->y);
+}
+
+// DoubleJacobian computes *out = a+a.
+void DoubleJacobian(Point* out, const Point& a) {
+  // See http://hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-3.html#doubling-dbl-2001-b
+  FieldElement delta, gamma, beta, alpha, t;
+
+  Square(&delta, a.z);
+  Square(&gamma, a.y);
+  Mul(&beta, a.x, gamma);
+
+  // alpha = 3*(X1-delta)*(X1+delta)
+  Add(&t, a.x, delta);
+  for (int i = 0; i < 8; i++) {
+          t[i] += t[i] << 1;
+  }
+  Reduce(&t);
+  Subtract(&alpha, a.x, delta);
+  Reduce(&alpha);
+  Mul(&alpha, alpha, t);
+
+  // Z3 = (Y1+Z1)²-gamma-delta
+  Add(&out->z, a.y, a.z);
+  Reduce(&out->z);
+  Square(&out->z, out->z);
+  Subtract(&out->z, out->z, gamma);
+  Reduce(&out->z);
+  Subtract(&out->z, out->z, delta);
+  Reduce(&out->z);
+
+  // X3 = alpha²-8*beta
+  for (int i = 0; i < 8; i++) {
+          delta[i] = beta[i] << 3;
+  }
+  Reduce(&delta);
+  Square(&out->x, alpha);
+  Subtract(&out->x, out->x, delta);
+  Reduce(&out->x);
+
+  // Y3 = alpha*(4*beta-X3)-8*gamma²
+  for (int i = 0; i < 8; i++) {
+          beta[i] <<= 2;
+  }
+  Reduce(&beta);
+  Subtract(&beta, beta, out->x);
+  Reduce(&beta);
+  Square(&gamma, gamma);
+  for (int i = 0; i < 8; i++) {
+          gamma[i] <<= 3;
+  }
+  Reduce(&gamma);
+  Mul(&out->y, alpha, beta);
+  Subtract(&out->y, out->y, gamma);
+  Reduce(&out->y);
+}
+
+// CopyConditional sets *out=a if mask is 0xffffffff. mask must be either 0 of
+// 0xffffffff.
+void CopyConditional(Point* out,
+                     const Point& a,
+                     uint32 mask) {
+  for (int i = 0; i < 8; i++) {
+    out->x[i] ^= mask & (a.x[i] ^ out->x[i]);
+    out->y[i] ^= mask & (a.y[i] ^ out->y[i]);
+    out->z[i] ^= mask & (a.z[i] ^ out->z[i]);
+  }
+}
+
+// ScalarMult calculates *out = a*scalar where scalar is a big-endian number of
+// length scalar_len and != 0.
+void ScalarMult(Point* out, const Point& a,
+                const uint8* scalar, size_t scalar_len) {
+  memset(out, 0, sizeof(*out));
+  Point tmp;
+
+  uint32 first_bit = 0xffffffff;
+  for (size_t i = 0; i < scalar_len; i++) {
+    for (unsigned int bit_num = 0; bit_num < 8; bit_num++) {
+      DoubleJacobian(out, *out);
+      uint32 bit = static_cast<uint32>(static_cast<int32>(
+          (((scalar[i] >> (7 - bit_num)) & 1) << 31) >> 31));
+      AddJacobian(&tmp, a, *out);
+      CopyConditional(out, a, first_bit & bit);
+      CopyConditional(out, tmp, ~first_bit & bit);
+      first_bit = first_bit & ~bit;
+    }
+  }
+}
+
+// Get224Bits reads 7 words from in and scatters their contents in
+// little-endian form into 8 words at out, 28 bits per output word.
+void Get224Bits(uint32* out, const uint32* in) {
+  out[0] = ntohl(in[6]) & kBottom28Bits;
+  out[1] = ((ntohl(in[5]) << 4) | (ntohl(in[6]) >> 28)) & kBottom28Bits;
+  out[2] = ((ntohl(in[4]) << 8) | (ntohl(in[5]) >> 24)) & kBottom28Bits;
+  out[3] = ((ntohl(in[3]) << 12) | (ntohl(in[4]) >> 20)) & kBottom28Bits;
+  out[4] = ((ntohl(in[2]) << 16) | (ntohl(in[3]) >> 16)) & kBottom28Bits;
+  out[5] = ((ntohl(in[1]) << 20) | (ntohl(in[2]) >> 12)) & kBottom28Bits;
+  out[6] = ((ntohl(in[0]) << 24) | (ntohl(in[1]) >> 8)) & kBottom28Bits;
+  out[7] = (ntohl(in[0]) >> 4) & kBottom28Bits;
+}
+
+// Put224Bits performs the inverse operation to Get224Bits: taking 28 bits from
+// each of 8 input words and writing them in big-endian order to 7 words at
+// out.
+void Put224Bits(uint32* out, const uint32* in) {
+  out[6] = htonl((in[0] >> 0) | (in[1] << 28));
+  out[5] = htonl((in[1] >> 4) | (in[2] << 24));
+  out[4] = htonl((in[2] >> 8) | (in[3] << 20));
+  out[3] = htonl((in[3] >> 12) | (in[4] << 16));
+  out[2] = htonl((in[4] >> 16) | (in[5] << 12));
+  out[1] = htonl((in[5] >> 20) | (in[6] << 8));
+  out[0] = htonl((in[6] >> 24) | (in[7] << 4));
+}
+
+} // anonymous namespace
+
+namespace crypto {
+
+namespace p224 {
+
+bool Point::SetFromString(const base::StringPiece& in) {
+  if (in.size() != 2*28)
+    return false;
+  const uint32* inwords = reinterpret_cast<const uint32*>(in.data());
+  Get224Bits(x, inwords);
+  Get224Bits(y, inwords + 7);
+  memset(&z, 0, sizeof(z));
+  z[0] = 1;
+
+  // Check that the point is on the curve, i.e. that y² = x³ - 3x + b.
+  FieldElement lhs;
+  Square(&lhs, y);
+  Contract(&lhs);
+
+  FieldElement rhs;
+  Square(&rhs, x);
+  Mul(&rhs, x, rhs);
+
+  FieldElement three_x;
+  for (int i = 0; i < 8; i++) {
+    three_x[i] = x[i] * 3;
+  }
+  Reduce(&three_x);
+  Subtract(&rhs, rhs, three_x);
+  Reduce(&rhs);
+
+  ::Add(&rhs, rhs, kB);
+  Contract(&rhs);
+  return memcmp(&lhs, &rhs, sizeof(lhs)) == 0;
+}
+
+std::string Point::ToString() const {
+  FieldElement zinv, zinv_sq, x, y;
+
+  Invert(&zinv, this->z);
+  Square(&zinv_sq, zinv);
+  Mul(&x, this->x, zinv_sq);
+  Mul(&zinv_sq, zinv_sq, zinv);
+  Mul(&y, this->y, zinv_sq);
+
+  Contract(&x);
+  Contract(&y);
+
+  uint32 outwords[14];
+  Put224Bits(outwords, x);
+  Put224Bits(outwords + 7, y);
+  return std::string(reinterpret_cast<const char*>(outwords), sizeof(outwords));
+}
+
+void ScalarMult(const Point& in, const uint8* scalar, Point* out) {
+  ::ScalarMult(out, in, scalar, 28);
+}
+
+// kBasePoint is the base point (generator) of the elliptic curve group.
+static const Point kBasePoint = {
+  {22813985, 52956513, 34677300, 203240812,
+   12143107, 133374265, 225162431, 191946955},
+  {83918388, 223877528, 122119236, 123340192,
+   266784067, 263504429, 146143011, 198407736},
+  {1, 0, 0, 0, 0, 0, 0, 0},
+};
+
+void ScalarBaseMult(const uint8* scalar, Point* out) {
+  ::ScalarMult(out, kBasePoint, scalar, 28);
+}
+
+void Add(const Point& a, const Point& b, Point* out) {
+  AddJacobian(out, a, b);
+}
+
+void Negate(const Point& in, Point* out) {
+  // Guide to elliptic curve cryptography, page 89 suggests that (X : X+Y : Z)
+  // is the negative in Jacobian coordinates, but it doesn't actually appear to
+  // be true in testing so this performs the negation in affine coordinates.
+  FieldElement zinv, zinv_sq, y;
+  Invert(&zinv, in.z);
+  Square(&zinv_sq, zinv);
+  Mul(&out->x, in.x, zinv_sq);
+  Mul(&zinv_sq, zinv_sq, zinv);
+  Mul(&y, in.y, zinv_sq);
+
+  Subtract(&out->y, kP, y);
+  Reduce(&out->y);
+
+  memset(&out->z, 0, sizeof(out->z));
+  out->z[0] = 1;
+}
+
+}  // namespace p224
+
+}  // namespace crypto
diff --git a/crypto/p224.h b/crypto/p224.h
new file mode 100644
index 0000000..58dc0f1
--- /dev/null
+++ b/crypto/p224.h
@@ -0,0 +1,56 @@
+// Copyright (c) 2011 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#ifndef CRYPTO_P224_H_
+#define CRYPTO_P224_H_
+#pragma once
+
+#include <string>
+
+#include "base/basictypes.h"
+#include "base/string_piece.h"
+
+namespace crypto {
+
+// P224 implements an elliptic curve group, commonly known as P224 and defined
+// in FIPS 186-3, section D.2.2.
+namespace p224 {
+
+// An element of the field (ℤ/pℤ) is represented with 8, 28-bit limbs in
+// little endian order.
+typedef uint32 FieldElement[8];
+
+struct Point {
+  // SetFromString the value of the point from the 56 byte, external
+  // representation. The external point representation is an (x, y) pair of a
+  // point on the curve. Each field element is represented as a big-endian
+  // number < p.
+  bool SetFromString(const base::StringPiece& in);
+
+  // ToString returns an external representation of the Point.
+  std::string ToString() const;
+
+  // An Point is represented in Jacobian form (x/z², y/z³).
+  FieldElement x, y, z;
+};
+
+// ScalarMult computes *out = in*scalar where scalar is a 28-byte, big-endian
+// number.
+void ScalarMult(const Point& in, const uint8* scalar, Point* out);
+
+// ScalarBaseMult computes *out = g*scalar where g is the base point of the
+// curve and scalar is a 28-byte, big-endian number.
+void ScalarBaseMult(const uint8* scalar, Point* out);
+
+// Add computes *out = a+b.
+void Add(const Point& a, const Point& b, Point* out);
+
+// Negate calculates out = -a;
+void Negate(const Point& a, Point* out);
+
+}  // namespace p224
+
+}  // namespace crypto
+
+#endif  // CRYPTO_P224_H_
diff --git a/crypto/p224_unittest.cc b/crypto/p224_unittest.cc
new file mode 100644
index 0000000..1ab2ff7
--- /dev/null
+++ b/crypto/p224_unittest.cc
@@ -0,0 +1,808 @@
+// Copyright (c) 2011 The Chromium Authors. All rights reserved.
+// Use of this source code is governed by a BSD-style license that can be
+// found in the LICENSE file.
+
+#include <string.h>
+#include <stdio.h>
+
+#include "crypto/p224.h"
+
+#include "testing/gtest/include/gtest/gtest.h"
+
+using namespace crypto;
+using p224::Point;
+
+// kBasePointExternal is the P224 base point in external representation.
+static const uint8 kBasePointExternal[56] = {
+  0xb7, 0x0e, 0x0c, 0xbd, 0x6b, 0xb4, 0xbf, 0x7f,
+  0x32, 0x13, 0x90, 0xb9, 0x4a, 0x03, 0xc1, 0xd3,
+  0x56, 0xc2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xd6,
+  0x11, 0x5c, 0x1d, 0x21, 0xbd, 0x37, 0x63, 0x88,
+  0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, 0xdf, 0xe6,
+  0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64,
+  0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34,
+};
+
+// TestVector represents a test of scalar multiplication of the base point.
+// |scalar| is a big-endian scalar and |affine| is the external representation
+// of g*scalar.
+struct TestVector {
+  uint8 scalar[28];
+  uint8 affine[28*2];
+};
+
+static const int kNumNISTTestVectors = 52;
+
+// kNISTTestVectors are the NIST test vectors for P224.
+static const TestVector kNISTTestVectors[kNumNISTTestVectors] = {
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x01},
+    {0xb7, 0x0e, 0x0c, 0xbd, 0x6b, 0xb4, 0xbf, 0x7f,
+     0x32, 0x13, 0x90, 0xb9, 0x4a, 0x03, 0xc1, 0xd3,
+     0x56, 0xc2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xd6,
+     0x11, 0x5c, 0x1d, 0x21, 0xbd, 0x37, 0x63, 0x88,
+     0xb5, 0xf7, 0x23, 0xfb, 0x4c, 0x22, 0xdf, 0xe6,
+     0xcd, 0x43, 0x75, 0xa0, 0x5a, 0x07, 0x47, 0x64,
+     0x44, 0xd5, 0x81, 0x99, 0x85, 0x00, 0x7e, 0x34
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x02, },
+
+    {0x70, 0x6a, 0x46, 0xdc, 0x76, 0xdc, 0xb7, 0x67,
+     0x98, 0xe6, 0x0e, 0x6d, 0x89, 0x47, 0x47, 0x88,
+     0xd1, 0x6d, 0xc1, 0x80, 0x32, 0xd2, 0x68, 0xfd,
+     0x1a, 0x70, 0x4f, 0xa6, 0x1c, 0x2b, 0x76, 0xa7,
+     0xbc, 0x25, 0xe7, 0x70, 0x2a, 0x70, 0x4f, 0xa9,
+     0x86, 0x89, 0x28, 0x49, 0xfc, 0xa6, 0x29, 0x48,
+     0x7a, 0xcf, 0x37, 0x09, 0xd2, 0xe4, 0xe8, 0xbb,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x03, },
+    {0xdf, 0x1b, 0x1d, 0x66, 0xa5, 0x51, 0xd0, 0xd3,
+     0x1e, 0xff, 0x82, 0x25, 0x58, 0xb9, 0xd2, 0xcc,
+     0x75, 0xc2, 0x18, 0x02, 0x79, 0xfe, 0x0d, 0x08,
+     0xfd, 0x89, 0x6d, 0x04, 0xa3, 0xf7, 0xf0, 0x3c,
+     0xad, 0xd0, 0xbe, 0x44, 0x4c, 0x0a, 0xa5, 0x68,
+     0x30, 0x13, 0x0d, 0xdf, 0x77, 0xd3, 0x17, 0x34,
+     0x4e, 0x1a, 0xf3, 0x59, 0x19, 0x81, 0xa9, 0x25,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x04, },
+    {0xae, 0x99, 0xfe, 0xeb, 0xb5, 0xd2, 0x69, 0x45,
+     0xb5, 0x48, 0x92, 0x09, 0x2a, 0x8a, 0xee, 0x02,
+     0x91, 0x29, 0x30, 0xfa, 0x41, 0xcd, 0x11, 0x4e,
+     0x40, 0x44, 0x73, 0x01, 0x04, 0x82, 0x58, 0x0a,
+     0x0e, 0xc5, 0xbc, 0x47, 0xe8, 0x8b, 0xc8, 0xc3,
+     0x78, 0x63, 0x2c, 0xd1, 0x96, 0xcb, 0x3f, 0xa0,
+     0x58, 0xa7, 0x11, 0x4e, 0xb0, 0x30, 0x54, 0xc9,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x05, },
+    {0x31, 0xc4, 0x9a, 0xe7, 0x5b, 0xce, 0x78, 0x07,
+     0xcd, 0xff, 0x22, 0x05, 0x5d, 0x94, 0xee, 0x90,
+     0x21, 0xfe, 0xdb, 0xb5, 0xab, 0x51, 0xc5, 0x75,
+     0x26, 0xf0, 0x11, 0xaa, 0x27, 0xe8, 0xbf, 0xf1,
+     0x74, 0x56, 0x35, 0xec, 0x5b, 0xa0, 0xc9, 0xf1,
+     0xc2, 0xed, 0xe1, 0x54, 0x14, 0xc6, 0x50, 0x7d,
+     0x29, 0xff, 0xe3, 0x7e, 0x79, 0x0a, 0x07, 0x9b,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x06, },
+    {0x1f, 0x24, 0x83, 0xf8, 0x25, 0x72, 0x25, 0x1f,
+     0xca, 0x97, 0x5f, 0xea, 0x40, 0xdb, 0x82, 0x1d,
+     0xf8, 0xad, 0x82, 0xa3, 0xc0, 0x02, 0xee, 0x6c,
+     0x57, 0x11, 0x24, 0x08, 0x89, 0xfa, 0xf0, 0xcc,
+     0xb7, 0x50, 0xd9, 0x9b, 0x55, 0x3c, 0x57, 0x4f,
+     0xad, 0x7e, 0xcf, 0xb0, 0x43, 0x85, 0x86, 0xeb,
+     0x39, 0x52, 0xaf, 0x5b, 0x4b, 0x15, 0x3c, 0x7e,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x07, },
+    {0xdb, 0x2f, 0x6b, 0xe6, 0x30, 0xe2, 0x46, 0xa5,
+     0xcf, 0x7d, 0x99, 0xb8, 0x51, 0x94, 0xb1, 0x23,
+     0xd4, 0x87, 0xe2, 0xd4, 0x66, 0xb9, 0x4b, 0x24,
+     0xa0, 0x3c, 0x3e, 0x28, 0x0f, 0x3a, 0x30, 0x08,
+     0x54, 0x97, 0xf2, 0xf6, 0x11, 0xee, 0x25, 0x17,
+     0xb1, 0x63, 0xef, 0x8c, 0x53, 0xb7, 0x15, 0xd1,
+     0x8b, 0xb4, 0xe4, 0x80, 0x8d, 0x02, 0xb9, 0x63,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x08, },
+    {0x85, 0x8e, 0x6f, 0x9c, 0xc6, 0xc1, 0x2c, 0x31,
+     0xf5, 0xdf, 0x12, 0x4a, 0xa7, 0x77, 0x67, 0xb0,
+     0x5c, 0x8b, 0xc0, 0x21, 0xbd, 0x68, 0x3d, 0x2b,
+     0x55, 0x57, 0x15, 0x50, 0x04, 0x6d, 0xcd, 0x3e,
+     0xa5, 0xc4, 0x38, 0x98, 0xc5, 0xc5, 0xfc, 0x4f,
+     0xda, 0xc7, 0xdb, 0x39, 0xc2, 0xf0, 0x2e, 0xbe,
+     0xe4, 0xe3, 0x54, 0x1d, 0x1e, 0x78, 0x04, 0x7a,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x09, },
+    {0x2f, 0xdc, 0xcc, 0xfe, 0xe7, 0x20, 0xa7, 0x7e,
+     0xf6, 0xcb, 0x3b, 0xfb, 0xb4, 0x47, 0xf9, 0x38,
+     0x31, 0x17, 0xe3, 0xda, 0xa4, 0xa0, 0x7e, 0x36,
+     0xed, 0x15, 0xf7, 0x8d, 0x37, 0x17, 0x32, 0xe4,
+     0xf4, 0x1b, 0xf4, 0xf7, 0x88, 0x30, 0x35, 0xe6,
+     0xa7, 0x9f, 0xce, 0xdc, 0x0e, 0x19, 0x6e, 0xb0,
+     0x7b, 0x48, 0x17, 0x16, 0x97, 0x51, 0x74, 0x63,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x0a, },
+    {0xae, 0xa9, 0xe1, 0x7a, 0x30, 0x65, 0x17, 0xeb,
+     0x89, 0x15, 0x2a, 0xa7, 0x09, 0x6d, 0x2c, 0x38,
+     0x1e, 0xc8, 0x13, 0xc5, 0x1a, 0xa8, 0x80, 0xe7,
+     0xbe, 0xe2, 0xc0, 0xfd, 0x39, 0xbb, 0x30, 0xea,
+     0xb3, 0x37, 0xe0, 0xa5, 0x21, 0xb6, 0xcb, 0xa1,
+     0xab, 0xe4, 0xb2, 0xb3, 0xa3, 0xe5, 0x24, 0xc1,
+     0x4a, 0x3f, 0xe3, 0xeb, 0x11, 0x6b, 0x65, 0x5f,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x0b, },
+    {0xef, 0x53, 0xb6, 0x29, 0x4a, 0xca, 0x43, 0x1f,
+     0x0f, 0x3c, 0x22, 0xdc, 0x82, 0xeb, 0x90, 0x50,
+     0x32, 0x4f, 0x1d, 0x88, 0xd3, 0x77, 0xe7, 0x16,
+     0x44, 0x8e, 0x50, 0x7c, 0x20, 0xb5, 0x10, 0x00,
+     0x40, 0x92, 0xe9, 0x66, 0x36, 0xcf, 0xb7, 0xe3,
+     0x2e, 0xfd, 0xed, 0x82, 0x65, 0xc2, 0x66, 0xdf,
+     0xb7, 0x54, 0xfa, 0x6d, 0x64, 0x91, 0xa6, 0xda,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x0c, },
+    {0x6e, 0x31, 0xee, 0x1d, 0xc1, 0x37, 0xf8, 0x1b,
+     0x05, 0x67, 0x52, 0xe4, 0xde, 0xab, 0x14, 0x43,
+     0xa4, 0x81, 0x03, 0x3e, 0x9b, 0x4c, 0x93, 0xa3,
+     0x04, 0x4f, 0x4f, 0x7a, 0x20, 0x7d, 0xdd, 0xf0,
+     0x38, 0x5b, 0xfd, 0xea, 0xb6, 0xe9, 0xac, 0xda,
+     0x8d, 0xa0, 0x6b, 0x3b, 0xbe, 0xf2, 0x24, 0xa9,
+     0x3a, 0xb1, 0xe9, 0xe0, 0x36, 0x10, 0x9d, 0x13,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x0d, },
+    {0x34, 0xe8, 0xe1, 0x7a, 0x43, 0x0e, 0x43, 0x28,
+     0x97, 0x93, 0xc3, 0x83, 0xfa, 0xc9, 0x77, 0x42,
+     0x47, 0xb4, 0x0e, 0x9e, 0xbd, 0x33, 0x66, 0x98,
+     0x1f, 0xcf, 0xae, 0xca, 0x25, 0x28, 0x19, 0xf7,
+     0x1c, 0x7f, 0xb7, 0xfb, 0xcb, 0x15, 0x9b, 0xe3,
+     0x37, 0xd3, 0x7d, 0x33, 0x36, 0xd7, 0xfe, 0xb9,
+     0x63, 0x72, 0x4f, 0xdf, 0xb0, 0xec, 0xb7, 0x67,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x0e, },
+    {0xa5, 0x36, 0x40, 0xc8, 0x3d, 0xc2, 0x08, 0x60,
+     0x3d, 0xed, 0x83, 0xe4, 0xec, 0xf7, 0x58, 0xf2,
+     0x4c, 0x35, 0x7d, 0x7c, 0xf4, 0x80, 0x88, 0xb2,
+     0xce, 0x01, 0xe9, 0xfa, 0xd5, 0x81, 0x4c, 0xd7,
+     0x24, 0x19, 0x9c, 0x4a, 0x5b, 0x97, 0x4a, 0x43,
+     0x68, 0x5f, 0xbf, 0x5b, 0x8b, 0xac, 0x69, 0x45,
+     0x9c, 0x94, 0x69, 0xbc, 0x8f, 0x23, 0xcc, 0xaf,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x0f, },
+    {0xba, 0xa4, 0xd8, 0x63, 0x55, 0x11, 0xa7, 0xd2,
+     0x88, 0xae, 0xbe, 0xed, 0xd1, 0x2c, 0xe5, 0x29,
+     0xff, 0x10, 0x2c, 0x91, 0xf9, 0x7f, 0x86, 0x7e,
+     0x21, 0x91, 0x6b, 0xf9, 0x97, 0x9a, 0x5f, 0x47,
+     0x59, 0xf8, 0x0f, 0x4f, 0xb4, 0xec, 0x2e, 0x34,
+     0xf5, 0x56, 0x6d, 0x59, 0x56, 0x80, 0xa1, 0x17,
+     0x35, 0xe7, 0xb6, 0x10, 0x46, 0x12, 0x79, 0x89,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x10, },
+    {0x0b, 0x6e, 0xc4, 0xfe, 0x17, 0x77, 0x38, 0x24,
+     0x04, 0xef, 0x67, 0x99, 0x97, 0xba, 0x8d, 0x1c,
+     0xc5, 0xcd, 0x8e, 0x85, 0x34, 0x92, 0x59, 0xf5,
+     0x90, 0xc4, 0xc6, 0x6d, 0x33, 0x99, 0xd4, 0x64,
+     0x34, 0x59, 0x06, 0xb1, 0x1b, 0x00, 0xe3, 0x63,
+     0xef, 0x42, 0x92, 0x21, 0xf2, 0xec, 0x72, 0x0d,
+     0x2f, 0x66, 0x5d, 0x7d, 0xea, 0xd5, 0xb4, 0x82,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x11, },
+    {0xb8, 0x35, 0x7c, 0x3a, 0x6c, 0xee, 0xf2, 0x88,
+     0x31, 0x0e, 0x17, 0xb8, 0xbf, 0xef, 0xf9, 0x20,
+     0x08, 0x46, 0xca, 0x8c, 0x19, 0x42, 0x49, 0x7c,
+     0x48, 0x44, 0x03, 0xbc, 0xff, 0x14, 0x9e, 0xfa,
+     0x66, 0x06, 0xa6, 0xbd, 0x20, 0xef, 0x7d, 0x1b,
+     0x06, 0xbd, 0x92, 0xf6, 0x90, 0x46, 0x39, 0xdc,
+     0xe5, 0x17, 0x4d, 0xb6, 0xcc, 0x55, 0x4a, 0x26,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x12, },
+    {0xc9, 0xff, 0x61, 0xb0, 0x40, 0x87, 0x4c, 0x05,
+     0x68, 0x47, 0x92, 0x16, 0x82, 0x4a, 0x15, 0xea,
+     0xb1, 0xa8, 0x38, 0xa7, 0x97, 0xd1, 0x89, 0x74,
+     0x62, 0x26, 0xe4, 0xcc, 0xea, 0x98, 0xd6, 0x0e,
+     0x5f, 0xfc, 0x9b, 0x8f, 0xcf, 0x99, 0x9f, 0xab,
+     0x1d, 0xf7, 0xe7, 0xef, 0x70, 0x84, 0xf2, 0x0d,
+     0xdb, 0x61, 0xbb, 0x04, 0x5a, 0x6c, 0xe0, 0x02,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x13, },
+    {0xa1, 0xe8, 0x1c, 0x04, 0xf3, 0x0c, 0xe2, 0x01,
+     0xc7, 0xc9, 0xac, 0xe7, 0x85, 0xed, 0x44, 0xcc,
+     0x33, 0xb4, 0x55, 0xa0, 0x22, 0xf2, 0xac, 0xdb,
+     0xc6, 0xca, 0xe8, 0x3c, 0xdc, 0xf1, 0xf6, 0xc3,
+     0xdb, 0x09, 0xc7, 0x0a, 0xcc, 0x25, 0x39, 0x1d,
+     0x49, 0x2f, 0xe2, 0x5b, 0x4a, 0x18, 0x0b, 0xab,
+     0xd6, 0xce, 0xa3, 0x56, 0xc0, 0x47, 0x19, 0xcd,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x14, },
+    {0xfc, 0xc7, 0xf2, 0xb4, 0x5d, 0xf1, 0xcd, 0x5a,
+     0x3c, 0x0c, 0x07, 0x31, 0xca, 0x47, 0xa8, 0xaf,
+     0x75, 0xcf, 0xb0, 0x34, 0x7e, 0x83, 0x54, 0xee,
+     0xfe, 0x78, 0x24, 0x55, 0x0d, 0x5d, 0x71, 0x10,
+     0x27, 0x4c, 0xba, 0x7c, 0xde, 0xe9, 0x0e, 0x1a,
+     0x8b, 0x0d, 0x39, 0x4c, 0x37, 0x6a, 0x55, 0x73,
+     0xdb, 0x6b, 0xe0, 0xbf, 0x27, 0x47, 0xf5, 0x30,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x01, 0x8e, 0xbb, 0xb9,
+     0x5e, 0xed, 0x0e, 0x13, },
+    {0x61, 0xf0, 0x77, 0xc6, 0xf6, 0x2e, 0xd8, 0x02,
+     0xda, 0xd7, 0xc2, 0xf3, 0x8f, 0x5c, 0x67, 0xf2,
+     0xcc, 0x45, 0x36, 0x01, 0xe6, 0x1b, 0xd0, 0x76,
+     0xbb, 0x46, 0x17, 0x9e, 0x22, 0x72, 0xf9, 0xe9,
+     0xf5, 0x93, 0x3e, 0x70, 0x38, 0x8e, 0xe6, 0x52,
+     0x51, 0x34, 0x43, 0xb5, 0xe2, 0x89, 0xdd, 0x13,
+     0x5d, 0xcc, 0x0d, 0x02, 0x99, 0xb2, 0x25, 0xe4,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x00, 0x00, 0x15, 0x9d, 0x89,
+     0x3d, 0x4c, 0xdd, 0x74, 0x72, 0x46, 0xcd, 0xca,
+     0x43, 0x59, 0x0e, 0x13, },
+    {0x02, 0x98, 0x95, 0xf0, 0xaf, 0x49, 0x6b, 0xfc,
+     0x62, 0xb6, 0xef, 0x8d, 0x8a, 0x65, 0xc8, 0x8c,
+     0x61, 0x39, 0x49, 0xb0, 0x36, 0x68, 0xaa, 0xb4,
+     0xf0, 0x42, 0x9e, 0x35, 0x3e, 0xa6, 0xe5, 0x3f,
+     0x9a, 0x84, 0x1f, 0x20, 0x19, 0xec, 0x24, 0xbd,
+     0xe1, 0xa7, 0x56, 0x77, 0xaa, 0x9b, 0x59, 0x02,
+     0xe6, 0x10, 0x81, 0xc0, 0x10, 0x64, 0xde, 0x93,
+    },
+  },
+  {
+    {0x41, 0xff, 0xc1, 0xff, 0xff, 0xfe, 0x01, 0xff,
+     0xfc, 0x00, 0x03, 0xff, 0xfe, 0x00, 0x07, 0xc0,
+     0x01, 0xff, 0xf0, 0x00, 0x03, 0xff, 0xf0, 0x7f,
+     0xfe, 0x00, 0x07, 0xc0, },
+    {0xab, 0x68, 0x99, 0x30, 0xbc, 0xae, 0x4a, 0x4a,
+     0xa5, 0xf5, 0xcb, 0x08, 0x5e, 0x82, 0x3e, 0x8a,
+     0xe3, 0x0f, 0xd3, 0x65, 0xeb, 0x1d, 0xa4, 0xab,
+     0xa9, 0xcf, 0x03, 0x79, 0x33, 0x45, 0xa1, 0x21,
+     0xbb, 0xd2, 0x33, 0x54, 0x8a, 0xf0, 0xd2, 0x10,
+     0x65, 0x4e, 0xb4, 0x0b, 0xab, 0x78, 0x8a, 0x03,
+     0x66, 0x64, 0x19, 0xbe, 0x6f, 0xbd, 0x34, 0xe7,
+    },
+  },
+  {
+    {0x7f, 0xff, 0xff, 0xc0, 0x3f, 0xff, 0xc0, 0x03,
+     0xff, 0xff, 0xfc, 0x00, 0x7f, 0xff, 0x00, 0x00,
+     0x00, 0x00, 0x07, 0x00, 0x00, 0x10, 0x00, 0x00,
+     0x00, 0x0e, 0x00, 0xff, },
+    {0xbd, 0xb6, 0xa8, 0x81, 0x7c, 0x1f, 0x89, 0xda,
+     0x1c, 0x2f, 0x3d, 0xd8, 0xe9, 0x7f, 0xeb, 0x44,
+     0x94, 0xf2, 0xed, 0x30, 0x2a, 0x4c, 0xe2, 0xbc,
+     0x7f, 0x5f, 0x40, 0x25, 0x4c, 0x70, 0x20, 0xd5,
+     0x7c, 0x00, 0x41, 0x18, 0x89, 0x46, 0x2d, 0x77,
+     0xa5, 0x43, 0x8b, 0xb4, 0xe9, 0x7d, 0x17, 0x77,
+     0x00, 0xbf, 0x72, 0x43, 0xa0, 0x7f, 0x16, 0x80,
+    },
+  },
+  {
+    {0x7f, 0xff, 0xff, 0x04, 0x00, 0x00, 0x00, 0x00,
+     0xff, 0xff, 0xf0, 0x1f, 0xff, 0xf8, 0xff, 0xff,
+     0xc0, 0x0f, 0xff, 0xff, 0xff, 0xff, 0xc0, 0x00,
+     0x00, 0x0f, 0xff, 0xff, },
+    {0xd5, 0x8b, 0x61, 0xaa, 0x41, 0xc3, 0x2d, 0xd5,
+     0xeb, 0xa4, 0x62, 0x64, 0x7d, 0xba, 0x75, 0xc5,
+     0xd6, 0x7c, 0x83, 0x60, 0x6c, 0x0a, 0xf2, 0xbd,
+     0x92, 0x84, 0x46, 0xa9, 0xd2, 0x4b, 0xa6, 0xa8,
+     0x37, 0xbe, 0x04, 0x60, 0xdd, 0x10, 0x7a, 0xe7,
+     0x77, 0x25, 0x69, 0x6d, 0x21, 0x14, 0x46, 0xc5,
+     0x60, 0x9b, 0x45, 0x95, 0x97, 0x6b, 0x16, 0xbd,
+    },
+  },
+  {
+    {0x7f, 0xff, 0xff, 0xc0, 0x00, 0xff, 0xfe, 0x3f,
+     0xff, 0xfc, 0x10, 0x00, 0x00, 0x20, 0x00, 0x3f,
+     0xff, 0xff, 0x00, 0x00, 0x00, 0xfc, 0x00, 0x00,
+     0x3f, 0xff, 0xff, 0xff, },
+    {0xdc, 0x9f, 0xa7, 0x79, 0x78, 0xa0, 0x05, 0x51,
+     0x09, 0x80, 0xe9, 0x29, 0xa1, 0x48, 0x5f, 0x63,
+     0x71, 0x6d, 0xf6, 0x95, 0xd7, 0xa0, 0xc1, 0x8b,
+     0xb5, 0x18, 0xdf, 0x03, 0xed, 0xe2, 0xb0, 0x16,
+     0xf2, 0xdd, 0xff, 0xc2, 0xa8, 0xc0, 0x15, 0xb1,
+     0x34, 0x92, 0x82, 0x75, 0xce, 0x09, 0xe5, 0x66,
+     0x1b, 0x7a, 0xb1, 0x4c, 0xe0, 0xd1, 0xd4, 0x03,
+    },
+  },
+  {
+    {0x70, 0x01, 0xf0, 0x00, 0x1c, 0x00, 0x01, 0xc0,
+     0x00, 0x00, 0x1f, 0xff, 0xff, 0xfc, 0x00, 0x00,
+     0x1f, 0xff, 0xff, 0xf8, 0x00, 0x0f, 0xc0, 0x00,
+     0x00, 0x01, 0xfc, 0x00, },
+    {0x49, 0x9d, 0x8b, 0x28, 0x29, 0xcf, 0xb8, 0x79,
+     0xc9, 0x01, 0xf7, 0xd8, 0x5d, 0x35, 0x70, 0x45,
+     0xed, 0xab, 0x55, 0x02, 0x88, 0x24, 0xd0, 0xf0,
+     0x5b, 0xa2, 0x79, 0xba, 0xbf, 0x92, 0x95, 0x37,
+     0xb0, 0x6e, 0x40, 0x15, 0x91, 0x96, 0x39, 0xd9,
+     0x4f, 0x57, 0x83, 0x8f, 0xa3, 0x3f, 0xc3, 0xd9,
+     0x52, 0x59, 0x8d, 0xcd, 0xbb, 0x44, 0xd6, 0x38,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x00, 0x1f, 0xfc, 0x00, 0x00,
+     0x00, 0xff, 0xf0, 0x30, 0x00, 0x1f, 0x00, 0x00,
+     0xff, 0xff, 0xf0, 0x00, 0x00, 0x38, 0x00, 0x00,
+     0x00, 0x00, 0x00, 0x02, },
+    {0x82, 0x46, 0xc9, 0x99, 0x13, 0x71, 0x86, 0x63,
+     0x2c, 0x5f, 0x9e, 0xdd, 0xf3, 0xb1, 0xb0, 0xe1,
+     0x76, 0x4c, 0x5e, 0x8b, 0xd0, 0xe0, 0xd8, 0xa5,
+     0x54, 0xb9, 0xcb, 0x77, 0xe8, 0x0e, 0xd8, 0x66,
+     0x0b, 0xc1, 0xcb, 0x17, 0xac, 0x7d, 0x84, 0x5b,
+     0xe4, 0x0a, 0x7a, 0x02, 0x2d, 0x33, 0x06, 0xf1,
+     0x16, 0xae, 0x9f, 0x81, 0xfe, 0xa6, 0x59, 0x47,
+    },
+  },
+  {
+    {0x7f, 0xff, 0x80, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x07, 0xff, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
+     0x00, 0x00, 0xff, 0xfe, 0x08, 0x00, 0x00, 0x1f,
+     0xf0, 0x00, 0x1f, 0xff, },
+    {0x66, 0x70, 0xc2, 0x0a, 0xfc, 0xce, 0xae, 0xa6,
+     0x72, 0xc9, 0x7f, 0x75, 0xe2, 0xe9, 0xdd, 0x5c,
+     0x84, 0x60, 0xe5, 0x4b, 0xb3, 0x85, 0x38, 0xeb,
+     0xb4, 0xbd, 0x30, 0xeb, 0xf2, 0x80, 0xd8, 0x00,
+     0x8d, 0x07, 0xa4, 0xca, 0xf5, 0x42, 0x71, 0xf9,
+     0x93, 0x52, 0x7d, 0x46, 0xff, 0x3f, 0xf4, 0x6f,
+     0xd1, 0x19, 0x0a, 0x3f, 0x1f, 0xaa, 0x4f, 0x74,
+    },
+  },
+  {
+    {0x00, 0x00, 0x7f, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xc0, 0x00, 0x07, 0xff, 0xff, 0xe0, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xf8, 0x00, 0xff,
+     0xff, 0xff, 0xff, 0xff, },
+    {0x00, 0x0e, 0xca, 0x93, 0x42, 0x47, 0x42, 0x5c,
+     0xfd, 0x94, 0x9b, 0x79, 0x5c, 0xb5, 0xce, 0x1e,
+     0xff, 0x40, 0x15, 0x50, 0x38, 0x6e, 0x28, 0xd1,
+     0xa4, 0xc5, 0xa8, 0xeb, 0xd4, 0xc0, 0x10, 0x40,
+     0xdb, 0xa1, 0x96, 0x28, 0x93, 0x1b, 0xc8, 0x85,
+     0x53, 0x70, 0x31, 0x7c, 0x72, 0x2c, 0xbd, 0x9c,
+     0xa6, 0x15, 0x69, 0x85, 0xf1, 0xc2, 0xe9, 0xce,
+    },
+  },
+  {
+    {0x7f, 0xff, 0xfc, 0x03, 0xff, 0x80, 0x7f, 0xff,
+     0xe0, 0x00, 0x1f, 0xff, 0xff, 0x80, 0x0f, 0xff,
+     0x80, 0x00, 0x01, 0xff, 0xff, 0x00, 0x01, 0xff,
+     0xff, 0xfe, 0x00, 0x1f, },
+    {0xef, 0x35, 0x3b, 0xf5, 0xc7, 0x3c, 0xd5, 0x51,
+     0xb9, 0x6d, 0x59, 0x6f, 0xbc, 0x9a, 0x67, 0xf1,
+     0x6d, 0x61, 0xdd, 0x9f, 0xe5, 0x6a, 0xf1, 0x9d,
+     0xe1, 0xfb, 0xa9, 0xcd, 0x21, 0x77, 0x1b, 0x9c,
+     0xdc, 0xe3, 0xe8, 0x43, 0x0c, 0x09, 0xb3, 0x83,
+     0x8b, 0xe7, 0x0b, 0x48, 0xc2, 0x1e, 0x15, 0xbc,
+     0x09, 0xee, 0x1f, 0x2d, 0x79, 0x45, 0xb9, 0x1f,
+    },
+  },
+  {
+    {0x00, 0x00, 0x00, 0x07, 0xff, 0xc0, 0x7f, 0xff,
+     0xff, 0xff, 0x01, 0xff, 0xfe, 0x03, 0xff, 0xfe,
+     0x40, 0x00, 0x38, 0x00, 0x07, 0xe0, 0x00, 0x3f,
+     0xfe, 0x00, 0x00, 0x00, },
+    {0x40, 0x36, 0x05, 0x2a, 0x30, 0x91, 0xeb, 0x48,
+     0x10, 0x46, 0xad, 0x32, 0x89, 0xc9, 0x5d, 0x3a,
+     0xc9, 0x05, 0xca, 0x00, 0x23, 0xde, 0x2c, 0x03,
+     0xec, 0xd4, 0x51, 0xcf, 0xd7, 0x68, 0x16, 0x5a,
+     0x38, 0xa2, 0xb9, 0x6f, 0x81, 0x25, 0x86, 0xa9,
+     0xd5, 0x9d, 0x41, 0x36, 0x03, 0x5d, 0x9c, 0x85,
+     0x3a, 0x5b, 0xf2, 0xe1, 0xc8, 0x6a, 0x49, 0x93,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x29, },
+    {0xfc, 0xc7, 0xf2, 0xb4, 0x5d, 0xf1, 0xcd, 0x5a,
+     0x3c, 0x0c, 0x07, 0x31, 0xca, 0x47, 0xa8, 0xaf,
+     0x75, 0xcf, 0xb0, 0x34, 0x7e, 0x83, 0x54, 0xee,
+     0xfe, 0x78, 0x24, 0x55, 0xf2, 0xa2, 0x8e, 0xef,
+     0xd8, 0xb3, 0x45, 0x83, 0x21, 0x16, 0xf1, 0xe5,
+     0x74, 0xf2, 0xc6, 0xb2, 0xc8, 0x95, 0xaa, 0x8c,
+     0x24, 0x94, 0x1f, 0x40, 0xd8, 0xb8, 0x0a, 0xd1,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x2a, },
+    {0xa1, 0xe8, 0x1c, 0x04, 0xf3, 0x0c, 0xe2, 0x01,
+     0xc7, 0xc9, 0xac, 0xe7, 0x85, 0xed, 0x44, 0xcc,
+     0x33, 0xb4, 0x55, 0xa0, 0x22, 0xf2, 0xac, 0xdb,
+     0xc6, 0xca, 0xe8, 0x3c, 0x23, 0x0e, 0x09, 0x3c,
+     0x24, 0xf6, 0x38, 0xf5, 0x33, 0xda, 0xc6, 0xe2,
+     0xb6, 0xd0, 0x1d, 0xa3, 0xb5, 0xe7, 0xf4, 0x54,
+     0x29, 0x31, 0x5c, 0xa9, 0x3f, 0xb8, 0xe6, 0x34,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x2b, },
+    {0xc9, 0xff, 0x61, 0xb0, 0x40, 0x87, 0x4c, 0x05,
+     0x68, 0x47, 0x92, 0x16, 0x82, 0x4a, 0x15, 0xea,
+     0xb1, 0xa8, 0x38, 0xa7, 0x97, 0xd1, 0x89, 0x74,
+     0x62, 0x26, 0xe4, 0xcc, 0x15, 0x67, 0x29, 0xf1,
+     0xa0, 0x03, 0x64, 0x70, 0x30, 0x66, 0x60, 0x54,
+     0xe2, 0x08, 0x18, 0x0f, 0x8f, 0x7b, 0x0d, 0xf2,
+     0x24, 0x9e, 0x44, 0xfb, 0xa5, 0x93, 0x1f, 0xff,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x2c, },
+    {0xb8, 0x35, 0x7c, 0x3a, 0x6c, 0xee, 0xf2, 0x88,
+     0x31, 0x0e, 0x17, 0xb8, 0xbf, 0xef, 0xf9, 0x20,
+     0x08, 0x46, 0xca, 0x8c, 0x19, 0x42, 0x49, 0x7c,
+     0x48, 0x44, 0x03, 0xbc, 0x00, 0xeb, 0x61, 0x05,
+     0x99, 0xf9, 0x59, 0x42, 0xdf, 0x10, 0x82, 0xe4,
+     0xf9, 0x42, 0x6d, 0x08, 0x6f, 0xb9, 0xc6, 0x23,
+     0x1a, 0xe8, 0xb2, 0x49, 0x33, 0xaa, 0xb5, 0xdb,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x2d, },
+    {0x0b, 0x6e, 0xc4, 0xfe, 0x17, 0x77, 0x38, 0x24,
+     0x04, 0xef, 0x67, 0x99, 0x97, 0xba, 0x8d, 0x1c,
+     0xc5, 0xcd, 0x8e, 0x85, 0x34, 0x92, 0x59, 0xf5,
+     0x90, 0xc4, 0xc6, 0x6d, 0xcc, 0x66, 0x2b, 0x9b,
+     0xcb, 0xa6, 0xf9, 0x4e, 0xe4, 0xff, 0x1c, 0x9c,
+     0x10, 0xbd, 0x6d, 0xdd, 0x0d, 0x13, 0x8d, 0xf2,
+     0xd0, 0x99, 0xa2, 0x82, 0x15, 0x2a, 0x4b, 0x7f,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x2e, },
+    {0xba, 0xa4, 0xd8, 0x63, 0x55, 0x11, 0xa7, 0xd2,
+     0x88, 0xae, 0xbe, 0xed, 0xd1, 0x2c, 0xe5, 0x29,
+     0xff, 0x10, 0x2c, 0x91, 0xf9, 0x7f, 0x86, 0x7e,
+     0x21, 0x91, 0x6b, 0xf9, 0x68, 0x65, 0xa0, 0xb8,
+     0xa6, 0x07, 0xf0, 0xb0, 0x4b, 0x13, 0xd1, 0xcb,
+     0x0a, 0xa9, 0x92, 0xa5, 0xa9, 0x7f, 0x5e, 0xe8,
+     0xca, 0x18, 0x49, 0xef, 0xb9, 0xed, 0x86, 0x78,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x2f, },
+    {0xa5, 0x36, 0x40, 0xc8, 0x3d, 0xc2, 0x08, 0x60,
+     0x3d, 0xed, 0x83, 0xe4, 0xec, 0xf7, 0x58, 0xf2,
+     0x4c, 0x35, 0x7d, 0x7c, 0xf4, 0x80, 0x88, 0xb2,
+     0xce, 0x01, 0xe9, 0xfa, 0x2a, 0x7e, 0xb3, 0x28,
+     0xdb, 0xe6, 0x63, 0xb5, 0xa4, 0x68, 0xb5, 0xbc,
+     0x97, 0xa0, 0x40, 0xa3, 0x74, 0x53, 0x96, 0xba,
+     0x63, 0x6b, 0x96, 0x43, 0x70, 0xdc, 0x33, 0x52,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x30, },
+    {0x34, 0xe8, 0xe1, 0x7a, 0x43, 0x0e, 0x43, 0x28,
+     0x97, 0x93, 0xc3, 0x83, 0xfa, 0xc9, 0x77, 0x42,
+     0x47, 0xb4, 0x0e, 0x9e, 0xbd, 0x33, 0x66, 0x98,
+     0x1f, 0xcf, 0xae, 0xca, 0xda, 0xd7, 0xe6, 0x08,
+     0xe3, 0x80, 0x48, 0x04, 0x34, 0xea, 0x64, 0x1c,
+     0xc8, 0x2c, 0x82, 0xcb, 0xc9, 0x28, 0x01, 0x46,
+     0x9c, 0x8d, 0xb0, 0x20, 0x4f, 0x13, 0x48, 0x9a,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x31, },
+    {0x6e, 0x31, 0xee, 0x1d, 0xc1, 0x37, 0xf8, 0x1b,
+     0x05, 0x67, 0x52, 0xe4, 0xde, 0xab, 0x14, 0x43,
+     0xa4, 0x81, 0x03, 0x3e, 0x9b, 0x4c, 0x93, 0xa3,
+     0x04, 0x4f, 0x4f, 0x7a, 0xdf, 0x82, 0x22, 0x0f,
+     0xc7, 0xa4, 0x02, 0x15, 0x49, 0x16, 0x53, 0x25,
+     0x72, 0x5f, 0x94, 0xc3, 0x41, 0x0d, 0xdb, 0x56,
+     0xc5, 0x4e, 0x16, 0x1f, 0xc9, 0xef, 0x62, 0xee,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x32, },
+    {0xef, 0x53, 0xb6, 0x29, 0x4a, 0xca, 0x43, 0x1f,
+     0x0f, 0x3c, 0x22, 0xdc, 0x82, 0xeb, 0x90, 0x50,
+     0x32, 0x4f, 0x1d, 0x88, 0xd3, 0x77, 0xe7, 0x16,
+     0x44, 0x8e, 0x50, 0x7c, 0xdf, 0x4a, 0xef, 0xff,
+     0xbf, 0x6d, 0x16, 0x99, 0xc9, 0x30, 0x48, 0x1c,
+     0xd1, 0x02, 0x12, 0x7c, 0x9a, 0x3d, 0x99, 0x20,
+     0x48, 0xab, 0x05, 0x92, 0x9b, 0x6e, 0x59, 0x27,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x33, },
+    {0xae, 0xa9, 0xe1, 0x7a, 0x30, 0x65, 0x17, 0xeb,
+     0x89, 0x15, 0x2a, 0xa7, 0x09, 0x6d, 0x2c, 0x38,
+     0x1e, 0xc8, 0x13, 0xc5, 0x1a, 0xa8, 0x80, 0xe7,
+     0xbe, 0xe2, 0xc0, 0xfd, 0xc6, 0x44, 0xcf, 0x15,
+     0x4c, 0xc8, 0x1f, 0x5a, 0xde, 0x49, 0x34, 0x5e,
+     0x54, 0x1b, 0x4d, 0x4b, 0x5c, 0x1a, 0xdb, 0x3e,
+     0xb5, 0xc0, 0x1c, 0x14, 0xee, 0x94, 0x9a, 0xa2,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x34, },
+    {0x2f, 0xdc, 0xcc, 0xfe, 0xe7, 0x20, 0xa7, 0x7e,
+     0xf6, 0xcb, 0x3b, 0xfb, 0xb4, 0x47, 0xf9, 0x38,
+     0x31, 0x17, 0xe3, 0xda, 0xa4, 0xa0, 0x7e, 0x36,
+     0xed, 0x15, 0xf7, 0x8d, 0xc8, 0xe8, 0xcd, 0x1b,
+     0x0b, 0xe4, 0x0b, 0x08, 0x77, 0xcf, 0xca, 0x19,
+     0x58, 0x60, 0x31, 0x22, 0xf1, 0xe6, 0x91, 0x4f,
+     0x84, 0xb7, 0xe8, 0xe9, 0x68, 0xae, 0x8b, 0x9e,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x35, },
+    {0x85, 0x8e, 0x6f, 0x9c, 0xc6, 0xc1, 0x2c, 0x31,
+     0xf5, 0xdf, 0x12, 0x4a, 0xa7, 0x77, 0x67, 0xb0,
+     0x5c, 0x8b, 0xc0, 0x21, 0xbd, 0x68, 0x3d, 0x2b,
+     0x55, 0x57, 0x15, 0x50, 0xfb, 0x92, 0x32, 0xc1,
+     0x5a, 0x3b, 0xc7, 0x67, 0x3a, 0x3a, 0x03, 0xb0,
+     0x25, 0x38, 0x24, 0xc5, 0x3d, 0x0f, 0xd1, 0x41,
+     0x1b, 0x1c, 0xab, 0xe2, 0xe1, 0x87, 0xfb, 0x87,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x36, },
+    {0xdb, 0x2f, 0x6b, 0xe6, 0x30, 0xe2, 0x46, 0xa5,
+     0xcf, 0x7d, 0x99, 0xb8, 0x51, 0x94, 0xb1, 0x23,
+     0xd4, 0x87, 0xe2, 0xd4, 0x66, 0xb9, 0x4b, 0x24,
+     0xa0, 0x3c, 0x3e, 0x28, 0xf0, 0xc5, 0xcf, 0xf7,
+     0xab, 0x68, 0x0d, 0x09, 0xee, 0x11, 0xda, 0xe8,
+     0x4e, 0x9c, 0x10, 0x72, 0xac, 0x48, 0xea, 0x2e,
+     0x74, 0x4b, 0x1b, 0x7f, 0x72, 0xfd, 0x46, 0x9e,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x37, },
+    {0x1f, 0x24, 0x83, 0xf8, 0x25, 0x72, 0x25, 0x1f,
+     0xca, 0x97, 0x5f, 0xea, 0x40, 0xdb, 0x82, 0x1d,
+     0xf8, 0xad, 0x82, 0xa3, 0xc0, 0x02, 0xee, 0x6c,
+     0x57, 0x11, 0x24, 0x08, 0x76, 0x05, 0x0f, 0x33,
+     0x48, 0xaf, 0x26, 0x64, 0xaa, 0xc3, 0xa8, 0xb0,
+     0x52, 0x81, 0x30, 0x4e, 0xbc, 0x7a, 0x79, 0x14,
+     0xc6, 0xad, 0x50, 0xa4, 0xb4, 0xea, 0xc3, 0x83,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x38, },
+    {0x31, 0xc4, 0x9a, 0xe7, 0x5b, 0xce, 0x78, 0x07,
+     0xcd, 0xff, 0x22, 0x05, 0x5d, 0x94, 0xee, 0x90,
+     0x21, 0xfe, 0xdb, 0xb5, 0xab, 0x51, 0xc5, 0x75,
+     0x26, 0xf0, 0x11, 0xaa, 0xd8, 0x17, 0x40, 0x0e,
+     0x8b, 0xa9, 0xca, 0x13, 0xa4, 0x5f, 0x36, 0x0e,
+     0x3d, 0x12, 0x1e, 0xaa, 0xeb, 0x39, 0xaf, 0x82,
+     0xd6, 0x00, 0x1c, 0x81, 0x86, 0xf5, 0xf8, 0x66,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x39, },
+    {0xae, 0x99, 0xfe, 0xeb, 0xb5, 0xd2, 0x69, 0x45,
+     0xb5, 0x48, 0x92, 0x09, 0x2a, 0x8a, 0xee, 0x02,
+     0x91, 0x29, 0x30, 0xfa, 0x41, 0xcd, 0x11, 0x4e,
+     0x40, 0x44, 0x73, 0x01, 0xfb, 0x7d, 0xa7, 0xf5,
+     0xf1, 0x3a, 0x43, 0xb8, 0x17, 0x74, 0x37, 0x3c,
+     0x87, 0x9c, 0xd3, 0x2d, 0x69, 0x34, 0xc0, 0x5f,
+     0xa7, 0x58, 0xee, 0xb1, 0x4f, 0xcf, 0xab, 0x38,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x3a, },
+    {0xdf, 0x1b, 0x1d, 0x66, 0xa5, 0x51, 0xd0, 0xd3,
+     0x1e, 0xff, 0x82, 0x25, 0x58, 0xb9, 0xd2, 0xcc,
+     0x75, 0xc2, 0x18, 0x02, 0x79, 0xfe, 0x0d, 0x08,
+     0xfd, 0x89, 0x6d, 0x04, 0x5c, 0x08, 0x0f, 0xc3,
+     0x52, 0x2f, 0x41, 0xbb, 0xb3, 0xf5, 0x5a, 0x97,
+     0xcf, 0xec, 0xf2, 0x1f, 0x88, 0x2c, 0xe8, 0xcb,
+     0xb1, 0xe5, 0x0c, 0xa6, 0xe6, 0x7e, 0x56, 0xdc,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x3b, },
+    {0x70, 0x6a, 0x46, 0xdc, 0x76, 0xdc, 0xb7, 0x67,
+     0x98, 0xe6, 0x0e, 0x6d, 0x89, 0x47, 0x47, 0x88,
+     0xd1, 0x6d, 0xc1, 0x80, 0x32, 0xd2, 0x68, 0xfd,
+     0x1a, 0x70, 0x4f, 0xa6, 0xe3, 0xd4, 0x89, 0x58,
+     0x43, 0xda, 0x18, 0x8f, 0xd5, 0x8f, 0xb0, 0x56,
+     0x79, 0x76, 0xd7, 0xb5, 0x03, 0x59, 0xd6, 0xb7,
+     0x85, 0x30, 0xc8, 0xf6, 0x2d, 0x1b, 0x17, 0x46,
+    },
+  },
+  {
+    {0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
+     0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0x16, 0xa2,
+     0xe0, 0xb8, 0xf0, 0x3e, 0x13, 0xdd, 0x29, 0x45,
+     0x5c, 0x5c, 0x2a, 0x3c, },
+    {0xb7, 0x0e, 0x0c, 0xbd, 0x6b, 0xb4, 0xbf, 0x7f,
+     0x32, 0x13, 0x90, 0xb9, 0x4a, 0x03, 0xc1, 0xd3,
+     0x56, 0xc2, 0x11, 0x22, 0x34, 0x32, 0x80, 0xd6,
+     0x11, 0x5c, 0x1d, 0x21, 0x42, 0xc8, 0x9c, 0x77,
+     0x4a, 0x08, 0xdc, 0x04, 0xb3, 0xdd, 0x20, 0x19,
+     0x32, 0xbc, 0x8a, 0x5e, 0xa5, 0xf8, 0xb8, 0x9b,
+     0xbb, 0x2a, 0x7e, 0x66, 0x7a, 0xff, 0x81, 0xcd,
+    },
+  },
+};
+
+TEST(P224, ExternalToInternalAndBack) {
+  Point point;
+
+  EXPECT_TRUE(point.SetFromString(base::StringPiece(
+      reinterpret_cast<const char *>(kBasePointExternal),
+      sizeof(kBasePointExternal))));
+
+  const std::string external = point.ToString();
+
+  ASSERT_EQ(external.size(), 56u);
+  EXPECT_TRUE(memcmp(external.data(), kBasePointExternal,
+                     sizeof(kBasePointExternal)) == 0);
+}
+
+TEST(P224, ScalarBaseMult) {
+  Point point;
+
+  for (size_t i = 0; i < arraysize(kNISTTestVectors); i++) {
+    p224::ScalarBaseMult(kNISTTestVectors[i].scalar, &point);
+    const std::string external = point.ToString();
+    ASSERT_EQ(external.size(), 56u);
+    EXPECT_TRUE(memcmp(external.data(), kNISTTestVectors[i].affine,
+                       external.size()) == 0);
+  }
+}
+
+TEST(P224, Addition) {
+  Point a, b, minus_b, sum, a_again;
+
+  ASSERT_TRUE(a.SetFromString(base::StringPiece(
+      reinterpret_cast<const char *>(kNISTTestVectors[10].affine), 56)));
+  ASSERT_TRUE(b.SetFromString(base::StringPiece(
+      reinterpret_cast<const char *>(kNISTTestVectors[11].affine), 56)));
+
+  p224::Negate(b, &minus_b);
+  p224::Add(a, b, &sum);
+  EXPECT_TRUE(memcmp(&sum, &a, sizeof(sum) != 0));
+  p224::Add(minus_b, sum, &a_again);
+  EXPECT_TRUE(a_again.ToString() == a.ToString());
+}