crypto/fipsmodule/ec/p256-x86_64_test.cc - boringssl - Git at Google

 /* Copyright (c) 2016, Google Inc.
  *
  * Permission to use, copy, modify, and/or distribute this software for any
  * purpose with or without fee is hereby granted, provided that the above
  * copyright notice and this permission notice appear in all copies.
  *
  * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
  * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
  * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
  * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
  * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
  * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
  * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */

 #if !defined(__STDC_FORMAT_MACROS)
 #define __STDC_FORMAT_MACROS
 #endif

 #include <openssl/base.h>

 #include <stdio.h>
 #include <string.h>

 #include <gtest/gtest.h>

 #include <openssl/bn.h>
 #include <openssl/mem.h>

 #include "../bn/internal.h"
 #include "../../internal.h"
 #include "../../test/file_test.h"
 #include "../../test/test_util.h"
 #include "p256-x86_64.h"


 // Disable tests if BORINGSSL_SHARED_LIBRARY is defined. These tests need access
 // to internal functions.
 #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
     !defined(OPENSSL_SMALL) && !defined(BORINGSSL_SHARED_LIBRARY)

 TEST(P256_X86_64Test, SelectW5) {
   // Fill a table with some garbage input.
   alignas(64) P256_POINT table[16];
   for (size_t i = 0; i < 16; i++) {
     OPENSSL_memset(table[i].X, 3 * i, sizeof(table[i].X));
     OPENSSL_memset(table[i].Y, 3 * i + 1, sizeof(table[i].Y));
     OPENSSL_memset(table[i].Z, 3 * i + 2, sizeof(table[i].Z));
   }

   for (int i = 0; i <= 16; i++) {
     P256_POINT val;
     ecp_nistz256_select_w5(&val, table, i);

     P256_POINT expected;
     if (i == 0) {
       OPENSSL_memset(&expected, 0, sizeof(expected));
     } else {
       expected = table[i-1];
     }

     EXPECT_EQ(Bytes(reinterpret_cast<const char *>(&expected), sizeof(expected)),
               Bytes(reinterpret_cast<const char *>(&val), sizeof(val)));
   }
 }

 TEST(P256_X86_64Test, SelectW7) {
   // Fill a table with some garbage input.
   alignas(64) P256_POINT_AFFINE table[64];
   for (size_t i = 0; i < 64; i++) {
     OPENSSL_memset(table[i].X, 2 * i, sizeof(table[i].X));
     OPENSSL_memset(table[i].Y, 2 * i + 1, sizeof(table[i].Y));
   }

   for (int i = 0; i <= 64; i++) {
     P256_POINT_AFFINE val;
     ecp_nistz256_select_w7(&val, table, i);

     P256_POINT_AFFINE expected;
     if (i == 0) {
       OPENSSL_memset(&expected, 0, sizeof(expected));
     } else {
       expected = table[i-1];
     }

     EXPECT_EQ(Bytes(reinterpret_cast<const char *>(&expected), sizeof(expected)),
               Bytes(reinterpret_cast<const char *>(&val), sizeof(val)));
   }
 }

 static bool GetFieldElement(FileTest *t, BN_ULONG out[P256_LIMBS],
                             const char *name) {
   std::vector<uint8_t> bytes;
   if (!t->GetBytes(&bytes, name)) {
     return false;
   }

   if (bytes.size() != BN_BYTES * P256_LIMBS) {
     ADD_FAILURE() << "Invalid length: " << name;
     return false;
   }

   // |byte| contains bytes in big-endian while |out| should contain |BN_ULONG|s
   // in little-endian.
   OPENSSL_memset(out, 0, P256_LIMBS * sizeof(BN_ULONG));
   for (size_t i = 0; i < bytes.size(); i++) {
     out[P256_LIMBS - 1 - (i / BN_BYTES)] <<= 8;
     out[P256_LIMBS - 1 - (i / BN_BYTES)] |= bytes[i];
   }

   return true;
 }

 static std::string FieldElementToString(const BN_ULONG a[P256_LIMBS]) {
   std::string ret;
   for (size_t i = P256_LIMBS-1; i < P256_LIMBS; i--) {
     char buf[2 * BN_BYTES + 1];
     BIO_snprintf(buf, sizeof(buf), BN_HEX_FMT2, a[i]);
     ret += buf;
   }
   return ret;
 }

 static testing::AssertionResult ExpectFieldElementsEqual(
     const char *expected_expr, const char *actual_expr,
     const BN_ULONG expected[P256_LIMBS], const BN_ULONG actual[P256_LIMBS]) {
   if (OPENSSL_memcmp(expected, actual, sizeof(BN_ULONG) * P256_LIMBS) == 0) {
     return testing::AssertionSuccess();
   }

   return testing::AssertionFailure()
          << "Expected: " << FieldElementToString(expected) << " ("
          << expected_expr << ")\n"
          << "Actual:   " << FieldElementToString(actual) << " (" << actual_expr
          << ")";
 }

 #define EXPECT_FIELD_ELEMENTS_EQUAL(a, b) \
   EXPECT_PRED_FORMAT2(ExpectFieldElementsEqual, a, b)

 static bool PointToAffine(P256_POINT_AFFINE *out, const P256_POINT *in) {
   static const uint8_t kP[] = {
       0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00,
       0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff,
       0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
   };

   bssl::UniquePtr<BIGNUM> x(BN_new()), y(BN_new()), z(BN_new());
   bssl::UniquePtr<BIGNUM> p(BN_bin2bn(kP, sizeof(kP), nullptr));
   if (!x || !y || !z || !p ||
       !bn_set_words(x.get(), in->X, P256_LIMBS) ||
       !bn_set_words(y.get(), in->Y, P256_LIMBS) ||
       !bn_set_words(z.get(), in->Z, P256_LIMBS)) {
     return false;
   }

   // Coordinates must be fully-reduced.
   if (BN_cmp(x.get(), p.get()) >= 0 ||
       BN_cmp(y.get(), p.get()) >= 0 ||
       BN_cmp(z.get(), p.get()) >= 0) {
     return false;
   }

   if (BN_is_zero(z.get())) {
     // The point at infinity is represented as (0, 0).
     OPENSSL_memset(out, 0, sizeof(P256_POINT_AFFINE));
     return true;
   }

   bssl::UniquePtr<BN_CTX> ctx(BN_CTX_new());
   bssl::UniquePtr<BN_MONT_CTX> mont(
       BN_MONT_CTX_new_for_modulus(p.get(), ctx.get()));
   if (!ctx || !mont ||
       // Invert Z.
       !BN_from_montgomery(z.get(), z.get(), mont.get(), ctx.get()) ||
       !BN_mod_inverse(z.get(), z.get(), p.get(), ctx.get()) ||
       !BN_to_montgomery(z.get(), z.get(), mont.get(), ctx.get()) ||
       // Convert (X, Y, Z) to (X/Z^2, Y/Z^3).
       !BN_mod_mul_montgomery(x.get(), x.get(), z.get(), mont.get(),
                              ctx.get()) ||
       !BN_mod_mul_montgomery(x.get(), x.get(), z.get(), mont.get(),
                              ctx.get()) ||
       !BN_mod_mul_montgomery(y.get(), y.get(), z.get(), mont.get(),
                              ctx.get()) ||
       !BN_mod_mul_montgomery(y.get(), y.get(), z.get(), mont.get(),
                              ctx.get()) ||
       !BN_mod_mul_montgomery(y.get(), y.get(), z.get(), mont.get(),
                              ctx.get()) ||
       !bn_copy_words(out->X, P256_LIMBS, x.get()) ||
       !bn_copy_words(out->Y, P256_LIMBS, y.get())) {
     return false;
   }
   return true;
 }

 static testing::AssertionResult ExpectPointsEqual(
     const char *expected_expr, const char *actual_expr,
     const P256_POINT_AFFINE *expected, const P256_POINT *actual) {
   // There are multiple representations of the same |P256_POINT|, so convert to
   // |P256_POINT_AFFINE| and compare.
   P256_POINT_AFFINE affine;
   if (!PointToAffine(&affine, actual)) {
     return testing::AssertionFailure()
            << "Could not convert " << actual_expr << " to affine: ("
            << FieldElementToString(actual->X) << ", "
            << FieldElementToString(actual->Y) << ", "
            << FieldElementToString(actual->Z) << ")";
   }

   if (OPENSSL_memcmp(expected, &affine, sizeof(P256_POINT_AFFINE)) != 0) {
     return testing::AssertionFailure()
            << "Expected: (" << FieldElementToString(expected->X) << ", "
            << FieldElementToString(expected->Y) << ") (" << expected_expr
            << "; affine)\n"
            << "Actual:   (" << FieldElementToString(affine.X) << ", "
            << FieldElementToString(affine.Y) << ") (" << actual_expr << ")";
   }

   return testing::AssertionSuccess();
 }

 #define EXPECT_POINTS_EQUAL(a, b) EXPECT_PRED_FORMAT2(ExpectPointsEqual, a, b)

 static void TestNegate(FileTest *t) {
   BN_ULONG a[P256_LIMBS], b[P256_LIMBS];
   ASSERT_TRUE(GetFieldElement(t, a, "A"));
   ASSERT_TRUE(GetFieldElement(t, b, "B"));

   // Test that -A = B.
   BN_ULONG ret[P256_LIMBS];
   ecp_nistz256_neg(ret, a);
   EXPECT_FIELD_ELEMENTS_EQUAL(b, ret);

   OPENSSL_memcpy(ret, a, sizeof(ret));
   ecp_nistz256_neg(ret, ret /* a */);
   EXPECT_FIELD_ELEMENTS_EQUAL(b, ret);

   // Test that -B = A.
   ecp_nistz256_neg(ret, b);
   EXPECT_FIELD_ELEMENTS_EQUAL(a, ret);

   OPENSSL_memcpy(ret, b, sizeof(ret));
   ecp_nistz256_neg(ret, ret /* b */);
   EXPECT_FIELD_ELEMENTS_EQUAL(a, ret);
 }

 static void TestMulMont(FileTest *t) {
   BN_ULONG a[P256_LIMBS], b[P256_LIMBS], result[P256_LIMBS];
   ASSERT_TRUE(GetFieldElement(t, a, "A"));
   ASSERT_TRUE(GetFieldElement(t, b, "B"));
   ASSERT_TRUE(GetFieldElement(t, result, "Result"));

   BN_ULONG ret[P256_LIMBS];
   ecp_nistz256_mul_mont(ret, a, b);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   ecp_nistz256_mul_mont(ret, b, a);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   OPENSSL_memcpy(ret, a, sizeof(ret));
   ecp_nistz256_mul_mont(ret, ret /* a */, b);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   OPENSSL_memcpy(ret, a, sizeof(ret));
   ecp_nistz256_mul_mont(ret, b, ret);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   OPENSSL_memcpy(ret, b, sizeof(ret));
   ecp_nistz256_mul_mont(ret, a, ret /* b */);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   OPENSSL_memcpy(ret, b, sizeof(ret));
   ecp_nistz256_mul_mont(ret, ret /* b */, a);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   if (OPENSSL_memcmp(a, b, sizeof(a)) == 0) {
     ecp_nistz256_sqr_mont(ret, a);
     EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

     OPENSSL_memcpy(ret, a, sizeof(ret));
     ecp_nistz256_sqr_mont(ret, ret /* a */);
     EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);
   }
 }

 static void TestFromMont(FileTest *t) {
   BN_ULONG a[P256_LIMBS], result[P256_LIMBS];
   ASSERT_TRUE(GetFieldElement(t, a, "A"));
   ASSERT_TRUE(GetFieldElement(t, result, "Result"));

   BN_ULONG ret[P256_LIMBS];
   ecp_nistz256_from_mont(ret, a);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   OPENSSL_memcpy(ret, a, sizeof(ret));
   ecp_nistz256_from_mont(ret, ret /* a */);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);
 }

 static void TestPointAdd(FileTest *t) {
   P256_POINT a, b;
   P256_POINT_AFFINE result;
   ASSERT_TRUE(GetFieldElement(t, a.X, "A.X"));
   ASSERT_TRUE(GetFieldElement(t, a.Y, "A.Y"));
   ASSERT_TRUE(GetFieldElement(t, a.Z, "A.Z"));
   ASSERT_TRUE(GetFieldElement(t, b.X, "B.X"));
   ASSERT_TRUE(GetFieldElement(t, b.Y, "B.Y"));
   ASSERT_TRUE(GetFieldElement(t, b.Z, "B.Z"));
   ASSERT_TRUE(GetFieldElement(t, result.X, "Result.X"));
   ASSERT_TRUE(GetFieldElement(t, result.Y, "Result.Y"));

   P256_POINT ret;
   ecp_nistz256_point_add(&ret, &a, &b);
   EXPECT_POINTS_EQUAL(&result, &ret);

   ecp_nistz256_point_add(&ret, &b, &a);
   EXPECT_POINTS_EQUAL(&result, &ret);

   OPENSSL_memcpy(&ret, &a, sizeof(ret));
   ecp_nistz256_point_add(&ret, &ret /* a */, &b);
   EXPECT_POINTS_EQUAL(&result, &ret);

   OPENSSL_memcpy(&ret, &a, sizeof(ret));
   ecp_nistz256_point_add(&ret, &b, &ret /* a */);
   EXPECT_POINTS_EQUAL(&result, &ret);

   OPENSSL_memcpy(&ret, &b, sizeof(ret));
   ecp_nistz256_point_add(&ret, &a, &ret /* b */);
   EXPECT_POINTS_EQUAL(&result, &ret);

   OPENSSL_memcpy(&ret, &b, sizeof(ret));
   ecp_nistz256_point_add(&ret, &ret /* b */, &a);
   EXPECT_POINTS_EQUAL(&result, &ret);

   P256_POINT_AFFINE a_affine, b_affine, infinity;
   OPENSSL_memset(&infinity, 0, sizeof(infinity));
   ASSERT_TRUE(PointToAffine(&a_affine, &a));
   ASSERT_TRUE(PointToAffine(&b_affine, &b));

   // ecp_nistz256_point_add_affine does not work when a == b unless doubling the
   // point at infinity.
   if (OPENSSL_memcmp(&a_affine, &b_affine, sizeof(a_affine)) != 0 ||
       OPENSSL_memcmp(&a_affine, &infinity, sizeof(a_affine)) == 0) {
     ecp_nistz256_point_add_affine(&ret, &a, &b_affine);
     EXPECT_POINTS_EQUAL(&result, &ret);

     OPENSSL_memcpy(&ret, &a, sizeof(ret));
     ecp_nistz256_point_add_affine(&ret, &ret /* a */, &b_affine);
     EXPECT_POINTS_EQUAL(&result, &ret);

     ecp_nistz256_point_add_affine(&ret, &b, &a_affine);
     EXPECT_POINTS_EQUAL(&result, &ret);

     OPENSSL_memcpy(&ret, &b, sizeof(ret));
     ecp_nistz256_point_add_affine(&ret, &ret /* b */, &a_affine);
     EXPECT_POINTS_EQUAL(&result, &ret);
   }

   if (OPENSSL_memcmp(&a, &b, sizeof(a)) == 0) {
     ecp_nistz256_point_double(&ret, &a);
     EXPECT_POINTS_EQUAL(&result, &ret);

     ret = a;
     ecp_nistz256_point_double(&ret, &ret /* a */);
     EXPECT_POINTS_EQUAL(&result, &ret);
   }
 }

 static void TestOrdMulMont(FileTest *t) {
   // This test works on scalars rather than field elements, but the
   // representation is the same.
   BN_ULONG a[P256_LIMBS], b[P256_LIMBS], result[P256_LIMBS];
   ASSERT_TRUE(GetFieldElement(t, a, "A"));
   ASSERT_TRUE(GetFieldElement(t, b, "B"));
   ASSERT_TRUE(GetFieldElement(t, result, "Result"));

   BN_ULONG ret[P256_LIMBS];
   ecp_nistz256_ord_mul_mont(ret, a, b);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   ecp_nistz256_ord_mul_mont(ret, b, a);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   OPENSSL_memcpy(ret, a, sizeof(ret));
   ecp_nistz256_ord_mul_mont(ret, ret /* a */, b);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   OPENSSL_memcpy(ret, a, sizeof(ret));
   ecp_nistz256_ord_mul_mont(ret, b, ret);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   OPENSSL_memcpy(ret, b, sizeof(ret));
   ecp_nistz256_ord_mul_mont(ret, a, ret /* b */);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   OPENSSL_memcpy(ret, b, sizeof(ret));
   ecp_nistz256_ord_mul_mont(ret, ret /* b */, a);
   EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

   if (OPENSSL_memcmp(a, b, sizeof(a)) == 0) {
     ecp_nistz256_ord_sqr_mont(ret, a, 1);
     EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

     OPENSSL_memcpy(ret, a, sizeof(ret));
     ecp_nistz256_ord_sqr_mont(ret, ret /* a */, 1);
     EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);
   }
 }

 TEST(P256_X86_64Test, TestVectors) {
   return FileTestGTest("crypto/fipsmodule/ec/p256-x86_64_tests.txt",
                        [](FileTest *t) {
     if (t->GetParameter() == "Negate") {
       TestNegate(t);
     } else if (t->GetParameter() == "MulMont") {
       TestMulMont(t);
     } else if (t->GetParameter() == "FromMont") {
       TestFromMont(t);
     } else if (t->GetParameter() == "PointAdd") {
       TestPointAdd(t);
     } else if (t->GetParameter() == "OrdMulMont") {
       TestOrdMulMont(t);
     } else {
       FAIL() << "Unknown test type:" << t->GetParameter();
     }
   });
 }

 #endif
	/* Copyright (c) 2016, Google Inc.
	*
	* Permission to use, copy, modify, and/or distribute this software for any
	* purpose with or without fee is hereby granted, provided that the above
	* copyright notice and this permission notice appear in all copies.
	*
	* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
	* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
	* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
	* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
	* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
	* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
	* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */

	#if !defined(__STDC_FORMAT_MACROS)
	#define __STDC_FORMAT_MACROS
	#endif

	#include <openssl/base.h>

	#include <stdio.h>
	#include <string.h>

	#include <gtest/gtest.h>

	#include <openssl/bn.h>
	#include <openssl/mem.h>

	#include "../bn/internal.h"
	#include "../../internal.h"
	#include "../../test/file_test.h"
	#include "../../test/test_util.h"
	#include "p256-x86_64.h"


	// Disable tests if BORINGSSL_SHARED_LIBRARY is defined. These tests need access
	// to internal functions.
	#if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \
	!defined(OPENSSL_SMALL) && !defined(BORINGSSL_SHARED_LIBRARY)

	TEST(P256_X86_64Test, SelectW5) {
	// Fill a table with some garbage input.
	alignas(64) P256_POINT table[16];
	for (size_t i = 0; i < 16; i++) {
	OPENSSL_memset(table[i].X, 3 * i, sizeof(table[i].X));
	OPENSSL_memset(table[i].Y, 3 * i + 1, sizeof(table[i].Y));
	OPENSSL_memset(table[i].Z, 3 * i + 2, sizeof(table[i].Z));
	}

	for (int i = 0; i <= 16; i++) {
	P256_POINT val;
	ecp_nistz256_select_w5(&val, table, i);

	P256_POINT expected;
	if (i == 0) {
	OPENSSL_memset(&expected, 0, sizeof(expected));
	} else {
	expected = table[i-1];
	}

	EXPECT_EQ(Bytes(reinterpret_cast<const char *>(&expected), sizeof(expected)),
	Bytes(reinterpret_cast<const char *>(&val), sizeof(val)));
	}
	}

	TEST(P256_X86_64Test, SelectW7) {
	// Fill a table with some garbage input.
	alignas(64) P256_POINT_AFFINE table[64];
	for (size_t i = 0; i < 64; i++) {
	OPENSSL_memset(table[i].X, 2 * i, sizeof(table[i].X));
	OPENSSL_memset(table[i].Y, 2 * i + 1, sizeof(table[i].Y));
	}

	for (int i = 0; i <= 64; i++) {
	P256_POINT_AFFINE val;
	ecp_nistz256_select_w7(&val, table, i);

	P256_POINT_AFFINE expected;
	if (i == 0) {
	OPENSSL_memset(&expected, 0, sizeof(expected));
	} else {
	expected = table[i-1];
	}

	EXPECT_EQ(Bytes(reinterpret_cast<const char *>(&expected), sizeof(expected)),
	Bytes(reinterpret_cast<const char *>(&val), sizeof(val)));
	}
	}

	static bool GetFieldElement(FileTest *t, BN_ULONG out[P256_LIMBS],
	const char *name) {
	std::vector<uint8_t> bytes;
	if (!t->GetBytes(&bytes, name)) {
	return false;
	}

	if (bytes.size() != BN_BYTES * P256_LIMBS) {
	ADD_FAILURE() << "Invalid length: " << name;
	return false;
	}

	// \|byte\| contains bytes in big-endian while \|out\| should contain \|BN_ULONG\|s
	// in little-endian.
	OPENSSL_memset(out, 0, P256_LIMBS * sizeof(BN_ULONG));
	for (size_t i = 0; i < bytes.size(); i++) {
	out[P256_LIMBS - 1 - (i / BN_BYTES)] <<= 8;
	out[P256_LIMBS - 1 - (i / BN_BYTES)] \|= bytes[i];
	}

	return true;
	}

	static std::string FieldElementToString(const BN_ULONG a[P256_LIMBS]) {
	std::string ret;
	for (size_t i = P256_LIMBS-1; i < P256_LIMBS; i--) {
	char buf[2 * BN_BYTES + 1];
	BIO_snprintf(buf, sizeof(buf), BN_HEX_FMT2, a[i]);
	ret += buf;
	}
	return ret;
	}

	static testing::AssertionResult ExpectFieldElementsEqual(
	const char expected_expr, const char actual_expr,
	const BN_ULONG expected[P256_LIMBS], const BN_ULONG actual[P256_LIMBS]) {
	if (OPENSSL_memcmp(expected, actual, sizeof(BN_ULONG) * P256_LIMBS) == 0) {
	return testing::AssertionSuccess();
	}

	return testing::AssertionFailure()
	<< "Expected: " << FieldElementToString(expected) << " ("
	<< expected_expr << ")\n"
	<< "Actual: " << FieldElementToString(actual) << " (" << actual_expr
	<< ")";
	}

	#define EXPECT_FIELD_ELEMENTS_EQUAL(a, b) \
	EXPECT_PRED_FORMAT2(ExpectFieldElementsEqual, a, b)

	static bool PointToAffine(P256_POINT_AFFINE out, const P256_POINT in) {
	static const uint8_t kP[] = {
	0xff, 0xff, 0xff, 0xff, 0x00, 0x00, 0x00, 0x01, 0x00, 0x00, 0x00,
	0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0xff, 0xff,
	0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
	};

	bssl::UniquePtr<BIGNUM> x(BN_new()), y(BN_new()), z(BN_new());
	bssl::UniquePtr<BIGNUM> p(BN_bin2bn(kP, sizeof(kP), nullptr));
	if (!x \|\| !y \|\| !z \|\| !p \|\|
	!bn_set_words(x.get(), in->X, P256_LIMBS) \|\|
	!bn_set_words(y.get(), in->Y, P256_LIMBS) \|\|
	!bn_set_words(z.get(), in->Z, P256_LIMBS)) {
	return false;
	}

	// Coordinates must be fully-reduced.
	if (BN_cmp(x.get(), p.get()) >= 0 \|\|
	BN_cmp(y.get(), p.get()) >= 0 \|\|
	BN_cmp(z.get(), p.get()) >= 0) {
	return false;
	}

	if (BN_is_zero(z.get())) {
	// The point at infinity is represented as (0, 0).
	OPENSSL_memset(out, 0, sizeof(P256_POINT_AFFINE));
	return true;
	}

	bssl::UniquePtr<BN_CTX> ctx(BN_CTX_new());
	bssl::UniquePtr<BN_MONT_CTX> mont(
	BN_MONT_CTX_new_for_modulus(p.get(), ctx.get()));
	if (!ctx \|\| !mont \|\|
	// Invert Z.
	!BN_from_montgomery(z.get(), z.get(), mont.get(), ctx.get()) \|\|
	!BN_mod_inverse(z.get(), z.get(), p.get(), ctx.get()) \|\|
	!BN_to_montgomery(z.get(), z.get(), mont.get(), ctx.get()) \|\|
	// Convert (X, Y, Z) to (X/Z^2, Y/Z^3).
	!BN_mod_mul_montgomery(x.get(), x.get(), z.get(), mont.get(),
	ctx.get()) \|\|
	!BN_mod_mul_montgomery(x.get(), x.get(), z.get(), mont.get(),
	ctx.get()) \|\|
	!BN_mod_mul_montgomery(y.get(), y.get(), z.get(), mont.get(),
	ctx.get()) \|\|
	!BN_mod_mul_montgomery(y.get(), y.get(), z.get(), mont.get(),
	ctx.get()) \|\|
	!BN_mod_mul_montgomery(y.get(), y.get(), z.get(), mont.get(),
	ctx.get()) \|\|
	!bn_copy_words(out->X, P256_LIMBS, x.get()) \|\|
	!bn_copy_words(out->Y, P256_LIMBS, y.get())) {
	return false;
	}
	return true;
	}

	static testing::AssertionResult ExpectPointsEqual(
	const char expected_expr, const char actual_expr,
	const P256_POINT_AFFINE expected, const P256_POINT actual) {
	// There are multiple representations of the same \|P256_POINT\|, so convert to
	// \|P256_POINT_AFFINE\| and compare.
	P256_POINT_AFFINE affine;
	if (!PointToAffine(&affine, actual)) {
	return testing::AssertionFailure()
	<< "Could not convert " << actual_expr << " to affine: ("
	<< FieldElementToString(actual->X) << ", "
	<< FieldElementToString(actual->Y) << ", "
	<< FieldElementToString(actual->Z) << ")";
	}

	if (OPENSSL_memcmp(expected, &affine, sizeof(P256_POINT_AFFINE)) != 0) {
	return testing::AssertionFailure()
	<< "Expected: (" << FieldElementToString(expected->X) << ", "
	<< FieldElementToString(expected->Y) << ") (" << expected_expr
	<< "; affine)\n"
	<< "Actual: (" << FieldElementToString(affine.X) << ", "
	<< FieldElementToString(affine.Y) << ") (" << actual_expr << ")";
	}

	return testing::AssertionSuccess();
	}

	#define EXPECT_POINTS_EQUAL(a, b) EXPECT_PRED_FORMAT2(ExpectPointsEqual, a, b)

	static void TestNegate(FileTest *t) {
	BN_ULONG a[P256_LIMBS], b[P256_LIMBS];
	ASSERT_TRUE(GetFieldElement(t, a, "A"));
	ASSERT_TRUE(GetFieldElement(t, b, "B"));

	// Test that -A = B.
	BN_ULONG ret[P256_LIMBS];
	ecp_nistz256_neg(ret, a);
	EXPECT_FIELD_ELEMENTS_EQUAL(b, ret);

	OPENSSL_memcpy(ret, a, sizeof(ret));
	ecp_nistz256_neg(ret, ret /* a */);
	EXPECT_FIELD_ELEMENTS_EQUAL(b, ret);

	// Test that -B = A.
	ecp_nistz256_neg(ret, b);
	EXPECT_FIELD_ELEMENTS_EQUAL(a, ret);

	OPENSSL_memcpy(ret, b, sizeof(ret));
	ecp_nistz256_neg(ret, ret /* b */);
	EXPECT_FIELD_ELEMENTS_EQUAL(a, ret);
	}

	static void TestMulMont(FileTest *t) {
	BN_ULONG a[P256_LIMBS], b[P256_LIMBS], result[P256_LIMBS];
	ASSERT_TRUE(GetFieldElement(t, a, "A"));
	ASSERT_TRUE(GetFieldElement(t, b, "B"));
	ASSERT_TRUE(GetFieldElement(t, result, "Result"));

	BN_ULONG ret[P256_LIMBS];
	ecp_nistz256_mul_mont(ret, a, b);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	ecp_nistz256_mul_mont(ret, b, a);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	OPENSSL_memcpy(ret, a, sizeof(ret));
	ecp_nistz256_mul_mont(ret, ret /* a */, b);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	OPENSSL_memcpy(ret, a, sizeof(ret));
	ecp_nistz256_mul_mont(ret, b, ret);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	OPENSSL_memcpy(ret, b, sizeof(ret));
	ecp_nistz256_mul_mont(ret, a, ret /* b */);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	OPENSSL_memcpy(ret, b, sizeof(ret));
	ecp_nistz256_mul_mont(ret, ret /* b */, a);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	if (OPENSSL_memcmp(a, b, sizeof(a)) == 0) {
	ecp_nistz256_sqr_mont(ret, a);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	OPENSSL_memcpy(ret, a, sizeof(ret));
	ecp_nistz256_sqr_mont(ret, ret /* a */);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);
	}
	}

	static void TestFromMont(FileTest *t) {
	BN_ULONG a[P256_LIMBS], result[P256_LIMBS];
	ASSERT_TRUE(GetFieldElement(t, a, "A"));
	ASSERT_TRUE(GetFieldElement(t, result, "Result"));

	BN_ULONG ret[P256_LIMBS];
	ecp_nistz256_from_mont(ret, a);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	OPENSSL_memcpy(ret, a, sizeof(ret));
	ecp_nistz256_from_mont(ret, ret /* a */);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);
	}

	static void TestPointAdd(FileTest *t) {
	P256_POINT a, b;
	P256_POINT_AFFINE result;
	ASSERT_TRUE(GetFieldElement(t, a.X, "A.X"));
	ASSERT_TRUE(GetFieldElement(t, a.Y, "A.Y"));
	ASSERT_TRUE(GetFieldElement(t, a.Z, "A.Z"));
	ASSERT_TRUE(GetFieldElement(t, b.X, "B.X"));
	ASSERT_TRUE(GetFieldElement(t, b.Y, "B.Y"));
	ASSERT_TRUE(GetFieldElement(t, b.Z, "B.Z"));
	ASSERT_TRUE(GetFieldElement(t, result.X, "Result.X"));
	ASSERT_TRUE(GetFieldElement(t, result.Y, "Result.Y"));

	P256_POINT ret;
	ecp_nistz256_point_add(&ret, &a, &b);
	EXPECT_POINTS_EQUAL(&result, &ret);

	ecp_nistz256_point_add(&ret, &b, &a);
	EXPECT_POINTS_EQUAL(&result, &ret);

	OPENSSL_memcpy(&ret, &a, sizeof(ret));
	ecp_nistz256_point_add(&ret, &ret /* a */, &b);
	EXPECT_POINTS_EQUAL(&result, &ret);

	OPENSSL_memcpy(&ret, &a, sizeof(ret));
	ecp_nistz256_point_add(&ret, &b, &ret /* a */);
	EXPECT_POINTS_EQUAL(&result, &ret);

	OPENSSL_memcpy(&ret, &b, sizeof(ret));
	ecp_nistz256_point_add(&ret, &a, &ret /* b */);
	EXPECT_POINTS_EQUAL(&result, &ret);

	OPENSSL_memcpy(&ret, &b, sizeof(ret));
	ecp_nistz256_point_add(&ret, &ret /* b */, &a);
	EXPECT_POINTS_EQUAL(&result, &ret);

	P256_POINT_AFFINE a_affine, b_affine, infinity;
	OPENSSL_memset(&infinity, 0, sizeof(infinity));
	ASSERT_TRUE(PointToAffine(&a_affine, &a));
	ASSERT_TRUE(PointToAffine(&b_affine, &b));

	// ecp_nistz256_point_add_affine does not work when a == b unless doubling the
	// point at infinity.
	if (OPENSSL_memcmp(&a_affine, &b_affine, sizeof(a_affine)) != 0 \|\|
	OPENSSL_memcmp(&a_affine, &infinity, sizeof(a_affine)) == 0) {
	ecp_nistz256_point_add_affine(&ret, &a, &b_affine);
	EXPECT_POINTS_EQUAL(&result, &ret);

	OPENSSL_memcpy(&ret, &a, sizeof(ret));
	ecp_nistz256_point_add_affine(&ret, &ret /* a */, &b_affine);
	EXPECT_POINTS_EQUAL(&result, &ret);

	ecp_nistz256_point_add_affine(&ret, &b, &a_affine);
	EXPECT_POINTS_EQUAL(&result, &ret);

	OPENSSL_memcpy(&ret, &b, sizeof(ret));
	ecp_nistz256_point_add_affine(&ret, &ret /* b */, &a_affine);
	EXPECT_POINTS_EQUAL(&result, &ret);
	}

	if (OPENSSL_memcmp(&a, &b, sizeof(a)) == 0) {
	ecp_nistz256_point_double(&ret, &a);
	EXPECT_POINTS_EQUAL(&result, &ret);

	ret = a;
	ecp_nistz256_point_double(&ret, &ret /* a */);
	EXPECT_POINTS_EQUAL(&result, &ret);
	}
	}

	static void TestOrdMulMont(FileTest *t) {
	// This test works on scalars rather than field elements, but the
	// representation is the same.
	BN_ULONG a[P256_LIMBS], b[P256_LIMBS], result[P256_LIMBS];
	ASSERT_TRUE(GetFieldElement(t, a, "A"));
	ASSERT_TRUE(GetFieldElement(t, b, "B"));
	ASSERT_TRUE(GetFieldElement(t, result, "Result"));

	BN_ULONG ret[P256_LIMBS];
	ecp_nistz256_ord_mul_mont(ret, a, b);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	ecp_nistz256_ord_mul_mont(ret, b, a);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	OPENSSL_memcpy(ret, a, sizeof(ret));
	ecp_nistz256_ord_mul_mont(ret, ret /* a */, b);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	OPENSSL_memcpy(ret, a, sizeof(ret));
	ecp_nistz256_ord_mul_mont(ret, b, ret);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	OPENSSL_memcpy(ret, b, sizeof(ret));
	ecp_nistz256_ord_mul_mont(ret, a, ret /* b */);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	OPENSSL_memcpy(ret, b, sizeof(ret));
	ecp_nistz256_ord_mul_mont(ret, ret /* b */, a);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	if (OPENSSL_memcmp(a, b, sizeof(a)) == 0) {
	ecp_nistz256_ord_sqr_mont(ret, a, 1);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);

	OPENSSL_memcpy(ret, a, sizeof(ret));
	ecp_nistz256_ord_sqr_mont(ret, ret /* a */, 1);
	EXPECT_FIELD_ELEMENTS_EQUAL(result, ret);
	}
	}

	TEST(P256_X86_64Test, TestVectors) {
	return FileTestGTest("crypto/fipsmodule/ec/p256-x86_64_tests.txt",
	[](FileTest *t) {
	if (t->GetParameter() == "Negate") {
	TestNegate(t);
	} else if (t->GetParameter() == "MulMont") {
	TestMulMont(t);
	} else if (t->GetParameter() == "FromMont") {
	TestFromMont(t);
	} else if (t->GetParameter() == "PointAdd") {
	TestPointAdd(t);
	} else if (t->GetParameter() == "OrdMulMont") {
	TestOrdMulMont(t);
	} else {
	FAIL() << "Unknown test type:" << t->GetParameter();
	}
	});
	}

	#endif