x25519_test.c

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/*
 * Copyright (C) 2024 Michael Brown <mbrown@fensystems.co.uk>.
 *
 * This program is free software; you can redistribute it and/or
 * modify it under the terms of the GNU General Public License as
 * published by the Free Software Foundation; either version 2 of the
 * License, or any later version.
 *
 * This program is distributed in the hope that it will be useful, but
 * WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU
 * General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
 * 02110-1301, USA.
 *
 * You can also choose to distribute this program under the terms of
 * the Unmodified Binary Distribution Licence (as given in the file
 * COPYING.UBDL), provided that you have satisfied its requirements.
 */
 
FILE_LICENCE ( GPL2_OR_LATER_OR_UBDL );
 
/** @file
 *
 * X25519 key exchange test
 *
 * Full key exchange test vectors are taken from RFC7748.
 *
 */
 
/* Forcibly enable assertions */
#undef NDEBUG
 
#include <stdint.h>
#include <string.h>
#include <ipxe/x25519.h>
#include <ipxe/test.h>
 
/** Define inline multiplicand */
#define MULTIPLICAND(...) { __VA_ARGS__ }
 
/** Define inline multiplier */
#define MULTIPLIER(...) { __VA_ARGS__ }
 
/** Define inline invertend */
#define INVERTEND(...) { __VA_ARGS__ }
 
/** Define inline base point */
#define BASE(...) { __VA_ARGS__ }
 
/** Define inline scalar multiple */
#define SCALAR(...) { __VA_ARGS__ }
 
/** Define inline expected result */
#define EXPECTED(...) { __VA_ARGS__ }
 
/** An X25519 multiplication self-test */
struct x25519_multiply_test {
        /** Multiplicand */
        const void *multiplicand;
        /** Length of multiplicand */
        size_t multiplicand_len;
        /** Multiplier */
        const void *multiplier;
        /** Length of multiplier */
        size_t multiplier_len;
        /** Expected result */
        const void *expected;
        /** Length of expected result */
        size_t expected_len;
};
 
/**
 * Define an X25519 multiplication test
 *
 * @v name              Test name
 * @v MULTIPLICAND      258-bit multiplicand
 * @v MULTIPLIER        258-bit multiplier
 * @v EXPECTED          255-bit expected result
 * @ret test            X25519 multiplication test
 */
#define X25519_MULTIPLY_TEST( name, MULTIPLICAND, MULTIPLIER,           \
                              EXPECTED )                                \
        static const uint8_t name ## _multiplicand[] = MULTIPLICAND;    \
        static const uint8_t name ## _multiplier[] = MULTIPLIER;        \
        static const uint8_t name ## _expected[] = EXPECTED;            \
        static struct x25519_multiply_test name = {                     \
                .multiplicand = name ## _multiplicand,                  \
                .multiplicand_len = sizeof ( name ## _multiplicand ),   \
                .multiplier = name ## _multiplier,                      \
                .multiplier_len = sizeof ( name ## _multiplier ),       \
                .expected = name ## _expected,                          \
                .expected_len = sizeof ( name ## _expected ),           \
        }
 
/** An X25519 multiplicative inversion self-test */
struct x25519_invert_test {
        /** Invertend */
        const void *invertend;
        /** Length of invertend */
        size_t invertend_len;
        /** Expected result */
        const void *expected;
        /** Length of expected result */
        size_t expected_len;
};
 
/**
 * Define an X25519 multiplicative inversion test
 *
 * @v name              Test name
 * @v INVERTEND         258-bit invertend
 * @v EXPECTED          255-bit expected result
 * @ret test            X25519 multiplicative inversion test
 */
#define X25519_INVERT_TEST( name, INVERTEND, EXPECTED )                 \
        static const uint8_t name ## _invertend[] = INVERTEND;          \
        static const uint8_t name ## _expected[] = EXPECTED;            \
        static struct x25519_invert_test name = {                       \
                .invertend = name ## _invertend,                        \
                .invertend_len = sizeof ( name ## _invertend ),         \
                .expected = name ## _expected,                          \
                .expected_len = sizeof ( name ## _expected ),           \
        }
 
/** An X25519 key exchange self-test */
struct x25519_key_test {
        /** Base */
        struct x25519_value base;
        /** Scalar */
        struct x25519_value scalar;
        /** Expected result */
        struct x25519_value expected;
        /** Number of iterations */
        unsigned int count;
        /** Key exchange is expected to fail (i.e. produce all-zeroes) */
        int fail;
};
 
/**
 * Define an X25519 key exchange test
 *
 * @v name              Test name
 * @v COUNT             Number of iterations
 * @v FAIL              Expected failure status
 * @v BASE              Base point
 * @v SCALAR            Scalar multiple
 * @v EXPECTED          Expected result
 * @ret test            X25519 key exchange test
 */
#define X25519_KEY_TEST( name, COUNT, FAIL, BASE, SCALAR, EXPECTED )    \
        static struct x25519_key_test name = {                          \
                .count = COUNT,                                         \
                .fail = FAIL,                                           \
                .base = { .raw = BASE },                                \
                .scalar = { .raw = SCALAR },                            \
                .expected = { .raw = EXPECTED },                        \
        }
 
/**
 * Report an X25519 multiplication test result
 *
 * @v test              X25519 multiplication test
 * @v file              Test code file
 * @v line              Test code line
 */
static void x25519_multiply_okx ( struct x25519_multiply_test *test,
                                  const char *file, unsigned int line ) {
        union x25519_oct258 multiplicand;
        union x25519_oct258 multiplier;
        union x25519_quad257 expected;
        union x25519_quad257 actual;
 
        /* Construct big integers */
        bigint_init ( &multiplicand.value, test->multiplicand,
                      test->multiplicand_len );
        DBGC ( test, "X25519 multiplicand:\n" );
        DBGC_HDA ( test, 0, &multiplicand, sizeof ( multiplicand ) );
        bigint_init ( &multiplier.value, test->multiplier,
                      test->multiplier_len );
        DBGC ( test, "X25519 multiplier:\n" );
        DBGC_HDA ( test, 0, &multiplier, sizeof ( multiplier ) );
        bigint_init ( &expected.value, test->expected, test->expected_len );
        DBGC ( test, "X25519 expected product:\n" );
        DBGC_HDA ( test, 0, &expected, sizeof ( expected ) );
 
        /* Perform multiplication */
        x25519_multiply ( &multiplicand, &multiplier, &actual );
 
        /* Reduce result to allow for comparison */
        x25519_reduce ( &actual );
        DBGC ( test, "X25519 actual product:\n" );
        DBGC_HDA ( test, 0, &actual, sizeof ( actual ) );
 
        /* Compare against expected result */
        okx ( memcmp ( &actual, &expected, sizeof ( expected ) ) == 0,
              file, line );
}
#define x25519_multiply_ok( test ) \
        x25519_multiply_okx ( test, __FILE__, __LINE__ )
 
/**
 * Report an X25519 multiplicative inversion test result
 *
 * @v test              X25519 multiplicative inversion test
 * @v file              Test code file
 * @v line              Test code line
 */
static void x25519_invert_okx ( struct x25519_invert_test *test,
                                const char *file, unsigned int line ) {
        static const uint8_t one[] = { 1 };
        union x25519_oct258 invertend;
        union x25519_quad257 expected;
        union x25519_quad257 actual;
        union x25519_quad257 product;
        union x25519_quad257 identity;
 
        /* Construct big integers */
        bigint_init ( &invertend.value, test->invertend, test->invertend_len );
        DBGC ( test, "X25519 invertend:\n" );
        DBGC_HDA ( test, 0, &invertend, sizeof ( invertend ) );
        bigint_init ( &expected.value, test->expected, test->expected_len );
        DBGC ( test, "X25519 expected inverse:\n" );
        DBGC_HDA ( test, 0, &expected, sizeof ( expected ) );
        bigint_init ( &identity.value, one, sizeof ( one ) );
 
        /* Perform inversion */
        x25519_invert ( &invertend, &actual );
 
        /* Multiply invertend by inverse */
        x25519_multiply ( &invertend, &actual.oct258, &product );
 
        /* Reduce results to allow for comparison */
        x25519_reduce ( &actual );
        DBGC ( test, "X25519 actual inverse:\n" );
        DBGC_HDA ( test, 0, &actual, sizeof ( actual ) );
        x25519_reduce ( &product );
        DBGC ( test, "X25519 actual product:\n" );
        DBGC_HDA ( test, 0, &product, sizeof ( product ) );
 
        /* Compare against expected results */
        okx ( memcmp ( &actual, &expected, sizeof ( expected ) ) == 0,
              file, line );
        okx ( memcmp ( &product, &identity, sizeof ( identity ) ) == 0,
              file, line );
}
#define x25519_invert_ok( test ) \
        x25519_invert_okx ( test, __FILE__, __LINE__ )
 
/**
 * Report an X25519 key exchange test result
 *
 * @v test              X25519 key exchange test
 * @v file              Test code file
 * @v line              Test code line
 */
static void x25519_key_okx ( struct x25519_key_test *test,
                             const char *file, unsigned int line ) {
        struct x25519_value base;
        struct x25519_value scalar;
        struct x25519_value actual;
        unsigned int i;
 
        /* Construct input values */
        memcpy ( &base, &test->base, sizeof ( test->base ) );
        memcpy ( &scalar, &test->scalar, sizeof ( test->scalar ) );
        DBGC ( test, "X25519 base:\n" );
        DBGC_HDA ( test, 0, &base, sizeof ( base ) );
        DBGC ( test, "X25519 scalar:\n" );
        DBGC_HDA ( test, 0, &scalar, sizeof ( scalar ) );
        DBGC ( test, "X25519 expected result (x%d):\n", test->count );
        DBGC_HDA ( test, 0, &test->expected, sizeof ( test->expected ) );
 
        /* Calculate key */
        for ( i = 0 ; i < test->count ; i++ ) {
                x25519_key ( &base, &scalar, &actual );
                if ( test->fail ) {
                        okx ( x25519_is_zero ( &actual ), file, line );
                } else {
                        okx ( ( ! x25519_is_zero ( &actual ) ), file, line );
                }
                memcpy ( &base, &scalar, sizeof ( base ) );
                memcpy ( &scalar, &actual, sizeof ( scalar ) );
        }
        DBGC ( test, "X25519 actual result (x%d):\n", test->count );
        DBGC_HDA ( test, 0, &actual, sizeof ( actual ) );
 
        /* Compare against expected result */
        okx ( memcmp ( &actual, &test->expected,
                       sizeof ( test->expected ) ) == 0, file, line );
}
#define x25519_key_ok( test ) \
        x25519_key_okx ( test, __FILE__, __LINE__ )
 
/* Test multiplying small numbers */
X25519_MULTIPLY_TEST ( multiply_small, MULTIPLICAND ( 6 ),
                       MULTIPLIER ( 9 ), EXPECTED ( 6 * 9 ) );
 
/* Test exact multiple of field prime */
X25519_MULTIPLY_TEST ( multiply_k_p,
        MULTIPLICAND ( 0x7f, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                       0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                       0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
                       0xff, 0xff, 0xff, 0xff, 0xed ),
        MULTIPLIER ( 0x00, 0xe8, 0x0d, 0x83, 0xd4, 0xe9, 0x1e, 0xdd, 0x7a,
                     0x45, 0x14, 0x87, 0xb7, 0xfc, 0x62, 0x54, 0x1f, 0xb2,
                     0x97, 0x24, 0xde, 0xfa, 0xd3, 0xe7, 0x3e, 0x83, 0x93,
                     0x60, 0xbc, 0x20, 0x97, 0x9b, 0x22 ),
        EXPECTED ( 0x00 ) );
 
/* 0x0223b8c1e9392456de3eb13b9046685257bdd640fb06671ad11c80317fa3b1799d *
 * 0x006c031199972a846916419f828b9d2434e465e150bd9c66b3ad3c2d6d1a3d1fa7 =
 * 0x1ba87e982f7c477616b4d5136ba54733e40081c1c2e27d864aa178ce893d1297 (mod p)
 */
X25519_MULTIPLY_TEST ( multiply_1,
        MULTIPLICAND ( 0x02, 0x23, 0xb8, 0xc1, 0xe9, 0x39, 0x24, 0x56, 0xde,
                       0x3e, 0xb1, 0x3b, 0x90, 0x46, 0x68, 0x52, 0x57, 0xbd,
                       0xd6, 0x40, 0xfb, 0x06, 0x67, 0x1a, 0xd1, 0x1c, 0x80,
                       0x31, 0x7f, 0xa3, 0xb1, 0x79, 0x9d ),
        MULTIPLIER ( 0x00, 0x6c, 0x03, 0x11, 0x99, 0x97, 0x2a, 0x84, 0x69,
                     0x16, 0x41, 0x9f, 0x82, 0x8b, 0x9d, 0x24, 0x34, 0xe4,
                     0x65, 0xe1, 0x50, 0xbd, 0x9c, 0x66, 0xb3, 0xad, 0x3c,
                     0x2d, 0x6d, 0x1a, 0x3d, 0x1f, 0xa7 ),
        EXPECTED ( 0x1b, 0xa8, 0x7e, 0x98, 0x2f, 0x7c, 0x47, 0x76, 0x16, 0xb4,
                   0xd5, 0x13, 0x6b, 0xa5, 0x47, 0x33, 0xe4, 0x00, 0x81, 0xc1,
                   0xc2, 0xe2, 0x7d, 0x86, 0x4a, 0xa1, 0x78, 0xce, 0x89, 0x3d,
                   0x12, 0x97 ) );
 
/* 0x008fadc1a606cb0fb39a1de644815ef6d13b8faa1837f8a88b17fc695a07a0ca6e *
 * 0x0196da1dac72ff5d2a386ecbe06b65a6a48b8148f6b38a088ca65ed389b74d0fb1 =
 * 0x351f7bf75ef580249ed6f9ff3996463b0730a1d49b5d36b863e192591157e950 (mod p)
 */
X25519_MULTIPLY_TEST ( multiply_2,
        MULTIPLICAND ( 0x00, 0x8f, 0xad, 0xc1, 0xa6, 0x06, 0xcb, 0x0f, 0xb3,
                       0x9a, 0x1d, 0xe6, 0x44, 0x81, 0x5e, 0xf6, 0xd1, 0x3b,
                       0x8f, 0xaa, 0x18, 0x37, 0xf8, 0xa8, 0x8b, 0x17, 0xfc,
                       0x69, 0x5a, 0x07, 0xa0, 0xca, 0x6e ),
        MULTIPLIER ( 0x01, 0x96, 0xda, 0x1d, 0xac, 0x72, 0xff, 0x5d, 0x2a,
                     0x38, 0x6e, 0xcb, 0xe0, 0x6b, 0x65, 0xa6, 0xa4, 0x8b,
                     0x81, 0x48, 0xf6, 0xb3, 0x8a, 0x08, 0x8c, 0xa6, 0x5e,
                     0xd3, 0x89, 0xb7, 0x4d, 0x0f, 0xb1 ),
        EXPECTED ( 0x35, 0x1f, 0x7b, 0xf7, 0x5e, 0xf5, 0x80, 0x24, 0x9e, 0xd6,
                   0xf9, 0xff, 0x39, 0x96, 0x46, 0x3b, 0x07, 0x30, 0xa1, 0xd4,
                   0x9b, 0x5d, 0x36, 0xb8, 0x63, 0xe1, 0x92, 0x59, 0x11, 0x57,
                   0xe9, 0x50 ) );
 
/* 0x016c307511b2b9437a28df6ec4ce4a2bbdc241330b01a9e71fde8a774bcf36d58b *
 * 0x0117be31111a2a73ed562b0f79c37459eef50bea63371ecd7b27cd813047229389 =
 * 0x6b43b5185965f8f0920f31ae1b2cefadd7b078fecf68dbeaa17b9c385b558329 (mod p)
 */
X25519_MULTIPLY_TEST ( multiply_3,
        MULTIPLICAND ( 0x01, 0x6c, 0x30, 0x75, 0x11, 0xb2, 0xb9, 0x43, 0x7a,
                       0x28, 0xdf, 0x6e, 0xc4, 0xce, 0x4a, 0x2b, 0xbd, 0xc2,
                       0x41, 0x33, 0x0b, 0x01, 0xa9, 0xe7, 0x1f, 0xde, 0x8a,
                       0x77, 0x4b, 0xcf, 0x36, 0xd5, 0x8b ),
        MULTIPLIER ( 0x01, 0x17, 0xbe, 0x31, 0x11, 0x1a, 0x2a, 0x73, 0xed,
                     0x56, 0x2b, 0x0f, 0x79, 0xc3, 0x74, 0x59, 0xee, 0xf5,
                     0x0b, 0xea, 0x63, 0x37, 0x1e, 0xcd, 0x7b, 0x27, 0xcd,
                     0x81, 0x30, 0x47, 0x22, 0x93, 0x89 ),
        EXPECTED ( 0x6b, 0x43, 0xb5, 0x18, 0x59, 0x65, 0xf8, 0xf0, 0x92, 0x0f,
                   0x31, 0xae, 0x1b, 0x2c, 0xef, 0xad, 0xd7, 0xb0, 0x78, 0xfe,
                   0xcf, 0x68, 0xdb, 0xea, 0xa1, 0x7b, 0x9c, 0x38, 0x5b, 0x55,
                   0x83, 0x29 ) );
 
/* 0x020b1f9163ce9ff57f43b7a3a69a8dca03580d7b71d8f564135be6128e18c26797 *
 * 0x018d5288f1142c3fe860e7a113ec1b8ca1f91e1d4c1ff49b7889463e85759cde66 =
 * 0x28a77d3c8a14323d63b288dbd40315b3f192b8485d86a02cb87d3dfb7a0b5447 (mod p)
 */
X25519_MULTIPLY_TEST ( multiply_4,
        MULTIPLICAND ( 0x02, 0x0b, 0x1f, 0x91, 0x63, 0xce, 0x9f, 0xf5, 0x7f,
                       0x43, 0xb7, 0xa3, 0xa6, 0x9a, 0x8d, 0xca, 0x03, 0x58,
                       0x0d, 0x7b, 0x71, 0xd8, 0xf5, 0x64, 0x13, 0x5b, 0xe6,
                       0x12, 0x8e, 0x18, 0xc2, 0x67, 0x97 ),
        MULTIPLIER ( 0x01, 0x8d, 0x52, 0x88, 0xf1, 0x14, 0x2c, 0x3f, 0xe8,
                     0x60, 0xe7, 0xa1, 0x13, 0xec, 0x1b, 0x8c, 0xa1, 0xf9,
                     0x1e, 0x1d, 0x4c, 0x1f, 0xf4, 0x9b, 0x78, 0x89, 0x46,
                     0x3e, 0x85, 0x75, 0x9c, 0xde, 0x66 ),
        EXPECTED ( 0x28, 0xa7, 0x7d, 0x3c, 0x8a, 0x14, 0x32, 0x3d, 0x63, 0xb2,
                   0x88, 0xdb, 0xd4, 0x03, 0x15, 0xb3, 0xf1, 0x92, 0xb8, 0x48,
                   0x5d, 0x86, 0xa0, 0x2c, 0xb8, 0x7d, 0x3d, 0xfb, 0x7a, 0x0b,
                   0x54, 0x47 ) );
 
/* 0x023139d32c93cd59bf5c941cf0dc98d2c1e2acf72f9e574f7aa0ee89aed453dd32 *
 * 0x03146d3f31fc377a4c4a15544dc5e7ce8a3a578a8ea9488d990bbb259911ce5dd2 =
 * 0x4bdb7a35c0a5182000aa67554741e88cfdf460a78c6fae07adf83d2f005d2767 (mod p)
 */
X25519_MULTIPLY_TEST ( multiply_5,
        MULTIPLICAND ( 0x02, 0x31, 0x39, 0xd3, 0x2c, 0x93, 0xcd, 0x59, 0xbf,
                       0x5c, 0x94, 0x1c, 0xf0, 0xdc, 0x98, 0xd2, 0xc1, 0xe2,
                       0xac, 0xf7, 0x2f, 0x9e, 0x57, 0x4f, 0x7a, 0xa0, 0xee,
                       0x89, 0xae, 0xd4, 0x53, 0xdd, 0x32 ),
        MULTIPLIER ( 0x03, 0x14, 0x6d, 0x3f, 0x31, 0xfc, 0x37, 0x7a, 0x4c,
                     0x4a, 0x15, 0x54, 0x4d, 0xc5, 0xe7, 0xce, 0x8a, 0x3a,
                     0x57, 0x8a, 0x8e, 0xa9, 0x48, 0x8d, 0x99, 0x0b, 0xbb,
                     0x25, 0x99, 0x11, 0xce, 0x5d, 0xd2 ),
        EXPECTED ( 0x4b, 0xdb, 0x7a, 0x35, 0xc0, 0xa5, 0x18, 0x20, 0x00, 0xaa,
                   0x67, 0x55, 0x47, 0x41, 0xe8, 0x8c, 0xfd, 0xf4, 0x60, 0xa7,
                   0x8c, 0x6f, 0xae, 0x07, 0xad, 0xf8, 0x3d, 0x2f, 0x00, 0x5d,
                   0x27, 0x67 ) );
 
/* 0x01d58842dea2bc372f7412b29347294739614ff3d719db3ad0ddd1dfb23b982ef8 ^ -1 =
 * 0x093ff51750809d181a9a5481c564e37cff618def8ec45f464b1a6e24f8b826bd (mod p)
 */
X25519_INVERT_TEST ( invert_1,
        INVERTEND ( 0x01, 0xd5, 0x88, 0x42, 0xde, 0xa2, 0xbc, 0x37, 0x2f,
                    0x74, 0x12, 0xb2, 0x93, 0x47, 0x29, 0x47, 0x39, 0x61,
                    0x4f, 0xf3, 0xd7, 0x19, 0xdb, 0x3a, 0xd0, 0xdd, 0xd1,
                    0xdf, 0xb2, 0x3b, 0x98, 0x2e, 0xf8 ),
        EXPECTED ( 0x09, 0x3f, 0xf5, 0x17, 0x50, 0x80, 0x9d, 0x18, 0x1a, 0x9a,
                   0x54, 0x81, 0xc5, 0x64, 0xe3, 0x7c, 0xff, 0x61, 0x8d, 0xef,
                   0x8e, 0xc4, 0x5f, 0x46, 0x4b, 0x1a, 0x6e, 0x24, 0xf8, 0xb8,
                   0x26, 0xbd ) );
 
/* 0x02efc89849b3aa7efe4458a885ab9099a435a240ae5af305535ec42e0829a3b2e9 ^ -1 =
 * 0x591607b163e89d0ac33a62c881e984a25d3826e3db5ce229af240dc58e5b579a (mod p)
 */
X25519_INVERT_TEST ( invert_2,
        INVERTEND ( 0x02, 0xef, 0xc8, 0x98, 0x49, 0xb3, 0xaa, 0x7e, 0xfe,
                    0x44, 0x58, 0xa8, 0x85, 0xab, 0x90, 0x99, 0xa4, 0x35,
                    0xa2, 0x40, 0xae, 0x5a, 0xf3, 0x05, 0x53, 0x5e, 0xc4,
                    0x2e, 0x08, 0x29, 0xa3, 0xb2, 0xe9 ),
        EXPECTED ( 0x59, 0x16, 0x07, 0xb1, 0x63, 0xe8, 0x9d, 0x0a, 0xc3, 0x3a,
                   0x62, 0xc8, 0x81, 0xe9, 0x84, 0xa2, 0x5d, 0x38, 0x26, 0xe3,
                   0xdb, 0x5c, 0xe2, 0x29, 0xaf, 0x24, 0x0d, 0xc5, 0x8e, 0x5b,
                   0x57, 0x9a ) );
 
/* 0x003eabedcbbaa80dd488bd64072bcfbe01a28defe39bf0027312476f57a5e5a5ab ^ -1 =
 * 0x7d87c2e565b27c5038181a0a7cae9ebe826c8afc1f77128a4d62cce96d2759a2 (mod p)
 */
X25519_INVERT_TEST ( invert_3,
        INVERTEND ( 0x00, 0x3e, 0xab, 0xed, 0xcb, 0xba, 0xa8, 0x0d, 0xd4,
                    0x88, 0xbd, 0x64, 0x07, 0x2b, 0xcf, 0xbe, 0x01, 0xa2,
                    0x8d, 0xef, 0xe3, 0x9b, 0xf0, 0x02, 0x73, 0x12, 0x47,
                    0x6f, 0x57, 0xa5, 0xe5, 0xa5, 0xab ),
        EXPECTED ( 0x7d, 0x87, 0xc2, 0xe5, 0x65, 0xb2, 0x7c, 0x50, 0x38, 0x18,
                   0x1a, 0x0a, 0x7c, 0xae, 0x9e, 0xbe, 0x82, 0x6c, 0x8a, 0xfc,
                   0x1f, 0x77, 0x12, 0x8a, 0x4d, 0x62, 0xcc, 0xe9, 0x6d, 0x27,
                   0x59, 0xa2 ) );
 
/* 0x008e944239b02b61c4a3d70628ece66fa2fd5166e6451b4cf36123fdf77656af72 ^ -1 =
 * 0x08e96161a0eee1b29af396f154950d5c715dc61aff66ee97377ab22adf3321d7 (mod p)
 */
X25519_INVERT_TEST ( invert_4,
        INVERTEND ( 0x00, 0x8e, 0x94, 0x42, 0x39, 0xb0, 0x2b, 0x61, 0xc4,
                    0xa3, 0xd7, 0x06, 0x28, 0xec, 0xe6, 0x6f, 0xa2, 0xfd,
                    0x51, 0x66, 0xe6, 0x45, 0x1b, 0x4c, 0xf3, 0x61, 0x23,
                    0xfd, 0xf7, 0x76, 0x56, 0xaf, 0x72 ),
        EXPECTED ( 0x08, 0xe9, 0x61, 0x61, 0xa0, 0xee, 0xe1, 0xb2, 0x9a, 0xf3,
                   0x96, 0xf1, 0x54, 0x95, 0x0d, 0x5c, 0x71, 0x5d, 0xc6, 0x1a,
                   0xff, 0x66, 0xee, 0x97, 0x37, 0x7a, 0xb2, 0x2a, 0xdf, 0x33,
                   0x21, 0xd7 ) );
 
/* 0x00d261a7ab3aa2e4f90e51f30dc6a7ee39c4b032ccd7c524a55304317faf42e12f ^ -1 =
 * 0x0738781c0aeabfbe6e840c85bd30996ef71bc54988ce16cedd5ab4f30c281597 (mod p)
 */
X25519_INVERT_TEST ( invert_5,
        INVERTEND ( 0x00, 0xd2, 0x61, 0xa7, 0xab, 0x3a, 0xa2, 0xe4, 0xf9,
                    0x0e, 0x51, 0xf3, 0x0d, 0xc6, 0xa7, 0xee, 0x39, 0xc4,
                    0xb0, 0x32, 0xcc, 0xd7, 0xc5, 0x24, 0xa5, 0x53, 0x04,
                    0x31, 0x7f, 0xaf, 0x42, 0xe1, 0x2f ),
        EXPECTED ( 0x07, 0x38, 0x78, 0x1c, 0x0a, 0xea, 0xbf, 0xbe, 0x6e, 0x84,
                   0x0c, 0x85, 0xbd, 0x30, 0x99, 0x6e, 0xf7, 0x1b, 0xc5, 0x49,
                   0x88, 0xce, 0x16, 0xce, 0xdd, 0x5a, 0xb4, 0xf3, 0x0c, 0x28,
                   0x15, 0x97 ) );
 
/* Base:   0xe6db6867583030db3594c1a424b15f7c726624ec26b3353b10a903a6d0ab1c4c
 * Scalar: 0xa546e36bf0527c9d3b16154b82465edd62144c0ac1fc5a18506a2244ba449ac4
 * Result: 0xc3da55379de9c6908e94ea4df28d084f32eccf03491c71f754b4075577a28552
 */
X25519_KEY_TEST ( rfc7748_1, 1, 0,
        BASE ( 0xe6, 0xdb, 0x68, 0x67, 0x58, 0x30, 0x30, 0xdb, 0x35, 0x94,
               0xc1, 0xa4, 0x24, 0xb1, 0x5f, 0x7c, 0x72, 0x66, 0x24, 0xec,
               0x26, 0xb3, 0x35, 0x3b, 0x10, 0xa9, 0x03, 0xa6, 0xd0, 0xab,
               0x1c, 0x4c ),
        SCALAR ( 0xa5, 0x46, 0xe3, 0x6b, 0xf0, 0x52, 0x7c, 0x9d, 0x3b, 0x16,
                 0x15, 0x4b, 0x82, 0x46, 0x5e, 0xdd, 0x62, 0x14, 0x4c, 0x0a,
                 0xc1, 0xfc, 0x5a, 0x18, 0x50, 0x6a, 0x22, 0x44, 0xba, 0x44,
                 0x9a, 0xc4 ),
        EXPECTED ( 0xc3, 0xda, 0x55, 0x37, 0x9d, 0xe9, 0xc6, 0x90, 0x8e, 0x94,
                   0xea, 0x4d, 0xf2, 0x8d, 0x08, 0x4f, 0x32, 0xec, 0xcf, 0x03,
                   0x49, 0x1c, 0x71, 0xf7, 0x54, 0xb4, 0x07, 0x55, 0x77, 0xa2,
                   0x85, 0x52 ) );
 
/* Base:   0xe5210f12786811d3f4b7959d0538ae2c31dbe7106fc03c3efc4cd549c715a493
 * Scalar: 0x4b66e9d4d1b4673c5ad22691957d6af5c11b6421e0ea01d42ca4169e7918ba0d
 * Result: 0x95cbde9476e8907d7aade45cb4b873f88b595a68799fa152e6f8f7647aac7957
 */
X25519_KEY_TEST ( rfc7748_2, 1, 0,
        BASE ( 0xe5, 0x21, 0x0f, 0x12, 0x78, 0x68, 0x11, 0xd3, 0xf4, 0xb7,
               0x95, 0x9d, 0x05, 0x38, 0xae, 0x2c, 0x31, 0xdb, 0xe7, 0x10,
               0x6f, 0xc0, 0x3c, 0x3e, 0xfc, 0x4c, 0xd5, 0x49, 0xc7, 0x15,
               0xa4, 0x93 ),
        SCALAR ( 0x4b, 0x66, 0xe9, 0xd4, 0xd1, 0xb4, 0x67, 0x3c, 0x5a, 0xd2,
                 0x26, 0x91, 0x95, 0x7d, 0x6a, 0xf5, 0xc1, 0x1b, 0x64, 0x21,
                 0xe0, 0xea, 0x01, 0xd4, 0x2c, 0xa4, 0x16, 0x9e, 0x79, 0x18,
                 0xba, 0x0d ),
        EXPECTED ( 0x95, 0xcb, 0xde, 0x94, 0x76, 0xe8, 0x90, 0x7d, 0x7a, 0xad,
                   0xe4, 0x5c, 0xb4, 0xb8, 0x73, 0xf8, 0x8b, 0x59, 0x5a, 0x68,
                   0x79, 0x9f, 0xa1, 0x52, 0xe6, 0xf8, 0xf7, 0x64, 0x7a, 0xac,
                   0x79, 0x57 ) );
 
/* Base:   0x0900000000000000000000000000000000000000000000000000000000000000
 * Scalar: 0x0900000000000000000000000000000000000000000000000000000000000000
 * Result: 0x422c8e7a6227d7bca1350b3e2bb7279f7897b87bb6854b783c60e80311ae3079
 */
X25519_KEY_TEST ( rfc7748_3, 1, 0,
        BASE ( 0x09, 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, 0x00, 0x00,
               0x00, 0x00 ),
        SCALAR ( 0x09, 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, 0x00, 0x00,
                 0x00, 0x00 ),
        EXPECTED ( 0x42, 0x2c, 0x8e, 0x7a, 0x62, 0x27, 0xd7, 0xbc, 0xa1, 0x35,
                   0x0b, 0x3e, 0x2b, 0xb7, 0x27, 0x9f, 0x78, 0x97, 0xb8, 0x7b,
                   0xb6, 0x85, 0x4b, 0x78, 0x3c, 0x60, 0xe8, 0x03, 0x11, 0xae,
                   0x30, 0x79 ) );
 
/* Base:   0x0900000000000000000000000000000000000000000000000000000000000000
 * Scalar: 0x0900000000000000000000000000000000000000000000000000000000000000
 * Result: 0xb1a5a73158904c020866c13939dd7e1aa26852ee1d2609c92e5a8f1debe2150a
 * (after 100 iterations)
 *
 * RFC7748 gives test vectors for 1000 and 1000000 iterations with
 * these starting values.  This test case stops after 100 iterations
 * to avoid a pointlessly slow test cycle in the common case of
 * running tests under Valgrind.
 */
X25519_KEY_TEST ( rfc7748_4_100, 100, 0,
        BASE ( 0x09, 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, 0x00, 0x00,
               0x00, 0x00 ),
        SCALAR ( 0x09, 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, 0x00, 0x00,
                 0x00, 0x00 ),
        EXPECTED ( 0xb1, 0xa5, 0xa7, 0x31, 0x58, 0x90, 0x4c, 0x02, 0x08, 0x66,
                   0xc1, 0x39, 0x39, 0xdd, 0x7e, 0x1a, 0xa2, 0x68, 0x52, 0xee,
                   0x1d, 0x26, 0x09, 0xc9, 0x2e, 0x5a, 0x8f, 0x1d, 0xeb, 0xe2,
                   0x15, 0x0a ) );
 
/* Base:   2^255 - 19 + 1 (deliberately malicious public key)
 * Scalar: 0x000102030405060708090a0b0c0d0e0f000102030405060708090a0b0c0d0e0f
 * Result: Failure (all zeros)
 */
X25519_KEY_TEST ( malicious, 1, 1,
        BASE ( 0xee, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff, 0xff,
               0xff, 0x7f ),
        SCALAR ( 0x00, 0x01, 0x02, 0x03, 0x04, 0x05, 0x06, 0x07, 0x08, 0x09,
                 0x0a, 0x0b, 0x0c, 0x0d, 0x0e, 0x0f, 0x00, 0x01, 0x02, 0x03,
                 0x04, 0x05, 0x06, 0x07, 0x08, 0x09, 0x0a, 0x0b, 0x0c, 0x0d,
                 0x0e, 0x0f ),
        EXPECTED ( 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, 0x00, 0x00, 0x00,
                   0x00, 0x00 ) );
 
/**
 * Perform X25519 self-tests
 *
 */
static void x25519_test_exec ( void ) {
 
        /* Perform multiplication tests */
        x25519_multiply_ok ( &multiply_small );
        x25519_multiply_ok ( &multiply_k_p );
        x25519_multiply_ok ( &multiply_1 );
        x25519_multiply_ok ( &multiply_2 );
        x25519_multiply_ok ( &multiply_3 );
        x25519_multiply_ok ( &multiply_4 );
        x25519_multiply_ok ( &multiply_5 );
 
        /* Perform multiplicative inversion tests */
        x25519_invert_ok ( &invert_1 );
        x25519_invert_ok ( &invert_2 );
        x25519_invert_ok ( &invert_3 );
        x25519_invert_ok ( &invert_4 );
        x25519_invert_ok ( &invert_5 );
 
        /* Perform key exchange tests */
        x25519_key_ok ( &rfc7748_1 );
        x25519_key_ok ( &rfc7748_2 );
        x25519_key_ok ( &rfc7748_3 );
        x25519_key_ok ( &rfc7748_4_100 );
        x25519_key_ok ( &malicious );
}
 
/** X25519 self-test */
struct self_test x25519_test __self_test = {
        .name = "x25519",
        .exec = x25519_test_exec,
};