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/*
* Embedded Linux library
* Copyright (C) 2018 Intel Corporation
*
* SPDX-License-Identifier: LGPL-2.1-or-later
*/
#ifdef HAVE_CONFIG_H
#include <config.h>
#endif
#include <string.h>
#include <assert.h>
#include <ell/ell.h>
#include "ell/ecc.h"
#include "ell/ecc-private.h"
#define HEX2BUF(s, buf) { \
unsigned char *tmp = l_util_from_hexstring(s, NULL); \
memcpy(buf, tmp, curve->ndigits * 8); \
l_free(tmp); \
}
#define CURVE_P_32_STR "ffffffffffffffffffffffff00000000"\
"000000000000000001000000ffffffff"
enum ecc_test_type {
TEST_ADD = 0,
TEST_SUB,
TEST_MULT,
TEST_INV,
TEST_EXP,
TEST_POINT_ADD,
TEST_SCALAR_MULT,
TEST_LEGENDRE,
};
struct ecc_test_data {
enum ecc_test_type type;
/* basic math arguments/result */
char *a;
char *b;
char *qr;
char *qnr;
char *r;
bool is_residue;
char *mod;
char *result;
int lres;
/* point operations */
char *scalar;
char *ax, *ay;
char *bx, *by;
char *rx, *ry;
};
/* (a + b) mod c */
struct ecc_test_data add_test = {
.type = TEST_ADD,
.a = "cae1d5624344984073fd955a72d4ebacedc084679333e4beebff94869e9f6ca8",
.b = "93a02ae89d15e38a33bf3fea4c99937825b279fa8fa81dded1ccb687cec88461",
.mod = CURVE_P_32_STR,
.result = "5e82004ae05a7bcaa7bcd545bf6e7f25"
"1372fe6222dc029dbccc4b0d6d67f10a"
};
/* (a - b) mod c */
struct ecc_test_data sub_test = {
.type = TEST_SUB,
.a = "cae1d5624344984073fd955a72d4ebacedc084679333e4beebff94869e9f6ca8",
.b = "93a02ae89d15e38a33bf3fea4c99937825b279fa8fa81dded1ccb687cec88461",
.mod = CURVE_P_32_STR,
.result = "3741aa79a62eb4b6403e5570263b5834"
"c80e0a6d038bc6e01a32ddfecfd6e847"
};
/* (a * b) mod c */
struct ecc_test_data mult_test = {
.type = TEST_MULT,
.a = "cae1d5624344984073fd955a72d4ebacedc084679333e4beebff94869e9f6ca8",
.b = "93a02ae89d15e38a33bf3fea4c99937825b279fa8fa81dded1ccb687cec88461",
.mod = CURVE_P_32_STR,
.result = "a31ff5c7d65d8bd806b0407f27d1f1bc"
"2c072e28c19720f6a654a75efc2faab5"
};
/* (a^-1) mod c */
struct ecc_test_data inv_test = {
.type = TEST_INV,
.a = "cae1d5624344984073fd955a72d4ebacedc084679333e4beebff94869e9f6ca8",
.mod = CURVE_P_32_STR,
.result = "48faaac115571047ead565911fc334fd"
"633c986755e87ab10fd79a4453a60bc5"
};
/* (a^-1) mod c */
struct ecc_test_data inv_test2 = {
.type = TEST_INV,
.a = "698e5c10b63a9c79a9720b3f7f4d2f5c9fbb31daf93ac0f8fa8ca5cde8234418",
.mod = CURVE_P_32_STR,
.result = "5fd113c3b6053c38e54e5917826c8520"
"c5a0708a8a47345edbb7fc1d67d9b42b"
};
/* (a ^ b) mod c */
struct ecc_test_data exp_test = {
.type = TEST_EXP,
.a = "cae1d5624344984073fd955a72d4ebacedc084679333e4beebff94869e9f6ca8",
.b = "93a02ae89d15e38a33bf3fea4c99937825b279fa8fa81dded1ccb687cec88461",
.mod = CURVE_P_32_STR,
.result = "e7488e3a4d56938bbddc2a615c768d48"
"9e5634aced9ceee37249fae1caa36fec"
};
struct ecc_test_data legendre_test1 = {
.type = TEST_LEGENDRE,
.a = "b59c0c366aa89ba229f857190497261d5a0a7a0a774caa72aef041ff00092447",
.mod = "ffffffff00000001000000000000000000000000ffffffffffffffffffffffff",
.lres = -1
};
struct ecc_test_data legendre_test2 = {
.type = TEST_LEGENDRE,
.a = "1214f9607d348c998b3fba332d884d65945561fd007ff56d8bf603148d74d2e4",
.mod = "ffffffff000000010000000000000000"
"00000000ffffffffffffffffffffffff",
.lres = 1
};
struct ecc_test_data legendre_test3 = {
.type = TEST_LEGENDRE,
.a = "282d751c898bfc593b1d21b6812df48e3ec811f40349b30b7294575c47b871d8",
.mod = "ffffffff000000010000000000000000"
"00000000ffffffffffffffffffffffff",
.lres = 1
};
struct ecc_test_data legendre_test4 = {
.type = TEST_LEGENDRE,
.a = "0694ccde1db3d02faa26856678bd9358ecc0d82791405eb3892a8b4f07f1e5d6",
.mod = "ffffffff000000010000000000000000"
"00000000ffffffffffffffffffffffff",
.lres = -1
};
struct ecc_test_data legendre_test5 = {
.type = TEST_LEGENDRE,
.a = "92247f96df65a6d04af0c57318e999fd493c42864d156f7e5bba75c964f3c6b0",
.mod = "ffffffff000000010000000000000000"
"00000000ffffffffffffffffffffffff",
.lres = 1
};
struct ecc_test_data legendre_test6 = {
.type = TEST_LEGENDRE,
.a = "084f7eb6ed8021d095787fd401b0f19b13937dc23f7c84dfe69bb9a204bb3768",
.mod = "ffffffff000000010000000000000000"
"00000000ffffffffffffffffffffffff",
.lres = -1
};
struct ecc_test_data point_add_test = {
.type = TEST_POINT_ADD,
.ax = "d36b6768a3279fbe23a5bf5cc19b13354"
"fa2c6d6fd9de467d62db007c39452df",
.ay = "4d601e7be3efd7f357452de7584274c54"
"c18ddb0ef2f0f4cf43375152a9780c4",
.bx = "c833c5d3ab916ed37f16597ace5dcf41f"
"080891c0c41b6ce561705bd736a29e0",
.by = "9d266e5ba8ba3e8d9679238f44a376b05"
"133df0510a7b8e6e7dd3a654d40a04a",
.rx = "24c4ede340dbdd144ccaaea67e5b1fca"
"87b3aa26dc11114fcd12186318533101",
.ry = "1d96391fb2942bf286e9251c257b960e"
"7d23d4caff4b6fc898aff87e1f6f5514"
};
struct ecc_test_data point_mult_test = {
.type = TEST_SCALAR_MULT,
.ax = "768bc2f17fbf4e49282fbd4068994562b"
"fc7145306762c26a90be1e9c346ac67",
.ay = "93a02ae89d15e38a33bf3fea4c9993782"
"5b279fa8fa81dded1ccb687cec88461",
.scalar = "7521d940aa073c1675114ed27b866561"
"9c826cac8eaa341f70d61b43ad32058b",
.rx = "d4c80de349966df5542c984e80885d36"
"a965ceb74ffe6a0fdc8343184dedfe66",
.ry = "6d3a1ac3d1d392413286a0e00e94b01e"
"ae8423c7f53b9d39cc7fc9c3a5880f3b"
};
static void run_test_p256(const void *arg)
{
const struct ecc_test_data *data = arg;
uint64_t a[L_ECC_MAX_DIGITS], b[L_ECC_MAX_DIGITS], mod[L_ECC_MAX_DIGITS],
scalar[L_ECC_MAX_DIGITS], result[L_ECC_MAX_DIGITS],
check[L_ECC_MAX_DIGITS];
struct l_ecc_point point1, point2, point_ret;
const struct l_ecc_curve *curve = l_ecc_curve_from_ike_group(19);
point_ret.curve = curve;
memset(result, 0, sizeof(result));
if (data->a) {
HEX2BUF(data->a, a);
_ecc_be2native(a, a, curve->ndigits);
}
if (data->b) {
HEX2BUF(data->b, b);
_ecc_be2native(b, b, curve->ndigits);
}
if (data->mod) {
HEX2BUF(data->mod, mod);
_ecc_be2native(mod, mod, curve->ndigits);
}
if (data->ax) {
HEX2BUF(data->ax, point1.x);
_ecc_be2native(point1.x, point1.x, curve->ndigits);
point1.curve = curve;
}
if (data->ay) {
HEX2BUF(data->ay, point1.y);
_ecc_be2native(point1.y, point1.y, curve->ndigits);
}
if (data->bx) {
HEX2BUF(data->bx, point2.x);
_ecc_be2native(point2.x, point2.x, curve->ndigits);
point2.curve = curve;
}
if (data->by) {
HEX2BUF(data->by, point2.y);
_ecc_be2native(point2.y, point2.y, curve->ndigits);
}
if (data->scalar) {
HEX2BUF(data->scalar, scalar);
_ecc_be2native(scalar, scalar, curve->ndigits);
}
switch (data->type) {
case TEST_ADD:
_vli_mod_add(result, a, b, mod, curve->ndigits);
break;
case TEST_SUB:
_vli_mod_sub(result, a, b, mod, curve->ndigits);
break;
case TEST_MULT:
_vli_mod_mult_fast(result, a, b, mod, curve->ndigits);
break;
case TEST_INV:
_vli_mod_inv(result, a, mod, curve->ndigits);
break;
case TEST_EXP:
_vli_mod_exp(result, a, b, mod, curve->ndigits);
break;
case TEST_LEGENDRE:
{
int lres = _vli_legendre(a, mod, curve->ndigits);
assert(data->lres == lres);
break;
}
case TEST_POINT_ADD:
_ecc_point_add(&point_ret, &point1, &point2, curve->p);
break;
case TEST_SCALAR_MULT:
_ecc_point_mult(&point_ret, &point1, scalar, NULL, curve->p);
break;
}
if (data->type <= TEST_EXP) {
HEX2BUF(data->result, check);
_ecc_native2be(check, check, curve->ndigits);
assert(memcmp(result, check, 32) == 0);
} else if (data->type <= TEST_SCALAR_MULT) {
uint64_t checkx[L_ECC_MAX_DIGITS];
uint64_t checky[L_ECC_MAX_DIGITS];
HEX2BUF(data->rx, checkx);
_ecc_native2be(checkx, checkx, curve->ndigits);
HEX2BUF(data->ry, checky);
_ecc_native2be(checky, checky, curve->ndigits);
assert(memcmp(checkx, point_ret.x, 32) == 0);
assert(memcmp(checky, point_ret.y, 32) == 0);
}
}
static void run_test_reduce(const void *arg)
{
static const uint8_t p_reduced[] = {
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
0x43, 0x19, 0x05, 0x53, 0x58, 0xe8, 0x61, 0x7b,
0x0c, 0x46, 0x35, 0x3d, 0x03, 0x9c, 0xda, 0xb0,
};
const struct l_ecc_curve *p256 = l_ecc_curve_from_ike_group(19);
struct l_ecc_scalar *tmp;
struct l_ecc_scalar *reduced;
char buf[32];
tmp = l_ecc_curve_get_prime(p256);
assert(tmp);
assert(l_ecc_scalar_get_data(tmp, buf, sizeof(buf)) > 0);
l_ecc_scalar_free(tmp);
reduced = l_ecc_scalar_new_reduced_1_to_n(p256, buf, sizeof(buf));
assert(reduced);
assert(l_ecc_scalar_get_data(reduced, buf, sizeof(buf)) > 0);
assert(!memcmp(buf, p_reduced, sizeof(p_reduced)));
l_ecc_scalar_free(reduced);
tmp = l_ecc_curve_get_order(p256);
assert(tmp);
assert(l_ecc_scalar_get_data(tmp, buf, sizeof(buf)) > 0);
l_ecc_scalar_free(tmp);
reduced = l_ecc_scalar_new_reduced_1_to_n(p256, buf, sizeof(buf));
assert(reduced);
assert(l_ecc_scalar_get_data(reduced, buf, sizeof(buf)) > 0);
assert(l_memeqzero(buf, 31));
assert(buf[31] == 0x02);
l_ecc_scalar_free(reduced);
}
static void run_test_zero_or_one(const void *arg)
{
uint64_t zero[L_ECC_MAX_DIGITS] = { };
uint64_t _1[L_ECC_MAX_DIGITS] = { 1ull };
uint64_t _2[L_ECC_MAX_DIGITS] = { 2ull };
assert(_vli_is_zero_or_one(zero, L_ECC_MAX_DIGITS));
assert(_vli_is_zero_or_one(_1, L_ECC_MAX_DIGITS));
assert(!_vli_is_zero_or_one(_2, L_ECC_MAX_DIGITS));
}
struct compressed_point_data {
char *x;
char *exp_y;
enum l_ecc_point_type type;
};
static struct compressed_point_data compressed_tests[] = {
{
/* BIT0, computed Y is odd, subtraction performed */
.x = "19b3fec1c000a888ee9c44272e4d7317e6e36577fc9d53e1edfb4e296b0b7ce1",
.exp_y = "a8f9efd0ab526cd930870779621f4e9a53d4e78887ac9f4ed45ff75ded32b158",
.type = L_ECC_POINT_TYPE_COMPRESSED_BIT0,
},
{
/* BIT0, computed Y is even, no subtraction */
.x = "958df5997362a9695ad73938c86be34a4730da877eccaaf8b189e73ff20e67c3",
.exp_y = "1042f37262ded34d8424c1728a1ed23a726645b71db30a38f2932001a2027f46",
.type = L_ECC_POINT_TYPE_COMPRESSED_BIT0,
},
{
/* BIT1, computed Y is even, subtraction performed */
.x = "069bd56634454ca76e7ba434244137509141cbbf532586c6b36e9b5be8a2cc34",
.exp_y = "f4f34d46e4bdc1473fec4b4c8724f349375a8a602f5e83c260d6724e64ec7e99",
.type = L_ECC_POINT_TYPE_COMPRESSED_BIT1,
},
{
/* BIT1, computed Y is odd, no subtraction */
.x = "8cade296a68e0c40bcf45a049f1993263bdc8524825e2be44b14ce114e475df0",
.exp_y = "94ed7d09b2a0e95d8df993eaf81eb64d5ff734d01da57e53b2e0277199bc5897",
.type = L_ECC_POINT_TYPE_COMPRESSED_BIT1,
},
};
static void run_test_compressed_points(const void *arg)
{
unsigned int i;
for (i = 0; i < L_ARRAY_SIZE(compressed_tests); i++) {
const struct l_ecc_curve *curve = l_ecc_curve_from_ike_group(19);
struct compressed_point_data *data = &compressed_tests[i];
uint64_t x[L_ECC_MAX_DIGITS];
uint64_t y[L_ECC_MAX_DIGITS];
uint64_t exp_y[L_ECC_MAX_DIGITS];
size_t bytes = l_ecc_curve_get_scalar_bytes(curve);
struct l_ecc_point *p;
HEX2BUF(data->x, x);
HEX2BUF(data->exp_y, exp_y);
p = l_ecc_point_from_data(curve, data->type, x, bytes);
assert(p);
l_ecc_point_get_y(p, y, bytes);
assert(!memcmp(exp_y, y, bytes));
l_ecc_point_free(p);
}
}
struct ecc_keypair {
const char *curve_name;
const char *private_key;
const char *public_key;
};
static void keypair_test(const void *arg)
{
const struct ecc_keypair *keypair = arg;
const struct l_ecc_curve *curve;
struct l_ecc_scalar *private_key;
struct l_ecc_point *public_key;
void *buf;
size_t len;
char *str;
curve = l_ecc_curve_from_name(keypair->curve_name);
assert(curve);
buf = l_util_from_hexstring(keypair->private_key, &len);
assert(buf);
private_key = l_ecc_scalar_new(curve, buf, len);
assert(private_key);
l_free(buf);
public_key = l_ecc_point_new(curve);
assert(public_key);
l_ecc_point_multiply_g(public_key, private_key);
buf = l_malloc(len * 2);
assert(buf);
l_ecc_point_get_data(public_key, buf, len * 2);
str = l_util_hexstring_upper(buf, len * 2);
assert(str);
assert(!strcmp(str, keypair->public_key));
l_free(str);
l_free(buf);
}
static const struct ecc_keypair keypair_p192 = {
/* RFC 6979 - Appendix A.2.3. ECDSA, 192 Bits (Prime Field) */
.curve_name = "secp192r1",
.private_key = "6FAB034934E4C0FC9AE67F5B5659A9D7"
"D1FEFD187EE09FD4",
.public_key = "AC2C77F529F91689FEA0EA5EFEC7F210"
"D8EEA0B9E047ED56"
"3BC723E57670BD4887EBC732C523063D"
"0A7C957BC97C1C43",
};
static const struct ecc_keypair keypair_p224 = {
/* RFC 6979 - Appendix A.2.4. ECDSA, 224 Bits (Prime Field) */
.curve_name = "secp224r1",
.private_key = "00000000"
"F220266E1105BFE3083E03EC7A3A6546"
"51F45E37167E88600BF257C1",
.public_key = "00000000"
"00CF08DA5AD719E42707FA431292DEA1"
"1244D64FC51610D94B130D6C"
"00000000"
"EEAB6F3DEBE455E3DBF85416F7030CBD"
"94F34F2D6F232C69F3C1385A",
};
static const struct ecc_keypair keypair_p256 = {
/* RFC 6979 - Appendix A.2.5. ECDSA, 256 Bits (Prime Field) */
.curve_name = "secp256r1",
.private_key = "C9AFA9D845BA75166B5C215767B1D693"
"4E50C3DB36E89B127B8A622B120F6721",
.public_key = "60FED4BA255A9D31C961EB74C6356D68"
"C049B8923B61FA6CE669622E60F29FB6"
"7903FE1008B8BC99A41AE9E95628BC64"
"F2F1B20C2D7E9F5177A3C294D4462299",
};
static const struct ecc_keypair keypair_p384 = {
/* RFC 6979 - Appendix A.2.6. ECDSA, 384 Bits (Prime Field) */
.curve_name = "secp384r1",
.private_key = "6B9D3DAD2E1B8C1C05B19875B6659F4D"
"E23C3B667BF297BA9AA47740787137D8"
"96D5724E4C70A825F872C9EA60D2EDF5",
.public_key = "EC3A4E415B4E19A4568618029F427FA5"
"DA9A8BC4AE92E02E06AAE5286B300C64"
"DEF8F0EA9055866064A254515480BC13"
"8015D9B72D7D57244EA8EF9AC0C62189"
"6708A59367F9DFB9F54CA84B3F1C9DB1"
"288B231C3AE0D4FE7344FD2533264720",
};
static const struct ecc_keypair keypair_p521 = {
/* RFC 6979 - Appendix A.2.7. ECDSA, 521 Bits (Prime Field) */
.curve_name = "secp521r1",
.private_key = "0000000000000"
"0FAD06DAA62BA3B25D2FB40133DA7572"
"05DE67F5BB0018FEE8C86E1B68C7E75C"
"AA896EB32F1F47C70855836A6D16FCC1"
"466F6D8FBEC67DB89EC0C08B0E996B83"
"538",
.public_key = "0000000000000"
"1894550D0785932E00EAA23B694F213F"
"8C3121F86DC97A04E5A7167DB4E5BCD3"
"71123D46E45DB6B5D5370A7F20FB6331"
"55D38FFA16D2BD761DCAC474B9A2F502"
"3A4"
"0000000000000"
"0493101C962CD4D2FDDF782285E64584"
"139C2F91B47F87FF82354D6630F746A2"
"8A0DB25741B5B34A828008B22ACC23F9"
"24FAAFBD4D33F81EA66956DFEAA2BFDF"
"CF5",
};
static const struct ecc_keypair keypair_p192_bt = {
/* Bluetooth debug key for P-192 */
.curve_name = "secp192r1",
.private_key = "07915F86918DDC27005DF1D6CF0C142B"
"625ED2EFF4A518FF",
.public_key = "15207009984421A6586F9FC3FE7E4329"
"D2809EA51125F8ED"
"B09D42B81BC5BD009F79E4B59DBBAA85"
"7FCA856FB9F7EA25",
};
static const struct ecc_keypair keypair_p256_bt = {
/* Bluetooth debug key for P-256 */
.curve_name = "secp256r1",
.private_key = "3F49F6D4A3C55F3874C9B3E3D2103F50"
"4AFF607BEB40B7995899B8A6CD3C1ABD",
.public_key = "20B003D2F297BE2C5E2C83A7E9F9A5B9"
"EFF49111ACF4FDDBCC0301480E359DE6"
"DC809C49652AEB6D63329ABF5A52155C"
"766345C28FED3024741C8ED01589D28B",
};
static const struct ecc_keypair keypair_p256_openssl = {
/* OpenSSL example from EVP_PKEY_fromdata() manual page */
.curve_name = "secp256r1",
.private_key = "B92F3CE62FFB45683996F02AAF6CDAF2"
"898A27BF399B7E5421C2A1E53612485D",
.public_key = "CF20FB9A1D116C5E9FEC38876C1D2F58"
"47ABA39B7923E6EB946F97DBA37DBDE5"
"26CA07178D2675FFCB8EB684D0240225"
"8FB9336ECF12162F5CCD8671A8BF1A47",
};
int main(int argc, char *argv[])
{
l_test_init(&argc, &argv);
l_test_add("ECC add test", run_test_p256, &add_test);
l_test_add("ECC sub test", run_test_p256, &sub_test);
l_test_add("ECC mult test", run_test_p256, &mult_test);
l_test_add("ECC inv test", run_test_p256, &inv_test);
l_test_add("ECC inv test", run_test_p256, &inv_test2);
l_test_add("ECC exp test", run_test_p256, &exp_test);
l_test_add("ECC point add test", run_test_p256, &point_add_test);
l_test_add("ECC point mult test", run_test_p256, &point_mult_test);
l_test_add("ECC legendre", run_test_p256, &legendre_test1);
l_test_add("ECC legendre", run_test_p256, &legendre_test2);
l_test_add("ECC legendre", run_test_p256, &legendre_test3);
l_test_add("ECC legendre", run_test_p256, &legendre_test4);
l_test_add("ECC legendre", run_test_p256, &legendre_test5);
l_test_add("ECC legendre", run_test_p256, &legendre_test6);
l_test_add("ECC reduce test", run_test_reduce, NULL);
l_test_add("ECC zero or one test", run_test_zero_or_one, NULL);
l_test_add("ECC compressed points", run_test_compressed_points, NULL);
l_test_add("ECC P-192 key pair test", keypair_test, &keypair_p192);
l_test_add("ECC P-224 key pair test", keypair_test, &keypair_p224);
l_test_add("ECC P-256 key pair test", keypair_test, &keypair_p256);
l_test_add("ECC P-384 key pair test", keypair_test, &keypair_p384);
l_test_add("ECC P-521 key pair test", keypair_test, &keypair_p521);
l_test_add("ECC P-192 Bluetooth debug key pair test",
keypair_test, &keypair_p192_bt);
l_test_add("ECC P-256 Bluetooth debug key pair test",
keypair_test, &keypair_p256_bt);
l_test_add("ECC P-256 OpenSSL example key pair test",
keypair_test, &keypair_p256_openssl);
return l_test_run();
}
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