diff --git a/library/ecp_curves.c b/library/ecp_curves.c index 2a97b8c000..1a027d6aa3 100644 --- a/library/ecp_curves.c +++ b/library/ecp_curves.c @@ -4584,6 +4584,8 @@ static int ecp_mod_p384(mbedtls_mpi *); #endif #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) static int ecp_mod_p521(mbedtls_mpi *); +MBEDTLS_STATIC_TESTABLE +int mbedtls_ecp_mod_p521_raw(mbedtls_mpi_uint *N_p, size_t N_n); #endif #define NIST_MODP(P) grp->modp = ecp_mod_ ## P; @@ -5189,11 +5191,6 @@ cleanup: MBEDTLS_ECP_DP_SECP384R1_ENABLED */ #if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) -/* - * Here we have an actual Mersenne prime, so things are more straightforward. - * However, chunks are aligned on a 'weird' boundary (521 bits). - */ - /* Size of p521 in terms of mbedtls_mpi_uint */ #define P521_WIDTH (521 / 8 / sizeof(mbedtls_mpi_uint) + 1) @@ -5201,48 +5198,81 @@ cleanup: #define P521_MASK 0x01FF /* - * Fast quasi-reduction modulo p521 (FIPS 186-3 D.2.5) - * Write N as A1 + 2^521 A0, return A0 + A1 + * Fast quasi-reduction modulo p521 = 2^521 - 1 (FIPS 186-3 D.2.5) */ static int ecp_mod_p521(mbedtls_mpi *N) { int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; - size_t i; - mbedtls_mpi M; - mbedtls_mpi_uint Mp[P521_WIDTH + 1]; - /* Worst case for the size of M is when mbedtls_mpi_uint is 16 bits: - * we need to hold bits 513 to 1056, which is 34 limbs, that is - * P521_WIDTH + 1. Otherwise P521_WIDTH is enough. */ - - if (N->n < P521_WIDTH) { - return 0; - } - - /* M = A1 */ - M.s = 1; - M.n = N->n - (P521_WIDTH - 1); - if (M.n > P521_WIDTH + 1) { - M.n = P521_WIDTH + 1; - } - M.p = Mp; - memcpy(Mp, N->p + P521_WIDTH - 1, M.n * sizeof(mbedtls_mpi_uint)); - MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&M, 521 % (8 * sizeof(mbedtls_mpi_uint)))); - - /* N = A0 */ - N->p[P521_WIDTH - 1] &= P521_MASK; - for (i = P521_WIDTH; i < N->n; i++) { - N->p[i] = 0; - } - - /* N = A0 + A1 */ - MBEDTLS_MPI_CHK(mbedtls_mpi_add_abs(N, N, &M)); - + size_t expected_width = 2 * P521_WIDTH; + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(N, expected_width)); + ret = mbedtls_ecp_mod_p521_raw(N->p, expected_width); cleanup: return ret; } +MBEDTLS_STATIC_TESTABLE +int mbedtls_ecp_mod_p521_raw(mbedtls_mpi_uint *X, size_t X_limbs) +{ + mbedtls_mpi_uint carry = 0; + + if (X_limbs != 2 * P521_WIDTH || X[2 * P521_WIDTH - 1] != 0) { + return MBEDTLS_ERR_ECP_BAD_INPUT_DATA; + } + + /* Step 1: Reduction to P521_WIDTH limbs */ + /* Helper references for bottom part of X */ + mbedtls_mpi_uint *X0 = X; + size_t X0_limbs = P521_WIDTH; + /* Helper references for top part of X */ + mbedtls_mpi_uint *X1 = X + X0_limbs; + size_t X1_limbs = X_limbs - X0_limbs; + /* Split X as X0 + 2^P521_WIDTH X1 and compute X0 + 2^(biL - 9) X1. + * (We are using that 2^P521_WIDTH = 2^(512 + biL) and that + * 2^(512 + biL) X1 = 2^(biL - 9) X1 mod P521.) + * The high order limb of the result will be held in carry and the rest + * in X0 (that is the result will be represented as + * 2^P521_WIDTH carry + X0). + * + * Also, note that the resulting carry is either 0 or 1: + * X0 < 2^P521_WIDTH = 2^(512 + biL) and X1 < 2^(P521_WIDTH-biL) = 2^512 + * therefore + * X0 + 2^(biL - 9) X1 < 2^(512 + biL) + 2^(512 + biL - 9) + * which in turn is less than 2 * 2^(512 + biL). + */ + mbedtls_mpi_uint shift = ((mbedtls_mpi_uint) 1u) << (biL - 9); + carry = mbedtls_mpi_core_mla(X0, X0_limbs, X1, X1_limbs, shift); + /* Set X to X0 (by clearing the top part). */ + memset(X1, 0, X1_limbs * sizeof(mbedtls_mpi_uint)); + + /* Step 2: Reduction modulo P521 + * + * At this point X is reduced to P521_WIDTH limbs. What remains is to add + * the carry (that is 2^P521_WIDTH carry) and to reduce mod P521. */ + + /* 2^P521_WIDTH carry = 2^(512 + biL) carry = 2^(biL - 9) carry mod P521. + * Also, recall that carry is either 0 or 1. */ + mbedtls_mpi_uint addend = carry << (biL - 9); + /* Keep the top 9 bits and reduce the rest, using 2^521 = 1 mod P521. */ + addend += (X[P521_WIDTH - 1] >> 9); + X[P521_WIDTH - 1] &= P521_MASK; + + /* Resuse the top part of X (already zeroed) as a helper array for + * carrying out the addition. */ + mbedtls_mpi_uint *addend_arr = X + P521_WIDTH; + addend_arr[0] = addend; + (void) mbedtls_mpi_core_add(X, X, addend_arr, P521_WIDTH); + /* Both addends were less than P521 therefore X < 2 * P521. (This also means + * that the result fit in P521_WIDTH limbs and there won't be any carry.) */ + + /* Clear the reused part of X. */ + addend_arr[0] = 0; + + return 0; +} + #undef P521_WIDTH #undef P521_MASK + #endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ #endif /* MBEDTLS_ECP_NIST_OPTIM */ diff --git a/library/ecp_invasive.h b/library/ecp_invasive.h index 3ee238ee53..3d1321c525 100644 --- a/library/ecp_invasive.h +++ b/library/ecp_invasive.h @@ -95,6 +95,28 @@ int mbedtls_ecp_mod_p192_raw(mbedtls_mpi_uint *Np, size_t Nn); #endif /* MBEDTLS_ECP_DP_SECP192R1_ENABLED */ +#if defined(MBEDTLS_ECP_DP_SECP521R1_ENABLED) + +/** Fast quasi-reduction modulo p521 = 2^521 - 1 (FIPS 186-3 D.2.5) + * + * \param[in,out] X The address of the MPI to be converted. + * Must have twice as many limbs as the modulus + * (the modulus is 521 bits long). Upon return this + * holds the reduced value. The reduced value is + * in range `0 <= X < 2 * N` (where N is the modulus). + * and its the bitlength is one plus the bitlength + * of the modulus. + * \param[in] X_limbs The length of \p X in limbs. + * + * \return \c 0 on success. + * \return #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if \p X_limbs does not have + * twice as many limbs as the modulus. + */ +MBEDTLS_STATIC_TESTABLE +int mbedtls_ecp_mod_p521_raw(mbedtls_mpi_uint *X, size_t X_limbs); + +#endif /* MBEDTLS_ECP_DP_SECP521R1_ENABLED */ + #endif /* MBEDTLS_TEST_HOOKS && MBEDTLS_ECP_C */ #endif /* MBEDTLS_ECP_INVASIVE_H */ diff --git a/scripts/mbedtls_dev/ecp.py b/scripts/mbedtls_dev/ecp.py index 93cd2123ff..6370d258aa 100644 --- a/scripts/mbedtls_dev/ecp.py +++ b/scripts/mbedtls_dev/ecp.py @@ -75,3 +75,94 @@ class EcpP192R1Raw(bignum_common.ModOperationCommon, @property def is_valid(self) -> bool: return True + +class EcpP521R1Raw(bignum_common.ModOperationCommon, + EcpTarget): + """Test cases for ecp quasi_reduction().""" + test_function = "ecp_mod_p521_raw" + test_name = "ecp_mod_p521_raw" + input_style = "arch_split" + arity = 1 + + moduli = [("01ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff" + "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff") + ] # type: List[str] + + input_values = [ + "0", "1", + + # Corner case: maximum canonical P521 multiplication result + ("0003ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff" + "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff" + "fffff800" + "0000000000000000000000000000000000000000000000000000000000000000" + "0000000000000000000000000000000000000000000000000000000000000004"), + + # Test case for overflow during addition + ("0001efffffffffffffffffffffffffffffffffffffffffffffffffffffffffff" + "ffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff" + "000001ef" + "0000000000000000000000000000000000000000000000000000000000000000" + "000000000000000000000000000000000000000000000000000000000f000000"), + + # First 8 number generated by random.getrandbits(1042) - seed(2,2) + ("0003cc2e82523e86feac7eb7dc38f519b91751dacdbd47d364be8049a372db8f" + "6e405d93ffed9235288bc781ae66267594c9c9500925e4749b575bd13653f8dd" + "9b1f282e" + "4067c3584ee207f8da94e3e8ab73738fcf1822ffbc6887782b491044d5e34124" + "5c6e433715ba2bdd177219d30e7a269fd95bafc8f2a4d27bdcf4bb99f4bea973"), + ("00017052829e07b0829a48d422fe99a22c70501e533c91352d3d854e061b9030" + "3b08c6e33c7295782d6c797f8f7d9b782a1be9cd8697bbd0e2520e33e44c5055" + "6c71c4a6" + "6148a86fe8624fab5186ee32ee8d7ee9770348a05d300cb90706a045defc044a" + "09325626e6b58de744ab6cce80877b6f71e1f6d2ef8acd128b4f2fc15f3f57eb"), + ("00021f15a7a83ee0761ebfd2bd143fa9b714210c665d7435c1066932f4767f26" + "294365b2721dea3bf63f23d0dbe53fcafb2147df5ca495fa5a91c89b97eeab64" + "ca2ce6bc" + "5d3fd983c34c769fe89204e2e8168561867e5e15bc01bfce6a27e0dfcbf87544" + "72154e76e4c11ab2fec3f6b32e8d4b8a8f54f8ceacaab39e83844b40ffa9b9f1"), + ("000381bc2a838af8d5c44a4eb3172062d08f1bb2531d6460f0caeef038c89b38" + "a8acb5137c9260dc74e088a9b9492f258ebdbfe3eb9ac688b9d39cca91551e82" + "59cc60b1" + "7604e4b4e73695c3e652c71a74667bffe202849da9643a295a9ac6decbd4d3e2" + "d4dec9ef83f0be4e80371eb97f81375eecc1cb6347733e847d718d733ff98ff3"), + ("00034816c8c69069134bccd3e1cf4f589f8e4ce0af29d115ef24bd625dd961e6" + "830b54fa7d28f93435339774bb1e386c4fd5079e681b8f5896838b769da59b74" + "a6c3181c" + "81e220df848b1df78feb994a81167346d4c0dca8b4c9e755cc9c3adcf515a823" + "4da4daeb4f3f87777ad1f45ae9500ec9c5e2486c44a4a8f69dc8db48e86ec9c6"), + ("000397846c4454b90f756132e16dce72f18e859835e1f291d322a7353ead4efe" + "440e2b4fda9c025a22f1a83185b98f5fc11e60de1b343f52ea748db9e020307a" + "aeb6db2c" + "3a038a709779ac1f45e9dd320c855fdfa7251af0930cdbd30f0ad2a81b2d19a2" + "beaa14a7ff3fe32a30ffc4eed0a7bd04e85bfcdd0227eeb7b9d7d01f5769da05"), + ("00002c3296e6bc4d62b47204007ee4fab105d83e85e951862f0981aebc1b00d9" + "2838e766ef9b6bf2d037fe2e20b6a8464174e75a5f834da70569c018eb2b5693" + "babb7fbb" + "0a76c196067cfdcb11457d9cf45e2fa01d7f4275153924800600571fac3a5b26" + "3fdf57cd2c0064975c3747465cc36c270e8a35b10828d569c268a20eb78ac332"), + ("00009d23b4917fc09f20dbb0dcc93f0e66dfe717c17313394391b6e2e6eacb0f" + "0bb7be72bd6d25009aeb7fa0c4169b148d2f527e72daf0a54ef25c0707e33868" + "7d1f7157" + "5653a45c49390aa51cf5192bbf67da14be11d56ba0b4a2969d8055a9f03f2d71" + "581d8e830112ff0f0948eccaf8877acf26c377c13f719726fd70bddacb4deeec"), + + # Next 2 number generated by random.getrandbits(521) + ("12b84ae65e920a63ac1f2b64df6dff07870c9d531ae72a47403063238da1a1fe" + "3f9d6a179fa50f96cd4aff9261aa92c0e6f17ec940639bc2ccdf572df00790813e3"), + ("166049dd332a73fa0b26b75196cf87eb8a09b27ec714307c68c425424a1574f1" + "eedf5b0f16cdfdb839424d201e653f53d6883ca1c107ca6e706649889c0c7f38608") + ] + + @property + def arg_a(self) -> str: + # Number of limbs: 2 * N + return super().format_arg('{:x}'.format(self.int_a)).zfill(2 * self.hex_digits) + + def result(self) -> List[str]: + result = self.int_a % self.int_n + return [self.format_result(result)] + + @property + def is_valid(self) -> bool: + return True diff --git a/tests/suites/test_suite_ecp.function b/tests/suites/test_suite_ecp.function index b9d2b5ea55..4e74d9b8eb 100644 --- a/tests/suites/test_suite_ecp.function +++ b/tests/suites/test_suite_ecp.function @@ -4,8 +4,8 @@ #include "mbedtls/ecdh.h" #include "bignum_core.h" -#include "bignum_mod_raw_invasive.h" #include "ecp_invasive.h" +#include "bignum_mod_raw_invasive.h" #if defined(MBEDTLS_TEST_HOOKS) && \ (defined(MBEDTLS_ECP_DP_SECP224R1_ENABLED) || \ @@ -1344,3 +1344,46 @@ exit: mbedtls_free(N); } /* END_CASE */ + +/* BEGIN_CASE depends_on:MBEDTLS_TEST_HOOKS */ +void ecp_mod_p521_raw(char *input_N, + char *input_X, + char *result) +{ + mbedtls_mpi_uint *X = NULL; + mbedtls_mpi_uint *N = NULL; + mbedtls_mpi_uint *res = NULL; + size_t limbs_X; + size_t limbs_N; + size_t limbs_res; + + mbedtls_mpi_mod_modulus m; + mbedtls_mpi_mod_modulus_init(&m); + + TEST_EQUAL(mbedtls_test_read_mpi_core(&X, &limbs_X, input_X), 0); + TEST_EQUAL(mbedtls_test_read_mpi_core(&N, &limbs_N, input_N), 0); + TEST_EQUAL(mbedtls_test_read_mpi_core(&res, &limbs_res, result), 0); + + size_t limbs = limbs_N; + size_t bytes = limbs * sizeof(mbedtls_mpi_uint); + + TEST_EQUAL(limbs_X, 2 * limbs); + TEST_EQUAL(limbs_res, limbs); + + TEST_EQUAL(mbedtls_mpi_mod_modulus_setup( + &m, N, limbs, + MBEDTLS_MPI_MOD_REP_MONTGOMERY), 0); + + TEST_EQUAL(mbedtls_ecp_mod_p521_raw(X, limbs_X), 0); + TEST_LE_U(mbedtls_mpi_core_bitlen(X, limbs_X), 522); + mbedtls_mpi_mod_raw_fix_quasi_reduction(X, &m); + ASSERT_COMPARE(X, bytes, res, bytes); + +exit: + mbedtls_free(X); + mbedtls_free(res); + + mbedtls_mpi_mod_modulus_free(&m); + mbedtls_free(N); +} +/* END_CASE */