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Diffstat (limited to 'library/bignum.c')
| -rw-r--r-- | library/bignum.c | 2464 |
1 files changed, 2464 insertions, 0 deletions
diff --git a/library/bignum.c b/library/bignum.c new file mode 100644 index 00000000000..c45fd5bf248 --- /dev/null +++ b/library/bignum.c @@ -0,0 +1,2464 @@ +/* + * Multi-precision integer library + * + * Copyright The Mbed TLS Contributors + * SPDX-License-Identifier: Apache-2.0 OR GPL-2.0-or-later + */ + +/* + * The following sources were referenced in the design of this Multi-precision + * Integer library: + * + * [1] Handbook of Applied Cryptography - 1997 + * Menezes, van Oorschot and Vanstone + * + * [2] Multi-Precision Math + * Tom St Denis + * https://github.com/libtom/libtommath/blob/develop/tommath.pdf + * + * [3] GNU Multi-Precision Arithmetic Library + * https://gmplib.org/manual/index.html + * + */ + +#include "common.h" + +#if defined(MBEDTLS_BIGNUM_C) + +#include "mbedtls/bignum.h" +#include "bignum_core.h" +#include "bn_mul.h" +#include "mbedtls/platform_util.h" +#include "mbedtls/error.h" +#include "constant_time_internal.h" + +#include <limits.h> +#include <string.h> + +#include "mbedtls/platform.h" + + + +/* + * Conditionally select an MPI sign in constant time. + * (MPI sign is the field s in mbedtls_mpi. It is unsigned short and only 1 and -1 are valid + * values.) + */ +static inline signed short mbedtls_ct_mpi_sign_if(mbedtls_ct_condition_t cond, + signed short sign1, signed short sign2) +{ + return (signed short) mbedtls_ct_uint_if(cond, sign1 + 1, sign2 + 1) - 1; +} + +/* + * Compare signed values in constant time + */ +int mbedtls_mpi_lt_mpi_ct(const mbedtls_mpi *X, + const mbedtls_mpi *Y, + unsigned *ret) +{ + mbedtls_ct_condition_t different_sign, X_is_negative, Y_is_negative, result; + + if (X->n != Y->n) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + /* + * Set N_is_negative to MBEDTLS_CT_FALSE if N >= 0, MBEDTLS_CT_TRUE if N < 0. + * We know that N->s == 1 if N >= 0 and N->s == -1 if N < 0. + */ + X_is_negative = mbedtls_ct_bool((X->s & 2) >> 1); + Y_is_negative = mbedtls_ct_bool((Y->s & 2) >> 1); + + /* + * If the signs are different, then the positive operand is the bigger. + * That is if X is negative (X_is_negative == 1), then X < Y is true and it + * is false if X is positive (X_is_negative == 0). + */ + different_sign = mbedtls_ct_bool_ne(X_is_negative, Y_is_negative); // true if different sign + result = mbedtls_ct_bool_and(different_sign, X_is_negative); + + /* + * Assuming signs are the same, compare X and Y. We switch the comparison + * order if they are negative so that we get the right result, regardles of + * sign. + */ + + /* This array is used to conditionally swap the pointers in const time */ + void * const p[2] = { X->p, Y->p }; + size_t i = mbedtls_ct_size_if_else_0(X_is_negative, 1); + mbedtls_ct_condition_t lt = mbedtls_mpi_core_lt_ct(p[i], p[i ^ 1], X->n); + + /* + * Store in result iff the signs are the same (i.e., iff different_sign == false). If + * the signs differ, result has already been set, so we don't change it. + */ + result = mbedtls_ct_bool_or(result, + mbedtls_ct_bool_and(mbedtls_ct_bool_not(different_sign), lt)); + + *ret = mbedtls_ct_uint_if_else_0(result, 1); + + return 0; +} + +/* + * Conditionally assign X = Y, without leaking information + * about whether the assignment was made or not. + * (Leaking information about the respective sizes of X and Y is ok however.) + */ +#if defined(_MSC_VER) && defined(MBEDTLS_PLATFORM_IS_WINDOWS_ON_ARM64) && \ + (_MSC_FULL_VER < 193131103) +/* + * MSVC miscompiles this function if it's inlined prior to Visual Studio 2022 version 17.1. See: + * https://developercommunity.visualstudio.com/t/c-compiler-miscompiles-part-of-mbedtls-library-on/1646989 + */ +__declspec(noinline) +#endif +int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, + const mbedtls_mpi *Y, + unsigned char assign) +{ + int ret = 0; + + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n)); + + { + mbedtls_ct_condition_t do_assign = mbedtls_ct_bool(assign); + + X->s = mbedtls_ct_mpi_sign_if(do_assign, Y->s, X->s); + + mbedtls_mpi_core_cond_assign(X->p, Y->p, Y->n, do_assign); + + mbedtls_ct_condition_t do_not_assign = mbedtls_ct_bool_not(do_assign); + for (size_t i = Y->n; i < X->n; i++) { + X->p[i] = mbedtls_ct_mpi_uint_if_else_0(do_not_assign, X->p[i]); + } + } + +cleanup: + return ret; +} + +/* + * Conditionally swap X and Y, without leaking information + * about whether the swap was made or not. + * Here it is not ok to simply swap the pointers, which would lead to + * different memory access patterns when X and Y are used afterwards. + */ +int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, + mbedtls_mpi *Y, + unsigned char swap) +{ + int ret = 0; + int s; + + if (X == Y) { + return 0; + } + + mbedtls_ct_condition_t do_swap = mbedtls_ct_bool(swap); + + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n)); + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(Y, X->n)); + + s = X->s; + X->s = mbedtls_ct_mpi_sign_if(do_swap, Y->s, X->s); + Y->s = mbedtls_ct_mpi_sign_if(do_swap, s, Y->s); + + mbedtls_mpi_core_cond_swap(X->p, Y->p, X->n, do_swap); + +cleanup: + return ret; +} + +/* Implementation that should never be optimized out by the compiler */ +#define mbedtls_mpi_zeroize_and_free(v, n) mbedtls_zeroize_and_free(v, ciL * (n)) + +/* + * Initialize one MPI + */ +void mbedtls_mpi_init(mbedtls_mpi *X) +{ + X->s = 1; + X->n = 0; + X->p = NULL; +} + +/* + * Unallocate one MPI + */ +void mbedtls_mpi_free(mbedtls_mpi *X) +{ + if (X == NULL) { + return; + } + + if (X->p != NULL) { + mbedtls_mpi_zeroize_and_free(X->p, X->n); + } + + X->s = 1; + X->n = 0; + X->p = NULL; +} + +/* + * Enlarge to the specified number of limbs + */ +int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs) +{ + mbedtls_mpi_uint *p; + + if (nblimbs > MBEDTLS_MPI_MAX_LIMBS) { + return MBEDTLS_ERR_MPI_ALLOC_FAILED; + } + + if (X->n < nblimbs) { + if ((p = (mbedtls_mpi_uint *) mbedtls_calloc(nblimbs, ciL)) == NULL) { + return MBEDTLS_ERR_MPI_ALLOC_FAILED; + } + + if (X->p != NULL) { + memcpy(p, X->p, X->n * ciL); + mbedtls_mpi_zeroize_and_free(X->p, X->n); + } + + /* nblimbs fits in n because we ensure that MBEDTLS_MPI_MAX_LIMBS + * fits, and we've checked that nblimbs <= MBEDTLS_MPI_MAX_LIMBS. */ + X->n = (unsigned short) nblimbs; + X->p = p; + } + + return 0; +} + +/* + * Resize down as much as possible, + * while keeping at least the specified number of limbs + */ +int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs) +{ + mbedtls_mpi_uint *p; + size_t i; + + if (nblimbs > MBEDTLS_MPI_MAX_LIMBS) { + return MBEDTLS_ERR_MPI_ALLOC_FAILED; + } + + /* Actually resize up if there are currently fewer than nblimbs limbs. */ + if (X->n <= nblimbs) { + return mbedtls_mpi_grow(X, nblimbs); + } + /* After this point, then X->n > nblimbs and in particular X->n > 0. */ + + for (i = X->n - 1; i > 0; i--) { + if (X->p[i] != 0) { + break; + } + } + i++; + + if (i < nblimbs) { + i = nblimbs; + } + + if ((p = (mbedtls_mpi_uint *) mbedtls_calloc(i, ciL)) == NULL) { + return MBEDTLS_ERR_MPI_ALLOC_FAILED; + } + + if (X->p != NULL) { + memcpy(p, X->p, i * ciL); + mbedtls_mpi_zeroize_and_free(X->p, X->n); + } + + /* i fits in n because we ensure that MBEDTLS_MPI_MAX_LIMBS + * fits, and we've checked that i <= nblimbs <= MBEDTLS_MPI_MAX_LIMBS. */ + X->n = (unsigned short) i; + X->p = p; + + return 0; +} + +/* Resize X to have exactly n limbs and set it to 0. */ +static int mbedtls_mpi_resize_clear(mbedtls_mpi *X, size_t limbs) +{ + if (limbs == 0) { + mbedtls_mpi_free(X); + return 0; + } else if (X->n == limbs) { + memset(X->p, 0, limbs * ciL); + X->s = 1; + return 0; + } else { + mbedtls_mpi_free(X); + return mbedtls_mpi_grow(X, limbs); + } +} + +/* + * Copy the contents of Y into X. + * + * This function is not constant-time. Leading zeros in Y may be removed. + * + * Ensure that X does not shrink. This is not guaranteed by the public API, + * but some code in the bignum module might still rely on this property. + */ +int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y) +{ + int ret = 0; + size_t i; + + if (X == Y) { + return 0; + } + + if (Y->n == 0) { + if (X->n != 0) { + X->s = 1; + memset(X->p, 0, X->n * ciL); + } + return 0; + } + + for (i = Y->n - 1; i > 0; i--) { + if (Y->p[i] != 0) { + break; + } + } + i++; + + X->s = Y->s; + + if (X->n < i) { + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, i)); + } else { + memset(X->p + i, 0, (X->n - i) * ciL); + } + + memcpy(X->p, Y->p, i * ciL); + +cleanup: + + return ret; +} + +/* + * Swap the contents of X and Y + */ +void mbedtls_mpi_swap(mbedtls_mpi *X, mbedtls_mpi *Y) +{ + mbedtls_mpi T; + + memcpy(&T, X, sizeof(mbedtls_mpi)); + memcpy(X, Y, sizeof(mbedtls_mpi)); + memcpy(Y, &T, sizeof(mbedtls_mpi)); +} + +static inline mbedtls_mpi_uint mpi_sint_abs(mbedtls_mpi_sint z) +{ + if (z >= 0) { + return z; + } + /* Take care to handle the most negative value (-2^(biL-1)) correctly. + * A naive -z would have undefined behavior. + * Write this in a way that makes popular compilers happy (GCC, Clang, + * MSVC). */ + return (mbedtls_mpi_uint) 0 - (mbedtls_mpi_uint) z; +} + +/* Convert x to a sign, i.e. to 1, if x is positive, or -1, if x is negative. + * This looks awkward but generates smaller code than (x < 0 ? -1 : 1) */ +#define TO_SIGN(x) ((mbedtls_mpi_sint) (((mbedtls_mpi_uint) x) >> (biL - 1)) * -2 + 1) + +/* + * Set value from integer + */ +int mbedtls_mpi_lset(mbedtls_mpi *X, mbedtls_mpi_sint z) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, 1)); + memset(X->p, 0, X->n * ciL); + + X->p[0] = mpi_sint_abs(z); + X->s = TO_SIGN(z); + +cleanup: + + return ret; +} + +/* + * Get a specific bit + */ +int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos) +{ + if (X->n * biL <= pos) { + return 0; + } + + return (X->p[pos / biL] >> (pos % biL)) & 0x01; +} + +/* + * Set a bit to a specific value of 0 or 1 + */ +int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val) +{ + int ret = 0; + size_t off = pos / biL; + size_t idx = pos % biL; + + if (val != 0 && val != 1) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + if (X->n * biL <= pos) { + if (val == 0) { + return 0; + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, off + 1)); + } + + X->p[off] &= ~((mbedtls_mpi_uint) 0x01 << idx); + X->p[off] |= (mbedtls_mpi_uint) val << idx; + +cleanup: + + return ret; +} + +/* + * Return the number of less significant zero-bits + */ +size_t mbedtls_mpi_lsb(const mbedtls_mpi *X) +{ + size_t i; + +#if defined(__has_builtin) +#if (MBEDTLS_MPI_UINT_MAX == UINT_MAX) && __has_builtin(__builtin_ctz) + #define mbedtls_mpi_uint_ctz __builtin_ctz +#elif (MBEDTLS_MPI_UINT_MAX == ULONG_MAX) && __has_builtin(__builtin_ctzl) + #define mbedtls_mpi_uint_ctz __builtin_ctzl +#elif (MBEDTLS_MPI_UINT_MAX == ULLONG_MAX) && __has_builtin(__builtin_ctzll) + #define mbedtls_mpi_uint_ctz __builtin_ctzll +#endif +#endif + +#if defined(mbedtls_mpi_uint_ctz) + for (i = 0; i < X->n; i++) { + if (X->p[i] != 0) { + return i * biL + mbedtls_mpi_uint_ctz(X->p[i]); + } + } +#else + size_t count = 0; + for (i = 0; i < X->n; i++) { + for (size_t j = 0; j < biL; j++, count++) { + if (((X->p[i] >> j) & 1) != 0) { + return count; + } + } + } +#endif + + return 0; +} + +/* + * Return the number of bits + */ +size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X) +{ + return mbedtls_mpi_core_bitlen(X->p, X->n); +} + +/* + * Return the total size in bytes + */ +size_t mbedtls_mpi_size(const mbedtls_mpi *X) +{ + return (mbedtls_mpi_bitlen(X) + 7) >> 3; +} + +/* + * Convert an ASCII character to digit value + */ +static int mpi_get_digit(mbedtls_mpi_uint *d, int radix, char c) +{ + *d = 255; + + if (c >= 0x30 && c <= 0x39) { + *d = c - 0x30; + } + if (c >= 0x41 && c <= 0x46) { + *d = c - 0x37; + } + if (c >= 0x61 && c <= 0x66) { + *d = c - 0x57; + } + + if (*d >= (mbedtls_mpi_uint) radix) { + return MBEDTLS_ERR_MPI_INVALID_CHARACTER; + } + + return 0; +} + +/* + * Import from an ASCII string + */ +int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i, j, slen, n; + int sign = 1; + mbedtls_mpi_uint d; + mbedtls_mpi T; + + if (radix < 2 || radix > 16) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + mbedtls_mpi_init(&T); + + if (s[0] == 0) { + mbedtls_mpi_free(X); + return 0; + } + + if (s[0] == '-') { + ++s; + sign = -1; + } + + slen = strlen(s); + + if (radix == 16) { + if (slen > SIZE_MAX >> 2) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + n = BITS_TO_LIMBS(slen << 2); + + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, n)); + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0)); + + for (i = slen, j = 0; i > 0; i--, j++) { + MBEDTLS_MPI_CHK(mpi_get_digit(&d, radix, s[i - 1])); + X->p[j / (2 * ciL)] |= d << ((j % (2 * ciL)) << 2); + } + } else { + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0)); + + for (i = 0; i < slen; i++) { + MBEDTLS_MPI_CHK(mpi_get_digit(&d, radix, s[i])); + MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T, X, radix)); + MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, &T, d)); + } + } + + if (sign < 0 && mbedtls_mpi_bitlen(X) != 0) { + X->s = -1; + } + +cleanup: + + mbedtls_mpi_free(&T); + + return ret; +} + +/* + * Helper to write the digits high-order first. + */ +static int mpi_write_hlp(mbedtls_mpi *X, int radix, + char **p, const size_t buflen) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi_uint r; + size_t length = 0; + char *p_end = *p + buflen; + + do { + if (length >= buflen) { + return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL; + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, radix)); + MBEDTLS_MPI_CHK(mbedtls_mpi_div_int(X, NULL, X, radix)); + /* + * Write the residue in the current position, as an ASCII character. + */ + if (r < 0xA) { + *(--p_end) = (char) ('0' + r); + } else { + *(--p_end) = (char) ('A' + (r - 0xA)); + } + + length++; + } while (mbedtls_mpi_cmp_int(X, 0) != 0); + + memmove(*p, p_end, length); + *p += length; + +cleanup: + + return ret; +} + +/* + * Export into an ASCII string + */ +int mbedtls_mpi_write_string(const mbedtls_mpi *X, int radix, + char *buf, size_t buflen, size_t *olen) +{ + int ret = 0; + size_t n; + char *p; + mbedtls_mpi T; + + if (radix < 2 || radix > 16) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + n = mbedtls_mpi_bitlen(X); /* Number of bits necessary to present `n`. */ + if (radix >= 4) { + n >>= 1; /* Number of 4-adic digits necessary to present + * `n`. If radix > 4, this might be a strict + * overapproximation of the number of + * radix-adic digits needed to present `n`. */ + } + if (radix >= 16) { + n >>= 1; /* Number of hexadecimal digits necessary to + * present `n`. */ + + } + n += 1; /* Terminating null byte */ + n += 1; /* Compensate for the divisions above, which round down `n` + * in case it's not even. */ + n += 1; /* Potential '-'-sign. */ + n += (n & 1); /* Make n even to have enough space for hexadecimal writing, + * which always uses an even number of hex-digits. */ + + if (buflen < n) { + *olen = n; + return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL; + } + + p = buf; + mbedtls_mpi_init(&T); + + if (X->s == -1) { + *p++ = '-'; + buflen--; + } + + if (radix == 16) { + int c; + size_t i, j, k; + + for (i = X->n, k = 0; i > 0; i--) { + for (j = ciL; j > 0; j--) { + c = (X->p[i - 1] >> ((j - 1) << 3)) & 0xFF; + + if (c == 0 && k == 0 && (i + j) != 2) { + continue; + } + + *(p++) = "0123456789ABCDEF" [c / 16]; + *(p++) = "0123456789ABCDEF" [c % 16]; + k = 1; + } + } + } else { + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&T, X)); + + if (T.s == -1) { + T.s = 1; + } + + MBEDTLS_MPI_CHK(mpi_write_hlp(&T, radix, &p, buflen)); + } + + *p++ = '\0'; + *olen = (size_t) (p - buf); + +cleanup: + + mbedtls_mpi_free(&T); + + return ret; +} + +#if defined(MBEDTLS_FS_IO) +/* + * Read X from an opened file + */ +int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin) +{ + mbedtls_mpi_uint d; + size_t slen; + char *p; + /* + * Buffer should have space for (short) label and decimal formatted MPI, + * newline characters and '\0' + */ + char s[MBEDTLS_MPI_RW_BUFFER_SIZE]; + + if (radix < 2 || radix > 16) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + memset(s, 0, sizeof(s)); + if (fgets(s, sizeof(s) - 1, fin) == NULL) { + return MBEDTLS_ERR_MPI_FILE_IO_ERROR; + } + + slen = strlen(s); + if (slen == sizeof(s) - 2) { + return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL; + } + + if (slen > 0 && s[slen - 1] == '\n') { + slen--; s[slen] = '\0'; + } + if (slen > 0 && s[slen - 1] == '\r') { + slen--; s[slen] = '\0'; + } + + p = s + slen; + while (p-- > s) { + if (mpi_get_digit(&d, radix, *p) != 0) { + break; + } + } + + return mbedtls_mpi_read_string(X, radix, p + 1); +} + +/* + * Write X into an opened file (or stdout if fout == NULL) + */ +int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X, int radix, FILE *fout) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t n, slen, plen; + /* + * Buffer should have space for (short) label and decimal formatted MPI, + * newline characters and '\0' + */ + char s[MBEDTLS_MPI_RW_BUFFER_SIZE]; + + if (radix < 2 || radix > 16) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + memset(s, 0, sizeof(s)); + + MBEDTLS_MPI_CHK(mbedtls_mpi_write_string(X, radix, s, sizeof(s) - 2, &n)); + + if (p == NULL) { + p = ""; + } + + plen = strlen(p); + slen = strlen(s); + s[slen++] = '\r'; + s[slen++] = '\n'; + + if (fout != NULL) { + if (fwrite(p, 1, plen, fout) != plen || + fwrite(s, 1, slen, fout) != slen) { + return MBEDTLS_ERR_MPI_FILE_IO_ERROR; + } + } else { + mbedtls_printf("%s%s", p, s); + } + +cleanup: + + return ret; +} +#endif /* MBEDTLS_FS_IO */ + +/* + * Import X from unsigned binary data, little endian + * + * This function is guaranteed to return an MPI with exactly the necessary + * number of limbs (in particular, it does not skip 0s in the input). + */ +int mbedtls_mpi_read_binary_le(mbedtls_mpi *X, + const unsigned char *buf, size_t buflen) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + const size_t limbs = CHARS_TO_LIMBS(buflen); + + /* Ensure that target MPI has exactly the necessary number of limbs */ + MBEDTLS_MPI_CHK(mbedtls_mpi_resize_clear(X, limbs)); + + MBEDTLS_MPI_CHK(mbedtls_mpi_core_read_le(X->p, X->n, buf, buflen)); + +cleanup: + + /* + * This function is also used to import keys. However, wiping the buffers + * upon failure is not necessary because failure only can happen before any + * input is copied. + */ + return ret; +} + +/* + * Import X from unsigned binary data, big endian + * + * This function is guaranteed to return an MPI with exactly the necessary + * number of limbs (in particular, it does not skip 0s in the input). + */ +int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf, size_t buflen) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + const size_t limbs = CHARS_TO_LIMBS(buflen); + + /* Ensure that target MPI has exactly the necessary number of limbs */ + MBEDTLS_MPI_CHK(mbedtls_mpi_resize_clear(X, limbs)); + + MBEDTLS_MPI_CHK(mbedtls_mpi_core_read_be(X->p, X->n, buf, buflen)); + +cleanup: + + /* + * This function is also used to import keys. However, wiping the buffers + * upon failure is not necessary because failure only can happen before any + * input is copied. + */ + return ret; +} + +/* + * Export X into unsigned binary data, little endian + */ +int mbedtls_mpi_write_binary_le(const mbedtls_mpi *X, + unsigned char *buf, size_t buflen) +{ + return mbedtls_mpi_core_write_le(X->p, X->n, buf, buflen); +} + +/* + * Export X into unsigned binary data, big endian + */ +int mbedtls_mpi_write_binary(const mbedtls_mpi *X, + unsigned char *buf, size_t buflen) +{ + return mbedtls_mpi_core_write_be(X->p, X->n, buf, buflen); +} + +/* + * Left-shift: X <<= count + */ +int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i; + + i = mbedtls_mpi_bitlen(X) + count; + + if (X->n * biL < i) { + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, BITS_TO_LIMBS(i))); + } + + ret = 0; + + mbedtls_mpi_core_shift_l(X->p, X->n, count); +cleanup: + + return ret; +} + +/* + * Right-shift: X >>= count + */ +int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count) +{ + if (X->n != 0) { + mbedtls_mpi_core_shift_r(X->p, X->n, count); + } + return 0; +} + +/* + * Compare unsigned values + */ +int mbedtls_mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y) +{ + size_t i, j; + + for (i = X->n; i > 0; i--) { + if (X->p[i - 1] != 0) { + break; + } + } + + for (j = Y->n; j > 0; j--) { + if (Y->p[j - 1] != 0) { + break; + } + } + + /* If i == j == 0, i.e. abs(X) == abs(Y), + * we end up returning 0 at the end of the function. */ + + if (i > j) { + return 1; + } + if (j > i) { + return -1; + } + + for (; i > 0; i--) { + if (X->p[i - 1] > Y->p[i - 1]) { + return 1; + } + if (X->p[i - 1] < Y->p[i - 1]) { + return -1; + } + } + + return 0; +} + +/* + * Compare signed values + */ +int mbedtls_mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y) +{ + size_t i, j; + + for (i = X->n; i > 0; i--) { + if (X->p[i - 1] != 0) { + break; + } + } + + for (j = Y->n; j > 0; j--) { + if (Y->p[j - 1] != 0) { + break; + } + } + + if (i == 0 && j == 0) { + return 0; + } + + if (i > j) { + return X->s; + } + if (j > i) { + return -Y->s; + } + + if (X->s > 0 && Y->s < 0) { + return 1; + } + if (Y->s > 0 && X->s < 0) { + return -1; + } + + for (; i > 0; i--) { + if (X->p[i - 1] > Y->p[i - 1]) { + return X->s; + } + if (X->p[i - 1] < Y->p[i - 1]) { + return -X->s; + } + } + + return 0; +} + +/* + * Compare signed values + */ +int mbedtls_mpi_cmp_int(const mbedtls_mpi *X, mbedtls_mpi_sint z) +{ + mbedtls_mpi Y; + mbedtls_mpi_uint p[1]; + + *p = mpi_sint_abs(z); + Y.s = TO_SIGN(z); + Y.n = 1; + Y.p = p; + + return mbedtls_mpi_cmp_mpi(X, &Y); +} + +/* + * Unsigned addition: X = |A| + |B| (HAC 14.7) + */ +int mbedtls_mpi_add_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t j; + mbedtls_mpi_uint *p; + mbedtls_mpi_uint c; + + if (X == B) { + const mbedtls_mpi *T = A; A = X; B = T; + } + + if (X != A) { + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A)); + } + + /* + * X must always be positive as a result of unsigned additions. + */ + X->s = 1; + + for (j = B->n; j > 0; j--) { + if (B->p[j - 1] != 0) { + break; + } + } + + /* Exit early to avoid undefined behavior on NULL+0 when X->n == 0 + * and B is 0 (of any size). */ + if (j == 0) { + return 0; + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, j)); + + /* j is the number of non-zero limbs of B. Add those to X. */ + + p = X->p; + + c = mbedtls_mpi_core_add(p, p, B->p, j); + + p += j; + + /* Now propagate any carry */ + + while (c != 0) { + if (j >= X->n) { + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, j + 1)); + p = X->p + j; + } + + *p += c; c = (*p < c); j++; p++; + } + +cleanup: + + return ret; +} + +/* + * Unsigned subtraction: X = |A| - |B| (HAC 14.9, 14.10) + */ +int mbedtls_mpi_sub_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t n; + mbedtls_mpi_uint carry; + + for (n = B->n; n > 0; n--) { + if (B->p[n - 1] != 0) { + break; + } + } + if (n > A->n) { + /* B >= (2^ciL)^n > A */ + ret = MBEDTLS_ERR_MPI_NEGATIVE_VALUE; + goto cleanup; + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, A->n)); + + /* Set the high limbs of X to match A. Don't touch the lower limbs + * because X might be aliased to B, and we must not overwrite the + * significant digits of B. */ + if (A->n > n && A != X) { + memcpy(X->p + n, A->p + n, (A->n - n) * ciL); + } + if (X->n > A->n) { + memset(X->p + A->n, 0, (X->n - A->n) * ciL); + } + + carry = mbedtls_mpi_core_sub(X->p, A->p, B->p, n); + if (carry != 0) { + /* Propagate the carry through the rest of X. */ + carry = mbedtls_mpi_core_sub_int(X->p + n, X->p + n, carry, X->n - n); + + /* If we have further carry/borrow, the result is negative. */ + if (carry != 0) { + ret = MBEDTLS_ERR_MPI_NEGATIVE_VALUE; + goto cleanup; + } + } + + /* X should always be positive as a result of unsigned subtractions. */ + X->s = 1; + +cleanup: + return ret; +} + +/* Common function for signed addition and subtraction. + * Calculate A + B * flip_B where flip_B is 1 or -1. + */ +static int add_sub_mpi(mbedtls_mpi *X, + const mbedtls_mpi *A, const mbedtls_mpi *B, + int flip_B) +{ + int ret, s; + + s = A->s; + if (A->s * B->s * flip_B < 0) { + int cmp = mbedtls_mpi_cmp_abs(A, B); + if (cmp >= 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, A, B)); + /* If |A| = |B|, the result is 0 and we must set the sign bit + * to +1 regardless of which of A or B was negative. Otherwise, + * since |A| > |B|, the sign is the sign of A. */ + X->s = cmp == 0 ? 1 : s; + } else { + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(X, B, A)); + /* Since |A| < |B|, the sign is the opposite of A. */ + X->s = -s; + } + } else { + MBEDTLS_MPI_CHK(mbedtls_mpi_add_abs(X, A, B)); + X->s = s; + } + +cleanup: + + return ret; +} + +/* + * Signed addition: X = A + B + */ +int mbedtls_mpi_add_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) +{ + return add_sub_mpi(X, A, B, 1); +} + +/* + * Signed subtraction: X = A - B + */ +int mbedtls_mpi_sub_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) +{ + return add_sub_mpi(X, A, B, -1); +} + +/* + * Signed addition: X = A + b + */ +int mbedtls_mpi_add_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b) +{ + mbedtls_mpi B; + mbedtls_mpi_uint p[1]; + + p[0] = mpi_sint_abs(b); + B.s = TO_SIGN(b); + B.n = 1; + B.p = p; + + return mbedtls_mpi_add_mpi(X, A, &B); +} + +/* + * Signed subtraction: X = A - b + */ +int mbedtls_mpi_sub_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b) +{ + mbedtls_mpi B; + mbedtls_mpi_uint p[1]; + + p[0] = mpi_sint_abs(b); + B.s = TO_SIGN(b); + B.n = 1; + B.p = p; + + return mbedtls_mpi_sub_mpi(X, A, &B); +} + +/* + * Baseline multiplication: X = A * B (HAC 14.12) + */ +int mbedtls_mpi_mul_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i, j; + mbedtls_mpi TA, TB; + int result_is_zero = 0; + + mbedtls_mpi_init(&TA); + mbedtls_mpi_init(&TB); + + if (X == A) { + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TA, A)); A = &TA; + } + if (X == B) { + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TB, B)); B = &TB; + } + + for (i = A->n; i > 0; i--) { + if (A->p[i - 1] != 0) { + break; + } + } + if (i == 0) { + result_is_zero = 1; + } + + for (j = B->n; j > 0; j--) { + if (B->p[j - 1] != 0) { + break; + } + } + if (j == 0) { + result_is_zero = 1; + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, i + j)); + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0)); + + mbedtls_mpi_core_mul(X->p, A->p, i, B->p, j); + + /* If the result is 0, we don't shortcut the operation, which reduces + * but does not eliminate side channels leaking the zero-ness. We do + * need to take care to set the sign bit properly since the library does + * not fully support an MPI object with a value of 0 and s == -1. */ + if (result_is_zero) { + X->s = 1; + } else { + X->s = A->s * B->s; + } + +cleanup: + + mbedtls_mpi_free(&TB); mbedtls_mpi_free(&TA); + + return ret; +} + +/* + * Baseline multiplication: X = A * b + */ +int mbedtls_mpi_mul_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b) +{ + size_t n = A->n; + while (n > 0 && A->p[n - 1] == 0) { + --n; + } + + /* The general method below doesn't work if b==0. */ + if (b == 0 || n == 0) { + return mbedtls_mpi_lset(X, 0); + } + + /* Calculate A*b as A + A*(b-1) to take advantage of mbedtls_mpi_core_mla */ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + /* In general, A * b requires 1 limb more than b. If + * A->p[n - 1] * b / b == A->p[n - 1], then A * b fits in the same + * number of limbs as A and the call to grow() is not required since + * copy() will take care of the growth if needed. However, experimentally, + * making the call to grow() unconditional causes slightly fewer + * calls to calloc() in ECP code, presumably because it reuses the + * same mpi for a while and this way the mpi is more likely to directly + * grow to its final size. + * + * Note that calculating A*b as 0 + A*b doesn't work as-is because + * A,X can be the same. */ + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, n + 1)); + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A)); + mbedtls_mpi_core_mla(X->p, X->n, A->p, n, b - 1); + +cleanup: + return ret; +} + +/* + * Unsigned integer divide - double mbedtls_mpi_uint dividend, u1/u0, and + * mbedtls_mpi_uint divisor, d + */ +static mbedtls_mpi_uint mbedtls_int_div_int(mbedtls_mpi_uint u1, + mbedtls_mpi_uint u0, + mbedtls_mpi_uint d, + mbedtls_mpi_uint *r) +{ +#if defined(MBEDTLS_HAVE_UDBL) + mbedtls_t_udbl dividend, quotient; +#else + const mbedtls_mpi_uint radix = (mbedtls_mpi_uint) 1 << biH; + const mbedtls_mpi_uint uint_halfword_mask = ((mbedtls_mpi_uint) 1 << biH) - 1; + mbedtls_mpi_uint d0, d1, q0, q1, rAX, r0, quotient; + mbedtls_mpi_uint u0_msw, u0_lsw; + size_t s; +#endif + + /* + * Check for overflow + */ + if (0 == d || u1 >= d) { + if (r != NULL) { + *r = ~(mbedtls_mpi_uint) 0u; + } + + return ~(mbedtls_mpi_uint) 0u; + } + +#if defined(MBEDTLS_HAVE_UDBL) + dividend = (mbedtls_t_udbl) u1 << biL; + dividend |= (mbedtls_t_udbl) u0; + quotient = dividend / d; + if (quotient > ((mbedtls_t_udbl) 1 << biL) - 1) { + quotient = ((mbedtls_t_udbl) 1 << biL) - 1; + } + + if (r != NULL) { + *r = (mbedtls_mpi_uint) (dividend - (quotient * d)); + } + + return (mbedtls_mpi_uint) quotient; +#else + + /* + * Algorithm D, Section 4.3.1 - The Art of Computer Programming + * Vol. 2 - Seminumerical Algorithms, Knuth + */ + + /* + * Normalize the divisor, d, and dividend, u0, u1 + */ + s = mbedtls_mpi_core_clz(d); + d = d << s; + + u1 = u1 << s; + u1 |= (u0 >> (biL - s)) & (-(mbedtls_mpi_sint) s >> (biL - 1)); + u0 = u0 << s; + + d1 = d >> biH; + d0 = d & uint_halfword_mask; + + u0_msw = u0 >> biH; + u0_lsw = u0 & uint_halfword_mask; + + /* + * Find the first quotient and remainder + */ + q1 = u1 / d1; + r0 = u1 - d1 * q1; + + while (q1 >= radix || (q1 * d0 > radix * r0 + u0_msw)) { + q1 -= 1; + r0 += d1; + + if (r0 >= radix) { + break; + } + } + + rAX = (u1 * radix) + (u0_msw - q1 * d); + q0 = rAX / d1; + r0 = rAX - q0 * d1; + + while (q0 >= radix || (q0 * d0 > radix * r0 + u0_lsw)) { + q0 -= 1; + r0 += d1; + + if (r0 >= radix) { + break; + } + } + + if (r != NULL) { + *r = (rAX * radix + u0_lsw - q0 * d) >> s; + } + + quotient = q1 * radix + q0; + + return quotient; +#endif +} + +/* + * Division by mbedtls_mpi: A = Q * B + R (HAC 14.20) + */ +int mbedtls_mpi_div_mpi(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, + const mbedtls_mpi *B) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t i, n, t, k; + mbedtls_mpi X, Y, Z, T1, T2; + mbedtls_mpi_uint TP2[3]; + + if (mbedtls_mpi_cmp_int(B, 0) == 0) { + return MBEDTLS_ERR_MPI_DIVISION_BY_ZERO; + } + + mbedtls_mpi_init(&X); mbedtls_mpi_init(&Y); mbedtls_mpi_init(&Z); + mbedtls_mpi_init(&T1); + /* + * Avoid dynamic memory allocations for constant-size T2. + * + * T2 is used for comparison only and the 3 limbs are assigned explicitly, + * so nobody increase the size of the MPI and we're safe to use an on-stack + * buffer. + */ + T2.s = 1; + T2.n = sizeof(TP2) / sizeof(*TP2); + T2.p = TP2; + + if (mbedtls_mpi_cmp_abs(A, B) < 0) { + if (Q != NULL) { + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(Q, 0)); + } + if (R != NULL) { + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(R, A)); + } + return 0; + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&X, A)); + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Y, B)); + X.s = Y.s = 1; + + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&Z, A->n + 2)); + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&Z, 0)); + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&T1, A->n + 2)); + + k = mbedtls_mpi_bitlen(&Y) % biL; + if (k < biL - 1) { + k = biL - 1 - k; + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&X, k)); + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&Y, k)); + } else { + k = 0; + } + + n = X.n - 1; + t = Y.n - 1; + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&Y, biL * (n - t))); + + while (mbedtls_mpi_cmp_mpi(&X, &Y) >= 0) { + Z.p[n - t]++; + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&X, &X, &Y)); + } + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&Y, biL * (n - t))); + + for (i = n; i > t; i--) { + if (X.p[i] >= Y.p[t]) { + Z.p[i - t - 1] = ~(mbedtls_mpi_uint) 0u; + } else { + Z.p[i - t - 1] = mbedtls_int_div_int(X.p[i], X.p[i - 1], + Y.p[t], NULL); + } + + T2.p[0] = (i < 2) ? 0 : X.p[i - 2]; + T2.p[1] = (i < 1) ? 0 : X.p[i - 1]; + T2.p[2] = X.p[i]; + + Z.p[i - t - 1]++; + do { + Z.p[i - t - 1]--; + + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&T1, 0)); + T1.p[0] = (t < 1) ? 0 : Y.p[t - 1]; + T1.p[1] = Y.p[t]; + MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T1, &T1, Z.p[i - t - 1])); + } while (mbedtls_mpi_cmp_mpi(&T1, &T2) > 0); + + MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T1, &Y, Z.p[i - t - 1])); + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&T1, biL * (i - t - 1))); + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&X, &X, &T1)); + + if (mbedtls_mpi_cmp_int(&X, 0) < 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&T1, &Y)); + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&T1, biL * (i - t - 1))); + MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&X, &X, &T1)); + Z.p[i - t - 1]--; + } + } + + if (Q != NULL) { + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(Q, &Z)); + Q->s = A->s * B->s; + } + + if (R != NULL) { + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&X, k)); + X.s = A->s; + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(R, &X)); + + if (mbedtls_mpi_cmp_int(R, 0) == 0) { + R->s = 1; + } + } + +cleanup: + + mbedtls_mpi_free(&X); mbedtls_mpi_free(&Y); mbedtls_mpi_free(&Z); + mbedtls_mpi_free(&T1); + mbedtls_platform_zeroize(TP2, sizeof(TP2)); + + return ret; +} + +/* + * Division by int: A = Q * b + R + */ +int mbedtls_mpi_div_int(mbedtls_mpi *Q, mbedtls_mpi *R, + const mbedtls_mpi *A, + mbedtls_mpi_sint b) +{ + mbedtls_mpi B; + mbedtls_mpi_uint p[1]; + + p[0] = mpi_sint_abs(b); + B.s = TO_SIGN(b); + B.n = 1; + B.p = p; + + return mbedtls_mpi_div_mpi(Q, R, A, &B); +} + +/* + * Modulo: R = A mod B + */ +int mbedtls_mpi_mod_mpi(mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + + if (mbedtls_mpi_cmp_int(B, 0) < 0) { + return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_div_mpi(NULL, R, A, B)); + + while (mbedtls_mpi_cmp_int(R, 0) < 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(R, R, B)); + } + + while (mbedtls_mpi_cmp_mpi(R, B) >= 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(R, R, B)); + } + +cleanup: + + return ret; +} + +/* + * Modulo: r = A mod b + */ +int mbedtls_mpi_mod_int(mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b) +{ + size_t i; + mbedtls_mpi_uint x, y, z; + + if (b == 0) { + return MBEDTLS_ERR_MPI_DIVISION_BY_ZERO; + } + + if (b < 0) { + return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; + } + + /* + * handle trivial cases + */ + if (b == 1 || A->n == 0) { + *r = 0; + return 0; + } + + if (b == 2) { + *r = A->p[0] & 1; + return 0; + } + + /* + * general case + */ + for (i = A->n, y = 0; i > 0; i--) { + x = A->p[i - 1]; + y = (y << biH) | (x >> biH); + z = y / b; + y -= z * b; + + x <<= biH; + y = (y << biH) | (x >> biH); + z = y / b; + y -= z * b; + } + + /* + * If A is negative, then the current y represents a negative value. + * Flipping it to the positive side. + */ + if (A->s < 0 && y != 0) { + y = b - y; + } + + *r = y; + + return 0; +} + +int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A, + const mbedtls_mpi *E, const mbedtls_mpi *N, + mbedtls_mpi *prec_RR) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + + if (mbedtls_mpi_cmp_int(N, 0) <= 0 || (N->p[0] & 1) == 0) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + if (mbedtls_mpi_cmp_int(E, 0) < 0) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + if (mbedtls_mpi_bitlen(E) > MBEDTLS_MPI_MAX_BITS || + mbedtls_mpi_bitlen(N) > MBEDTLS_MPI_MAX_BITS) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + /* + * Ensure that the exponent that we are passing to the core is not NULL. + */ + if (E->n == 0) { + ret = mbedtls_mpi_lset(X, 1); + return ret; + } + + /* + * Allocate working memory for mbedtls_mpi_core_exp_mod() + */ + size_t T_limbs = mbedtls_mpi_core_exp_mod_working_limbs(N->n, E->n); + mbedtls_mpi_uint *T = (mbedtls_mpi_uint *) mbedtls_calloc(T_limbs, sizeof(mbedtls_mpi_uint)); + if (T == NULL) { + return MBEDTLS_ERR_MPI_ALLOC_FAILED; + } + + mbedtls_mpi RR; + mbedtls_mpi_init(&RR); + + /* + * If 1st call, pre-compute R^2 mod N + */ + if (prec_RR == NULL || prec_RR->p == NULL) { + MBEDTLS_MPI_CHK(mbedtls_mpi_core_get_mont_r2_unsafe(&RR, N)); + + if (prec_RR != NULL) { + *prec_RR = RR; + } + } else { + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(prec_RR, N->n)); + RR = *prec_RR; + } + + /* + * To preserve constness we need to make a copy of A. Using X for this to + * save memory. + */ + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A)); + + /* + * Compensate for negative A (and correct at the end). + */ + X->s = 1; + + /* + * Make sure that X is in a form that is safe for consumption by + * the core functions. + * + * - The core functions will not touch the limbs of X above N->n. The + * result will be correct if those limbs are 0, which the mod call + * ensures. + * - Also, X must have at least as many limbs as N for the calls to the + * core functions. + */ + if (mbedtls_mpi_cmp_mpi(X, N) >= 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(X, X, N)); + } + MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, N->n)); + + /* + * Convert to and from Montgomery around mbedtls_mpi_core_exp_mod(). + */ + { + mbedtls_mpi_uint mm = mbedtls_mpi_core_montmul_init(N->p); + mbedtls_mpi_core_to_mont_rep(X->p, X->p, N->p, N->n, mm, RR.p, T); + mbedtls_mpi_core_exp_mod(X->p, X->p, N->p, N->n, E->p, E->n, RR.p, T); + mbedtls_mpi_core_from_mont_rep(X->p, X->p, N->p, N->n, mm, T); + } + + /* + * Correct for negative A. + */ + if (A->s == -1 && (E->p[0] & 1) != 0) { + mbedtls_ct_condition_t is_x_non_zero = mbedtls_mpi_core_check_zero_ct(X->p, X->n); + X->s = mbedtls_ct_mpi_sign_if(is_x_non_zero, -1, 1); + + MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(X, N, X)); + } + +cleanup: + + mbedtls_mpi_zeroize_and_free(T, T_limbs); + + if (prec_RR == NULL || prec_RR->p == NULL) { + mbedtls_mpi_free(&RR); + } + + return ret; +} + +/* + * Greatest common divisor: G = gcd(A, B) (HAC 14.54) + */ +int mbedtls_mpi_gcd(mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + size_t lz, lzt; + mbedtls_mpi TA, TB; + + mbedtls_mpi_init(&TA); mbedtls_mpi_init(&TB); + + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TA, A)); + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TB, B)); + + lz = mbedtls_mpi_lsb(&TA); + lzt = mbedtls_mpi_lsb(&TB); + + /* The loop below gives the correct result when A==0 but not when B==0. + * So have a special case for B==0. Leverage the fact that we just + * calculated the lsb and lsb(B)==0 iff B is odd or 0 to make the test + * slightly more efficient than cmp_int(). */ + if (lzt == 0 && mbedtls_mpi_get_bit(&TB, 0) == 0) { + ret = mbedtls_mpi_copy(G, A); + goto cleanup; + } + + if (lzt < lz) { + lz = lzt; + } + + TA.s = TB.s = 1; + + /* We mostly follow the procedure described in HAC 14.54, but with some + * minor differences: + * - Sequences of multiplications or divisions by 2 are grouped into a + * single shift operation. + * - The procedure in HAC assumes that 0 < TB <= TA. + * - The condition TB <= TA is not actually necessary for correctness. + * TA and TB have symmetric roles except for the loop termination + * condition, and the shifts at the beginning of the loop body + * remove any significance from the ordering of TA vs TB before + * the shifts. + * - If TA = 0, the loop goes through 0 iterations and the result is + * correctly TB. + * - The case TB = 0 was short-circuited above. + * + * For the correctness proof below, decompose the original values of + * A and B as + * A = sa * 2^a * A' with A'=0 or A' odd, and sa = +-1 + * B = sb * 2^b * B' with B'=0 or B' odd, and sb = +-1 + * Then gcd(A, B) = 2^{min(a,b)} * gcd(A',B'), + * and gcd(A',B') is odd or 0. + * + * At the beginning, we have TA = |A| and TB = |B| so gcd(A,B) = gcd(TA,TB). + * The code maintains the following invariant: + * gcd(A,B) = 2^k * gcd(TA,TB) for some k (I) + */ + + /* Proof that the loop terminates: + * At each iteration, either the right-shift by 1 is made on a nonzero + * value and the nonnegative integer bitlen(TA) + bitlen(TB) decreases + * by at least 1, or the right-shift by 1 is made on zero and then + * TA becomes 0 which ends the loop (TB cannot be 0 if it is right-shifted + * since in that case TB is calculated from TB-TA with the condition TB>TA). + */ + while (mbedtls_mpi_cmp_int(&TA, 0) != 0) { + /* Divisions by 2 preserve the invariant (I). */ + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TA, mbedtls_mpi_lsb(&TA))); + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TB, mbedtls_mpi_lsb(&TB))); + + /* Set either TA or TB to |TA-TB|/2. Since TA and TB are both odd, + * TA-TB is even so the division by 2 has an integer result. + * Invariant (I) is preserved since any odd divisor of both TA and TB + * also divides |TA-TB|/2, and any odd divisor of both TA and |TA-TB|/2 + * also divides TB, and any odd divisor of both TB and |TA-TB|/2 also + * divides TA. + */ + if (mbedtls_mpi_cmp_mpi(&TA, &TB) >= 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(&TA, &TA, &TB)); + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TA, 1)); + } else { + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_abs(&TB, &TB, &TA)); + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TB, 1)); + } + /* Note that one of TA or TB is still odd. */ + } + + /* By invariant (I), gcd(A,B) = 2^k * gcd(TA,TB) for some k. + * At the loop exit, TA = 0, so gcd(TA,TB) = TB. + * - If there was at least one loop iteration, then one of TA or TB is odd, + * and TA = 0, so TB is odd and gcd(TA,TB) = gcd(A',B'). In this case, + * lz = min(a,b) so gcd(A,B) = 2^lz * TB. + * - If there was no loop iteration, then A was 0, and gcd(A,B) = B. + * In this case, lz = 0 and B = TB so gcd(A,B) = B = 2^lz * TB as well. + */ + + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&TB, lz)); + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(G, &TB)); + +cleanup: + + mbedtls_mpi_free(&TA); mbedtls_mpi_free(&TB); + + return ret; +} + +/* + * Fill X with size bytes of random. + * The bytes returned from the RNG are used in a specific order which + * is suitable for deterministic ECDSA (see the specification of + * mbedtls_mpi_random() and the implementation in mbedtls_mpi_fill_random()). + */ +int mbedtls_mpi_fill_random(mbedtls_mpi *X, size_t size, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + const size_t limbs = CHARS_TO_LIMBS(size); + + /* Ensure that target MPI has exactly the necessary number of limbs */ + MBEDTLS_MPI_CHK(mbedtls_mpi_resize_clear(X, limbs)); + if (size == 0) { + return 0; + } + + ret = mbedtls_mpi_core_fill_random(X->p, X->n, size, f_rng, p_rng); + +cleanup: + return ret; +} + +int mbedtls_mpi_random(mbedtls_mpi *X, + mbedtls_mpi_sint min, + const mbedtls_mpi *N, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng) +{ + if (min < 0) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + if (mbedtls_mpi_cmp_int(N, min) <= 0) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + /* Ensure that target MPI has exactly the same number of limbs + * as the upper bound, even if the upper bound has leading zeros. + * This is necessary for mbedtls_mpi_core_random. */ + int ret = mbedtls_mpi_resize_clear(X, N->n); + if (ret != 0) { + return ret; + } + + return mbedtls_mpi_core_random(X->p, min, N->p, X->n, f_rng, p_rng); +} + +/* + * Modular inverse: X = A^-1 mod N (HAC 14.61 / 14.64) + */ +int mbedtls_mpi_inv_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2; + + if (mbedtls_mpi_cmp_int(N, 1) <= 0) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + mbedtls_mpi_init(&TA); mbedtls_mpi_init(&TU); mbedtls_mpi_init(&U1); mbedtls_mpi_init(&U2); + mbedtls_mpi_init(&G); mbedtls_mpi_init(&TB); mbedtls_mpi_init(&TV); + mbedtls_mpi_init(&V1); mbedtls_mpi_init(&V2); + + MBEDTLS_MPI_CHK(mbedtls_mpi_gcd(&G, A, N)); + + if (mbedtls_mpi_cmp_int(&G, 1) != 0) { + ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + goto cleanup; + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&TA, A, N)); + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TU, &TA)); + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TB, N)); + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&TV, N)); + + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&U1, 1)); + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&U2, 0)); + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&V1, 0)); + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&V2, 1)); + + do { + while ((TU.p[0] & 1) == 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TU, 1)); + + if ((U1.p[0] & 1) != 0 || (U2.p[0] & 1) != 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&U1, &U1, &TB)); + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&U2, &U2, &TA)); + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&U1, 1)); + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&U2, 1)); + } + + while ((TV.p[0] & 1) == 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&TV, 1)); + + if ((V1.p[0] & 1) != 0 || (V2.p[0] & 1) != 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&V1, &V1, &TB)); + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V2, &V2, &TA)); + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&V1, 1)); + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&V2, 1)); + } + + if (mbedtls_mpi_cmp_mpi(&TU, &TV) >= 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&TU, &TU, &TV)); + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&U1, &U1, &V1)); + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&U2, &U2, &V2)); + } else { + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&TV, &TV, &TU)); + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V1, &V1, &U1)); + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V2, &V2, &U2)); + } + } while (mbedtls_mpi_cmp_int(&TU, 0) != 0); + + while (mbedtls_mpi_cmp_int(&V1, 0) < 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&V1, &V1, N)); + } + + while (mbedtls_mpi_cmp_mpi(&V1, N) >= 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V1, &V1, N)); + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, &V1)); + +cleanup: + + mbedtls_mpi_free(&TA); mbedtls_mpi_free(&TU); mbedtls_mpi_free(&U1); mbedtls_mpi_free(&U2); + mbedtls_mpi_free(&G); mbedtls_mpi_free(&TB); mbedtls_mpi_free(&TV); + mbedtls_mpi_free(&V1); mbedtls_mpi_free(&V2); + + return ret; +} + +#if defined(MBEDTLS_GENPRIME) + +/* Gaps between primes, starting at 3. https://oeis.org/A001223 */ +static const unsigned char small_prime_gaps[] = { + 2, 2, 4, 2, 4, 2, 4, 6, + 2, 6, 4, 2, 4, 6, 6, 2, + 6, 4, 2, 6, 4, 6, 8, 4, + 2, 4, 2, 4, 14, 4, 6, 2, + 10, 2, 6, 6, 4, 6, 6, 2, + 10, 2, 4, 2, 12, 12, 4, 2, + 4, 6, 2, 10, 6, 6, 6, 2, + 6, 4, 2, 10, 14, 4, 2, 4, + 14, 6, 10, 2, 4, 6, 8, 6, + 6, 4, 6, 8, 4, 8, 10, 2, + 10, 2, 6, 4, 6, 8, 4, 2, + 4, 12, 8, 4, 8, 4, 6, 12, + 2, 18, 6, 10, 6, 6, 2, 6, + 10, 6, 6, 2, 6, 6, 4, 2, + 12, 10, 2, 4, 6, 6, 2, 12, + 4, 6, 8, 10, 8, 10, 8, 6, + 6, 4, 8, 6, 4, 8, 4, 14, + 10, 12, 2, 10, 2, 4, 2, 10, + 14, 4, 2, 4, 14, 4, 2, 4, + 20, 4, 8, 10, 8, 4, 6, 6, + 14, 4, 6, 6, 8, 6, /*reaches 997*/ + 0 /* the last entry is effectively unused */ +}; + +/* + * Small divisors test (X must be positive) + * + * Return values: + * 0: no small factor (possible prime, more tests needed) + * 1: certain prime + * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE: certain non-prime + * other negative: error + */ +static int mpi_check_small_factors(const mbedtls_mpi *X) +{ + int ret = 0; + size_t i; + mbedtls_mpi_uint r; + unsigned p = 3; /* The first odd prime */ + + if ((X->p[0] & 1) == 0) { + return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + } + + for (i = 0; i < sizeof(small_prime_gaps); p += small_prime_gaps[i], i++) { + MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, p)); + if (r == 0) { + if (mbedtls_mpi_cmp_int(X, p) == 0) { + return 1; + } else { + return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + } + } + } + +cleanup: + return ret; +} + +/* + * Miller-Rabin pseudo-primality test (HAC 4.24) + */ +static int mpi_miller_rabin(const mbedtls_mpi *X, size_t rounds, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng) +{ + int ret, count; + size_t i, j, k, s; + mbedtls_mpi W, R, T, A, RR; + + mbedtls_mpi_init(&W); mbedtls_mpi_init(&R); + mbedtls_mpi_init(&T); mbedtls_mpi_init(&A); + mbedtls_mpi_init(&RR); + + /* + * W = |X| - 1 + * R = W >> lsb( W ) + */ + MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(&W, X, 1)); + s = mbedtls_mpi_lsb(&W); + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&R, &W)); + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&R, s)); + + for (i = 0; i < rounds; i++) { + /* + * pick a random A, 1 < A < |X| - 1 + */ + count = 0; + do { + MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(&A, X->n * ciL, f_rng, p_rng)); + + j = mbedtls_mpi_bitlen(&A); + k = mbedtls_mpi_bitlen(&W); + if (j > k) { + A.p[A.n - 1] &= ((mbedtls_mpi_uint) 1 << (k - (A.n - 1) * biL - 1)) - 1; + } + + if (count++ > 30) { + ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + goto cleanup; + } + + } while (mbedtls_mpi_cmp_mpi(&A, &W) >= 0 || + mbedtls_mpi_cmp_int(&A, 1) <= 0); + + /* + * A = A^R mod |X| + */ + MBEDTLS_MPI_CHK(mbedtls_mpi_exp_mod(&A, &A, &R, X, &RR)); + + if (mbedtls_mpi_cmp_mpi(&A, &W) == 0 || + mbedtls_mpi_cmp_int(&A, 1) == 0) { + continue; + } + + j = 1; + while (j < s && mbedtls_mpi_cmp_mpi(&A, &W) != 0) { + /* + * A = A * A mod |X| + */ + MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(&T, &A, &A)); + MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&A, &T, X)); + + if (mbedtls_mpi_cmp_int(&A, 1) == 0) { + break; + } + + j++; + } + + /* + * not prime if A != |X| - 1 or A == 1 + */ + if (mbedtls_mpi_cmp_mpi(&A, &W) != 0 || + mbedtls_mpi_cmp_int(&A, 1) == 0) { + ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + break; + } + } + +cleanup: + mbedtls_mpi_free(&W); mbedtls_mpi_free(&R); + mbedtls_mpi_free(&T); mbedtls_mpi_free(&A); + mbedtls_mpi_free(&RR); + + return ret; +} + +/* + * Pseudo-primality test: small factors, then Miller-Rabin + */ +int mbedtls_mpi_is_prime_ext(const mbedtls_mpi *X, int rounds, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng) +{ + int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED; + mbedtls_mpi XX; + + XX.s = 1; + XX.n = X->n; + XX.p = X->p; + + if (mbedtls_mpi_cmp_int(&XX, 0) == 0 || + mbedtls_mpi_cmp_int(&XX, 1) == 0) { + return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + } + + if (mbedtls_mpi_cmp_int(&XX, 2) == 0) { + return 0; + } + + if ((ret = mpi_check_small_factors(&XX)) != 0) { + if (ret == 1) { + return 0; + } + + return ret; + } + + return mpi_miller_rabin(&XX, rounds, f_rng, p_rng); +} + +/* + * Prime number generation + * + * To generate an RSA key in a way recommended by FIPS 186-4, both primes must + * be either 1024 bits or 1536 bits long, and flags must contain + * MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR. + */ +int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags, + int (*f_rng)(void *, unsigned char *, size_t), + void *p_rng) +{ +#ifdef MBEDTLS_HAVE_INT64 +// ceil(2^63.5) +#define CEIL_MAXUINT_DIV_SQRT2 0xb504f333f9de6485ULL +#else +// ceil(2^31.5) +#define CEIL_MAXUINT_DIV_SQRT2 0xb504f334U +#endif + int ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; + size_t k, n; + int rounds; + mbedtls_mpi_uint r; + mbedtls_mpi Y; + + if (nbits < 3 || nbits > MBEDTLS_MPI_MAX_BITS) { + return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; + } + + mbedtls_mpi_init(&Y); + + n = BITS_TO_LIMBS(nbits); + + if ((flags & MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR) == 0) { + /* + * 2^-80 error probability, number of rounds chosen per HAC, table 4.4 + */ + rounds = ((nbits >= 1300) ? 2 : (nbits >= 850) ? 3 : + (nbits >= 650) ? 4 : (nbits >= 350) ? 8 : + (nbits >= 250) ? 12 : (nbits >= 150) ? 18 : 27); + } else { + /* + * 2^-100 error probability, number of rounds computed based on HAC, + * fact 4.48 + */ + rounds = ((nbits >= 1450) ? 4 : (nbits >= 1150) ? 5 : + (nbits >= 1000) ? 6 : (nbits >= 850) ? 7 : + (nbits >= 750) ? 8 : (nbits >= 500) ? 13 : + (nbits >= 250) ? 28 : (nbits >= 150) ? 40 : 51); + } + + while (1) { + MBEDTLS_MPI_CHK(mbedtls_mpi_fill_random(X, n * ciL, f_rng, p_rng)); + /* make sure generated number is at least (nbits-1)+0.5 bits (FIPS 186-4 §B.3.3 steps 4.4, 5.5) */ + if (X->p[n-1] < CEIL_MAXUINT_DIV_SQRT2) { + continue; + } + + k = n * biL; + if (k > nbits) { + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(X, k - nbits)); + } + X->p[0] |= 1; + + if ((flags & MBEDTLS_MPI_GEN_PRIME_FLAG_DH) == 0) { + ret = mbedtls_mpi_is_prime_ext(X, rounds, f_rng, p_rng); + + if (ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) { + goto cleanup; + } + } else { + /* + * A necessary condition for Y and X = 2Y + 1 to be prime + * is X = 2 mod 3 (which is equivalent to Y = 2 mod 3). + * Make sure it is satisfied, while keeping X = 3 mod 4 + */ + + X->p[0] |= 2; + + MBEDTLS_MPI_CHK(mbedtls_mpi_mod_int(&r, X, 3)); + if (r == 0) { + MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, X, 8)); + } else if (r == 1) { + MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, X, 4)); + } + + /* Set Y = (X-1) / 2, which is X / 2 because X is odd */ + MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Y, X)); + MBEDTLS_MPI_CHK(mbedtls_mpi_shift_r(&Y, 1)); + + while (1) { + /* + * First, check small factors for X and Y + * before doing Miller-Rabin on any of them + */ + if ((ret = mpi_check_small_factors(X)) == 0 && + (ret = mpi_check_small_factors(&Y)) == 0 && + (ret = mpi_miller_rabin(X, rounds, f_rng, p_rng)) + == 0 && + (ret = mpi_miller_rabin(&Y, rounds, f_rng, p_rng)) + == 0) { + goto cleanup; + } + + if (ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) { + goto cleanup; + } + + /* + * Next candidates. We want to preserve Y = (X-1) / 2 and + * Y = 1 mod 2 and Y = 2 mod 3 (eq X = 3 mod 4 and X = 2 mod 3) + * so up Y by 6 and X by 12. + */ + MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, X, 12)); + MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(&Y, &Y, 6)); + } + } + } + +cleanup: + + mbedtls_mpi_free(&Y); + + return ret; +} + +#endif /* MBEDTLS_GENPRIME */ + +#if defined(MBEDTLS_SELF_TEST) + +#define GCD_PAIR_COUNT 3 + +static const int gcd_pairs[GCD_PAIR_COUNT][3] = +{ + { 693, 609, 21 }, + { 1764, 868, 28 }, + { 768454923, 542167814, 1 } +}; + +/* + * Checkup routine + */ +int mbedtls_mpi_self_test(int verbose) +{ + int ret, i; + mbedtls_mpi A, E, N, X, Y, U, V; + + mbedtls_mpi_init(&A); mbedtls_mpi_init(&E); mbedtls_mpi_init(&N); mbedtls_mpi_init(&X); + mbedtls_mpi_init(&Y); mbedtls_mpi_init(&U); mbedtls_mpi_init(&V); + + MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&A, 16, + "EFE021C2645FD1DC586E69184AF4A31E" \ + "D5F53E93B5F123FA41680867BA110131" \ + "944FE7952E2517337780CB0DB80E61AA" \ + "E7C8DDC6C5C6AADEB34EB38A2F40D5E6")); + + MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&E, 16, + "B2E7EFD37075B9F03FF989C7C5051C20" \ + "34D2A323810251127E7BF8625A4F49A5" \ + "F3E27F4DA8BD59C47D6DAABA4C8127BD" \ + "5B5C25763222FEFCCFC38B832366C29E")); + + MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&N, 16, + "0066A198186C18C10B2F5ED9B522752A" \ + "9830B69916E535C8F047518A889A43A5" \ + "94B6BED27A168D31D4A52F88925AA8F5")); + + MBEDTLS_MPI_CHK(mbedtls_mpi_mul_mpi(&X, &A, &N)); + + MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16, + "602AB7ECA597A3D6B56FF9829A5E8B85" \ + "9E857EA95A03512E2BAE7391688D264A" \ + "A5663B0341DB9CCFD2C4C5F421FEC814" \ + "8001B72E848A38CAE1C65F78E56ABDEF" \ + "E12D3C039B8A02D6BE593F0BBBDA56F1" \ + "ECF677152EF804370C1A305CAF3B5BF1" \ + "30879B56C61DE584A0F53A2447A51E")); + + if (verbose != 0) { + mbedtls_printf(" MPI test #1 (mul_mpi): "); + } + + if (mbedtls_mpi_cmp_mpi(&X, &U) != 0) { + if (verbose != 0) { + mbedtls_printf("failed\n"); + } + + ret = 1; + goto cleanup; + } + + if (verbose != 0) { + mbedtls_printf("passed\n"); + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_div_mpi(&X, &Y, &A, &N)); + + MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16, + "256567336059E52CAE22925474705F39A94")); + + MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&V, 16, + "6613F26162223DF488E9CD48CC132C7A" \ + "0AC93C701B001B092E4E5B9F73BCD27B" \ + "9EE50D0657C77F374E903CDFA4C642")); + + if (verbose != 0) { + mbedtls_printf(" MPI test #2 (div_mpi): "); + } + + if (mbedtls_mpi_cmp_mpi(&X, &U) != 0 || + mbedtls_mpi_cmp_mpi(&Y, &V) != 0) { + if (verbose != 0) { + mbedtls_printf("failed\n"); + } + + ret = 1; + goto cleanup; + } + + if (verbose != 0) { + mbedtls_printf("passed\n"); + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_exp_mod(&X, &A, &E, &N, NULL)); + + MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16, + "36E139AEA55215609D2816998ED020BB" \ + "BD96C37890F65171D948E9BC7CBAA4D9" \ + "325D24D6A3C12710F10A09FA08AB87")); + + if (verbose != 0) { + mbedtls_printf(" MPI test #3 (exp_mod): "); + } + + if (mbedtls_mpi_cmp_mpi(&X, &U) != 0) { + if (verbose != 0) { + mbedtls_printf("failed\n"); + } + + ret = 1; + goto cleanup; + } + + if (verbose != 0) { + mbedtls_printf("passed\n"); + } + + MBEDTLS_MPI_CHK(mbedtls_mpi_inv_mod(&X, &A, &N)); + + MBEDTLS_MPI_CHK(mbedtls_mpi_read_string(&U, 16, + "003A0AAEDD7E784FC07D8F9EC6E3BFD5" \ + "C3DBA76456363A10869622EAC2DD84EC" \ + "C5B8A74DAC4D09E03B5E0BE779F2DF61")); + + if (verbose != 0) { + mbedtls_printf(" MPI test #4 (inv_mod): "); + } + + if (mbedtls_mpi_cmp_mpi(&X, &U) != 0) { + if (verbose != 0) { + mbedtls_printf("failed\n"); + } + + ret = 1; + goto cleanup; + } + + if (verbose != 0) { + mbedtls_printf("passed\n"); + } + + if (verbose != 0) { + mbedtls_printf(" MPI test #5 (simple gcd): "); + } + + for (i = 0; i < GCD_PAIR_COUNT; i++) { + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&X, gcd_pairs[i][0])); + MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&Y, gcd_pairs[i][1])); + + MBEDTLS_MPI_CHK(mbedtls_mpi_gcd(&A, &X, &Y)); + + if (mbedtls_mpi_cmp_int(&A, gcd_pairs[i][2]) != 0) { + if (verbose != 0) { + mbedtls_printf("failed at %d\n", i); + } + + ret = 1; + goto cleanup; + } + } + + if (verbose != 0) { + mbedtls_printf("passed\n"); + } + +cleanup: + + if (ret != 0 && verbose != 0) { + mbedtls_printf("Unexpected error, return code = %08X\n", (unsigned int) ret); + } + + mbedtls_mpi_free(&A); mbedtls_mpi_free(&E); mbedtls_mpi_free(&N); mbedtls_mpi_free(&X); + mbedtls_mpi_free(&Y); mbedtls_mpi_free(&U); mbedtls_mpi_free(&V); + + if (verbose != 0) { + mbedtls_printf("\n"); + } + + return ret; +} + +#endif /* MBEDTLS_SELF_TEST */ + +#endif /* MBEDTLS_BIGNUM_C */ |