/*-*- mode:c;indent-tabs-mode:nil;c-basic-offset:4;tab-width:4;coding:utf-8 -*-│ │vi: set net ft=c ts=2 sts=2 sw=2 fenc=utf-8 :vi│ ╞══════════════════════════════════════════════════════════════════════════════╡ │ Copyright The Mbed TLS Contributors │ │ │ │ Licensed under the Apache License, Version 2.0 (the "License"); │ │ you may not use this file except in compliance with the License. │ │ You may obtain a copy of the License at │ │ │ │ http://www.apache.org/licenses/LICENSE-2.0 │ │ │ │ Unless required by applicable law or agreed to in writing, software │ │ distributed under the License is distributed on an "AS IS" BASIS, │ │ WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. │ │ See the License for the specific language governing permissions and │ │ limitations under the License. │ ╚─────────────────────────────────────────────────────────────────────────────*/ #include "libc/assert.h" #include "libc/bits/bits.h" #include "libc/bits/bswap.h" #include "libc/log/backtrace.internal.h" #include "libc/log/check.h" #include "libc/log/log.h" #include "libc/macros.internal.h" #include "libc/nexgen32e/bsf.h" #include "libc/nexgen32e/nexgen32e.h" #include "libc/nexgen32e/x86feature.h" #include "libc/runtime/runtime.h" #include "libc/stdio/stdio.h" #include "third_party/mbedtls/bignum.h" #include "third_party/mbedtls/bignum_internal.h" #include "third_party/mbedtls/chk.h" #include "third_party/mbedtls/common.h" #include "third_party/mbedtls/error.h" #include "third_party/mbedtls/fastdiv.h" #include "third_party/mbedtls/math.h" #include "third_party/mbedtls/platform.h" #include "third_party/mbedtls/profile.h" #include "third_party/mbedtls/select.h" #include "third_party/mbedtls/traceme.h" asm(".ident\t\"\\n\\n\ Mbed TLS (Apache 2.0)\\n\ Copyright ARM Limited\\n\ Copyright Mbed TLS Contributors\""); asm(".include \"libc/disclaimer.inc\""); /* clang-format off */ /** * @fileoverview Big Numbers. * * 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 */ #if defined(MBEDTLS_BIGNUM_C) #if __BYTE_ORDER__ == __ORDER_BIG_ENDIAN__ #define mpi_uint_bigendian_to_host(x) (x) #elif __SIZEOF_LONG__ == 8 #define mpi_uint_bigendian_to_host(x) __builtin_bswap64(x) #elif __SIZEOF_LONG__ == 4 #define mpi_uint_bigendian_to_host(x) __builtin_bswap32(x) #endif /* Get a specific byte, without range checks. */ #define GET_BYTE(X, i) (((X)->p[(i) / ciL] >> (((i) % ciL) * 8)) & 0xff) static inline void mbedtls_mpi_zeroize(mbedtls_mpi_uint *v, size_t n) { mbedtls_platform_zeroize(v, ciL * n); } /** * \brief This function frees the components of an MPI context. * * \param X The MPI context to be cleared. This may be \c NULL, * in which case this function is a no-op. If it is * not \c NULL, it must point to an initialized MPI. */ void mbedtls_mpi_free(mbedtls_mpi *X) { if (!X) return; if (X->p) { mbedtls_mpi_zeroize(X->p, X->n); mbedtls_free(X->p); } mbedtls_mpi_init(X); } /** * \brief Enlarge an MPI to the specified number of limbs. * * \note This function does nothing if the MPI is * already large enough. * * \param X The MPI to grow. It must be initialized. * \param nblimbs The target number of limbs. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs) { mbedtls_mpi_uint *p; MPI_VALIDATE_RET(X); if (nblimbs > MBEDTLS_MPI_MAX_LIMBS) return MBEDTLS_ERR_MPI_ALLOC_FAILED; if (nblimbs > X->n) { if (X->p && (p = realloc_in_place(X->p, nblimbs * ciL))) { mbedtls_mpi_zeroize(p + X->n, nblimbs - X->n); } else { if (!(p = malloc(nblimbs * ciL))) return MBEDTLS_ERR_MPI_ALLOC_FAILED; if (X->p) { memcpy(p, X->p, X->n * ciL); mbedtls_mpi_zeroize(p + X->n, nblimbs - X->n); mbedtls_mpi_zeroize(X->p, X->n); free(X->p); } else { mbedtls_mpi_zeroize(p, nblimbs); } } X->n = nblimbs; X->p = p; } return 0; } /** * \brief This function resizes an MPI to a number of limbs. * * \param X The MPI to resize. This must point to an initialized MPI. * \param n The minimum number of limbs to keep. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed * which can only happen when resizing up * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_resize(mbedtls_mpi *X, size_t n) { mbedtls_mpi_uint *p; MPI_VALIDATE_RET(X); if (X->n == n) return 0; if (X->n <= n) return mbedtls_mpi_grow(X, n); if (n > MBEDTLS_MPI_MAX_LIMBS) return MBEDTLS_ERR_MPI_ALLOC_FAILED; mbedtls_mpi_zeroize(X->p + n, X->n - n); if (!realloc_in_place(X->p, n * ciL)) { if (!(p = malloc(n * ciL))) return MBEDTLS_ERR_MPI_ALLOC_FAILED; memcpy(p, X->p, n * ciL); mbedtls_mpi_zeroize(X->p, n); free(X->p); X->p = p; } X->n = n; return 0; } /** * \brief This function resizes an MPI downwards, keeping at * least the specified number of limbs. * * If \c X is smaller than \c nblimbs, it is resized up * instead. * * \param X The MPI to shrink. This must point to an initialized MPI. * \param nblimbs The minimum number of limbs to keep. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed * which can only happen when resizing up * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs) { MPI_VALIDATE_RET(X); if (X->n <= nblimbs) return mbedtls_mpi_grow(X, nblimbs); return mbedtls_mpi_resize(X, MAX(MAX(1, nblimbs), mbedtls_mpi_limbs(X))); } /** * \brief Make a copy of an MPI. * * \param X The destination MPI. This must point to an initialized MPI. * \param Y The source MPI. This must point to an initialized MPI. * * \note The limb-buffer in the destination MPI is enlarged * if necessary to hold the value in the source MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y) { int ret = 0; size_t i; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(Y); if (X == Y) return 0; if (!Y->n) { mbedtls_mpi_free(X); return 0; } i = MAX(1, mbedtls_mpi_limbs(Y)); X->s = Y->s; if (X->n < i) MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, i)); else mbedtls_mpi_zeroize(X->p + i, X->n - i); memcpy(X->p, Y->p, i * ciL); cleanup: return ret; } /** * \brief Swap the contents of two MPIs. * * \param X The first MPI. It must be initialized. * \param Y The second MPI. It must be initialized. */ void mbedtls_mpi_swap(mbedtls_mpi *X, mbedtls_mpi *Y) { mbedtls_mpi T; MPI_VALIDATE(X); MPI_VALIDATE(Y); memcpy(&T, X, sizeof(mbedtls_mpi)); memcpy(X, Y, sizeof(mbedtls_mpi)); memcpy(Y, &T, sizeof(mbedtls_mpi)); } /** * \brief Perform a safe conditional copy of MPI which doesn't * reveal whether the condition was true or not. * * \param X The MPI to conditionally assign to. This must point * to an initialized MPI. * \param Y The MPI to be assigned from. This must point to an * initialized MPI. * \param assign The condition deciding whether to perform the * assignment or not. Possible values: * * \c 1: Perform the assignment `X = Y`. * * \c 0: Keep the original value of \p X. * * \note This function is equivalent to * `if( assign ) mbedtls_mpi_copy( X, Y );` * except that it avoids leaking any information about whether * the assignment was done or not (the above code may leak * information through branch prediction and/or memory access * patterns analysis). * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign) { int ret = 0; size_t i; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(Y); /* make sure assign is 0 or 1 in a time-constant manner */ if (Y->n > X->n) MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n)); assign = (assign | (unsigned char)-assign) >> 7; X->s = Select(Y->s, X->s, -assign); for (i = 0; i < Y->n; i++) X->p[i] = Select(Y->p[i], X->p[i], -assign); for (i = Y->n; i < X->n; i++) X->p[i] &= CONCEAL("r", assign - 1); cleanup: return ret; } /** * \brief Perform a safe conditional swap which doesn't * reveal whether the condition was true or not. * * \param X The first MPI. This must be initialized. * \param Y The second MPI. This must be initialized. * \param assign The condition deciding whether to perform * the swap or not. Possible values: * * \c 1: Swap the values of \p X and \p Y. * * \c 0: Keep the original values of \p X and \p Y. * * \note This function is equivalent to * if( assign ) mbedtls_mpi_swap( X, Y ); * except that it avoids leaking any information about whether * the assignment was done or not (the above code may leak * information through branch prediction and/or memory access * patterns analysis). * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. * */ int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap) { int ret, s; size_t i; mbedtls_mpi_uint tmp; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(Y); if (X == Y) return (0); /* make sure swap is 0 or 1 in a time-constant manner */ swap = (swap | (unsigned char)-swap) >> 7; MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, Y->n)); MBEDTLS_MPI_CHK(mbedtls_mpi_grow(Y, X->n)); s = X->s; X->s = X->s * (1 - swap) + Y->s * swap; Y->s = Y->s * (1 - swap) + s * swap; for (i = 0; i < X->n; i++) { tmp = X->p[i]; X->p[i] = X->p[i] * (1 - swap) + Y->p[i] * swap; Y->p[i] = Y->p[i] * (1 - swap) + tmp * swap; } cleanup: return ret; } /** * \brief Store integer value in MPI. * * \param X The MPI to set. This must be initialized. * \param z The value to use. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. */ int mbedtls_mpi_lset(mbedtls_mpi *X, mbedtls_mpi_sint z) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; MPI_VALIDATE_RET(X); MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, 1)); mbedtls_mpi_zeroize(X->p, X->n); X->p[0] = (z < 0) ? -z : z; X->s = (z < 0) ? -1 : 1; cleanup: return ret; } /** * \brief Get a specific bit from an MPI. * * \param X The MPI to query. This must be initialized. * \param pos Zero-based index of the bit to query. * * \return \c 0 or \c 1 on success, depending on whether bit \c pos * of \c X is unset or set. * \return A negative error code on failure. */ int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos) { MPI_VALIDATE_RET(X); if (X->n * biL <= pos) return 0; return ((X->p[pos / biL] >> (pos % biL)) & 0x01); } /** * \brief Modify a specific bit in an MPI. * * \note This function will grow the target MPI if necessary to set a * bit to \c 1 in a not yet existing limb. It will not grow if * the bit should be set to \c 0. * * \param X The MPI to modify. This must be initialized. * \param pos Zero-based index of the bit to modify. * \param val The desired value of bit \c pos: \c 0 or \c 1. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on other kinds of failure. */ 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; MPI_VALIDATE_RET(X); if (val && val != 1) return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; if (X->n * biL <= pos) { if (!val) 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; } /** * \brief Return the number of bits of value \c 0 before the * least significant bit of value \c 1. * * \note This is the same as the zero-based index of * the least significant bit of value \c 1. * * \param X The MPI to query. * * \return The number of bits of value \c 0 before the least significant * bit of value \c 1 in \p X. */ size_t mbedtls_mpi_lsb(const mbedtls_mpi *X) { size_t i, j, count = 0; MBEDTLS_INTERNAL_VALIDATE_RET(X, 0); for (i = 0; i < X->n; i++) { if (X->p[i]) return count + __builtin_ctzll(X->p[i]); else count += biL; } return 0; } /* * Count leading zero bits in a given integer */ static inline size_t mbedtls_clz(const mbedtls_mpi_uint x) { return x ? __builtin_clzll(x) : biL; } /** * \brief Return the number of bits up to and including the most * significant bit of value \c 1. * * \note This is same as the one-based index of the most * significant bit of value \c 1. * * \param X The MPI to query. This must point to an initialized MPI. * * \return The number of bits up to and including the most * significant bit of value \c 1. */ size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X) { size_t n; n = mbedtls_mpi_limbs(X); if (!n) return 0; return biL - __builtin_clzll(X->p[n - 1]) + (n - 1) * biL; } /** * \brief Return the total size of an MPI value in bytes. * * \param X The MPI to use. This must point to an initialized MPI. * * \note The value returned by this function may be less than * the number of bytes used to store \p X internally. * This happens if and only if there are trailing bytes * of value zero. * * \return The least number of bytes capable of storing * the absolute value of \p X. */ 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; } /** * \brief Import an MPI from an ASCII string. * * \param X The destination MPI. This must point to an initialized MPI. * \param radix The numeric base of the input string. * \param s Null-terminated string buffer. * * \return \c 0 if successful. * \return A negative error code on failure. */ int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; size_t i, j, slen, n; mbedtls_mpi_uint d; mbedtls_mpi T; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(s); if (radix < 2 || radix > 16) return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; mbedtls_mpi_init(&T); slen = strlen(s); if (radix == 16) { if (slen > MPI_SIZE_T_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++) { if (i == 1 && s[i - 1] == '-') { X->s = -1; break; } 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++) { if (!i && s[i] == '-') { X->s = -1; continue; } MBEDTLS_MPI_CHK(mpi_get_digit(&d, radix, s[i])); MBEDTLS_MPI_CHK(mbedtls_mpi_mul_int(&T, X, radix)); if (X->s == 1) MBEDTLS_MPI_CHK(mbedtls_mpi_add_int(X, &T, d)); else MBEDTLS_MPI_CHK(mbedtls_mpi_sub_int(X, &T, d)); } } 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_THIS_CORRUPTION; 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_is_zero(X)); memmove(*p, p_end, length); *p += length; cleanup: return ret; } /** * \brief Export an MPI to an ASCII string. * * \param X The source MPI. This must point to an initialized MPI. * \param radix The numeric base of the output string. * \param buf The buffer to write the string to. This must be writable * buffer of length \p buflen Bytes. * \param buflen The available size in Bytes of \p buf. * \param olen The address at which to store the length of the string * written, including the final \c NULL byte. This must * not be \c NULL. * * \note You can call this function with `buflen == 0` to obtain the * minimum required buffer size in `*olen`. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer \p buf * is too small to hold the value of \p X in the desired base. * In this case, `*olen` is nonetheless updated to contain the * size of \p buf required for a successful call. * \return Another negative error code on different kinds of failure. */ 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; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(olen); MPI_VALIDATE_RET(!buflen || buf); 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 && !k && (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 = p - buf; cleanup: mbedtls_mpi_free(&T); return ret; } /** * \brief Read an MPI from a line in an opened file. * * \param X The destination MPI. This must point to an initialized MPI. * \param radix The numeric base of the string representation used * in the source line. * \param fin The input file handle to use. This must not be \c NULL. * * \note On success, this function advances the file stream * to the end of the current line or to EOF. * * The function returns \c 0 on an empty line. * * Leading whitespaces are ignored, as is a * '0x' prefix for radix \c 16. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer * is too small. * \return Another negative error code on failure. */ 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]; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(fin); if (radix < 2 || radix > 16) return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; mbedtls_platform_zeroize(s, sizeof(s)); if (!fgets(s, sizeof(s) - 1, fin)) 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)) break; return mbedtls_mpi_read_string(X, radix, p + 1); } /** * \brief Export an MPI into an opened file. * * \param p A string prefix to emit prior to the MPI data. * For example, this might be a label, or "0x" when * printing in base \c 16. This may be \c NULL if no prefix * is needed. * \param X The source MPI. This must point to an initialized MPI. * \param radix The numeric base to be used in the emitted string. * \param fout The output file handle. This may be \c NULL, in which case * the output is written to \c stdout. * * \return \c 0 if successful. * \return A negative error code on failure. */ int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X, int radix, FILE *fout) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; 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]; MPI_VALIDATE_RET(X); if (radix < 2 || radix > 16) return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; mbedtls_platform_zeroize(s, sizeof(s)); MBEDTLS_MPI_CHK(mbedtls_mpi_write_string(X, radix, s, sizeof(s) - 2, &n)); if (!p) p = ""; plen = strlen(p); slen = strlen(s); s[slen++] = '\r'; s[slen++] = '\n'; if (fout) { 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; } static void mpi_bigendian_to_host(mbedtls_mpi_uint *const p, size_t limbs) { mbedtls_mpi_uint *cur_limb_left; mbedtls_mpi_uint *cur_limb_right; if (!limbs) return; /* * Traverse limbs and * - adapt byte-order in each limb * - swap the limbs themselves. * For that, simultaneously traverse the limbs from left to right * and from right to left, as long as the left index is not bigger * than the right index (it's not a problem if limbs is odd and the * indices coincide in the last iteration). */ for (cur_limb_left = p, cur_limb_right = p + (limbs - 1); cur_limb_left <= cur_limb_right; cur_limb_left++, cur_limb_right--) { mbedtls_mpi_uint tmp; /* Note that if cur_limb_left == cur_limb_right, * this code effectively swaps the bytes only once. */ tmp = mpi_uint_bigendian_to_host(*cur_limb_left); *cur_limb_left = mpi_uint_bigendian_to_host(*cur_limb_right); *cur_limb_right = tmp; } } /** * \brief Import X from unsigned binary data, little endian * * \param X The destination MPI. This must point to an initialized MPI. * \param p The input buffer with \p n bytes. * \param n The length of the input buffer \p p in Bytes. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_read_binary_le(mbedtls_mpi *X, const unsigned char *p, size_t n) { int ret; size_t i; mbedtls_mpi_uint w; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(!n || p); if ((ret = mbedtls_mpi_resize(X, MAX(1, CHARS_TO_LIMBS(n))))) return ret; if (n) { for (i = 0; i + 8 <= n; i += 8) X->p[i / ciL] = READ64LE(p + i); if (i < n) { w = 0; do { w <<= 8; w |= p[i]; } while (++i < n); X->p[i / ciL] = w; } } else { X->p[0] = 0; } X->s = 1; return 0; } /** * \brief Import an MPI from unsigned big endian binary data. * * \param X The destination MPI. This must point to an initialized MPI. * \param p The input buffer. This must be a readable buffer of length * \p n Bytes. * \param n The length of the input buffer \p p in Bytes. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *p, size_t n) { int ret; size_t i, j, k; mbedtls_mpi_uint w; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(!n || p); if ((ret = mbedtls_mpi_resize(X, MAX(1, CHARS_TO_LIMBS(n))))) return ret; if (n) { for (j = 0, i = n; i >= 8; i -= 8) X->p[j++] = READ64BE(p + i - ciL); if (i) { k = 0; w = 0; do { --i; w <<= 8; w |= p[k++]; } while (i); X->p[j] = w; } } else { X->p[0] = 0; } X->s = 1; return 0; } /** * \brief Export X into unsigned binary data, little endian. * Always fills the whole buffer, which will end with zeros * if the number is smaller. * * \param X The source MPI. This must point to an initialized MPI. * \param buf The output buffer. This must be a writable buffer of length * \p buflen Bytes. * \param buflen The size of the output buffer \p buf in Bytes. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't * large enough to hold the value of \p X. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_write_binary_le(const mbedtls_mpi *X, unsigned char *buf, size_t buflen) { size_t stored_bytes = X->n * ciL; size_t bytes_to_copy; size_t i; if (stored_bytes < buflen) { bytes_to_copy = stored_bytes; } else { bytes_to_copy = buflen; /* The output buffer is smaller than the allocated size of X. * However X may fit if its leading bytes are zero. */ for (i = bytes_to_copy; i < stored_bytes; i++) { if (GET_BYTE(X, i)) return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL; } } for (i = 0; i < bytes_to_copy; i++) buf[i] = GET_BYTE(X, i); if (stored_bytes < buflen) { /* Write trailing 0 bytes */ mbedtls_platform_zeroize(buf + stored_bytes, buflen - stored_bytes); } return 0; } /** * \brief Export X into unsigned binary data, big endian. * Always fills the whole buffer, which will start with zeros * if the number is smaller. * * \param X The source MPI. This must point to an initialized MPI. * \param buf The output buffer. This must be a writable buffer of length * \p buflen Bytes. * \param buflen The size of the output buffer \p buf in Bytes. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't * large enough to hold the value of \p X. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_write_binary(const mbedtls_mpi *X, unsigned char *buf, size_t buflen) { size_t stored_bytes; size_t bytes_to_copy; unsigned char *p; size_t i; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(!buflen || buf); stored_bytes = X->n * ciL; if (stored_bytes < buflen) { /* There is enough space in the output buffer. Write initial * null bytes and record the position at which to start * writing the significant bytes. In this case, the execution * trace of this function does not depend on the value of the * number. */ bytes_to_copy = stored_bytes; p = buf + buflen - stored_bytes; mbedtls_platform_zeroize(buf, buflen - stored_bytes); } else { /* The output buffer is smaller than the allocated size of X. * However X may fit if its leading bytes are zero. */ bytes_to_copy = buflen; p = buf; for (i = bytes_to_copy; i < stored_bytes; i++) { if (GET_BYTE(X, i)) return MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL; } } for (i = 0; i < bytes_to_copy; i++) p[bytes_to_copy - i - 1] = GET_BYTE(X, i); return 0; } static int mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t *Xn, size_t *Yn) { size_t i, j; i = mbedtls_mpi_limbs(X); j = mbedtls_mpi_limbs(Y); *Xn = i; *Yn = j; if (!i && !j) return 0; 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; } /** * \brief Compare the absolute values of two MPIs. * * \param X The left-hand MPI. This must point to an initialized MPI. * \param Y The right-hand MPI. This must point to an initialized MPI. * * \return \c 1 if `|X|` is greater than `|Y|`. * \return \c -1 if `|X|` is lesser than `|Y|`. * \return \c 0 if `|X|` is equal to `|Y|`. */ int mbedtls_mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y) { size_t i, j; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(Y); return mpi_cmp_abs(X, Y, &i, &j); } static int mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t *Xn, size_t *Yn) { size_t i, j; i = mbedtls_mpi_limbs(X); j = mbedtls_mpi_limbs(Y); *Xn = i; *Yn = j; if (!i && !j) 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; } /** * \brief Compare two MPIs. * * \param X The left-hand MPI. This must point to an initialized MPI. * \param Y The right-hand MPI. This must point to an initialized MPI. * * \return \c 1 if \p X is greater than \p Y. * \return \c -1 if \p X is lesser than \p Y. * \return \c 0 if \p X is equal to \p Y. */ int mbedtls_mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y) { size_t i, j; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(Y); return mpi_cmp_mpi(X, Y, &i, &j); } /** * Decide if an integer is less than the other, without branches. * * \param x First integer. * \param y Second integer. * * \return 1 if \p x is less than \p y, 0 otherwise */ static unsigned ct_lt_mpi_uint(const mbedtls_mpi_uint x, const mbedtls_mpi_uint y) { mbedtls_mpi_uint ret; mbedtls_mpi_uint cond; /* * Check if the most significant bits (MSB) of the operands are different. */ cond = (x ^ y); /* * If the MSB are the same then the difference x-y will be negative (and * have its MSB set to 1 during conversion to unsigned) if and only if x> (biL - 1); return (unsigned)ret; } /** * \brief Check if an MPI is less than the other in constant time. * * \param X The left-hand MPI. This must point to an initialized MPI * with the same allocated length as Y. * \param Y The right-hand MPI. This must point to an initialized MPI * with the same allocated length as X. * \param ret The result of the comparison: * \c 1 if \p X is less than \p Y. * \c 0 if \p X is greater than or equal to \p Y. * * \return 0 on success. * \return MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of * the two input MPIs is not the same. */ int mbedtls_mpi_lt_mpi_ct(const mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned *ret) { size_t i; /* The value of any of these variables is either 0 or 1 at all times. */ unsigned cond, done, X_is_negative, Y_is_negative; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(Y); MPI_VALIDATE_RET(ret); if (X->n != Y->n) return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; /* * Set sign_N to 1 if N >= 0, 0 if N < 0. * We know that N->s == 1 if N >= 0 and N->s == -1 if N < 0. */ X_is_negative = (X->s & 2) >> 1; Y_is_negative = (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). */ cond = (X_is_negative ^ Y_is_negative); *ret = cond & X_is_negative; /* * This is a constant-time function. We might have the result, but we still * need to go through the loop. Record if we have the result already. */ done = cond; for (i = X->n; i > 0; i--) { /* * If Y->p[i - 1] < X->p[i - 1] then X < Y is true if and only if both * X and Y are negative. * * Again even if we can make a decision, we just mark the result and * the fact that we are done and continue looping. */ cond = ct_lt_mpi_uint(Y->p[i - 1], X->p[i - 1]); *ret |= cond & (1 - done) & X_is_negative; done |= cond; /* * If X->p[i - 1] < Y->p[i - 1] then X < Y is true if and only if both * X and Y are positive. * * Again even if we can make a decision, we just mark the result and * the fact that we are done and continue looping. */ cond = ct_lt_mpi_uint(X->p[i - 1], Y->p[i - 1]); *ret |= cond & (1 - done) & (1 - X_is_negative); done |= cond; } return 0; } /** * \brief Compare an MPI with an integer. * * \param X The left-hand MPI. This must point to an initialized MPI. * \param z The integer value to compare \p X to. * * \return \c 1 if \p X is greater than \p z. * \return \c -1 if \p X is lesser than \p z. * \return \c 0 if \p X is equal to \p z. */ int mbedtls_mpi_cmp_int(const mbedtls_mpi *X, mbedtls_mpi_sint z) { mbedtls_mpi Y; mbedtls_mpi_uint p[1]; MPI_VALIDATE_RET(X); *p = (z < 0) ? -z : z; Y.s = (z < 0) ? -1 : 1; Y.n = 1; Y.p = p; return mbedtls_mpi_cmp_mpi(X, &Y); } forceinline mbedtls_mpi_uint mpi_add_hlp(mbedtls_mpi_uint *d, const mbedtls_mpi_uint *b, size_t n) { size_t i; unsigned char cf; mbedtls_mpi_uint c, t, *e; e = d + n; c = i = 0; #ifdef __x86_64__ for (; d + 4 <= e; d += 4, b += 4, c = cf) { asm("add\t%5,%1\n\t" "adc\t%6,%2\n\t" "adc\t%7,%3\n\t" "adc\t%8,%4" : "=@ccc"(cf), "+m"(d[0]), "+m"(d[1]), "+m"(d[2]), "+m"(d[3]) : "r"(b[0] + c), "r"(b[1]), "r"(b[2]), "r"(b[3]) : "cc"); } #endif for (; d < e; ++d, ++b) ADC(*d, *d, *b, c, c); return c; } /** * Helper for mbedtls_mpi subtraction. * * Calculate d = a - b where d, a, and b have the same size. * This function operates modulo (2^ciL)^n and returns the carry * (1 if there was a wraparound, i.e. if `a < b`, and 0 otherwise). * * \param[out] d Result of subtraction. * \param[in] a Left operand. * \param[in] b Right operand. * \param n Number of limbs of \p a and \p b. * \return 1 if `d < s`. * 0 if `d >= s`. */ forceinline mbedtls_mpi_uint mpi_sub_hlp(mbedtls_mpi_uint *d, const mbedtls_mpi_uint *a, const mbedtls_mpi_uint *b, size_t n) { size_t i; unsigned char cf; uint64_t q, r, s, t; mbedtls_mpi_uint c, z, x, y; cf = c = i = 0; #ifdef __x86_64__ for (; i + 4 <= n; i += 4, c = cf) { q = a[i + 0]; r = a[i + 1]; s = a[i + 2]; t = a[i + 3]; asm volatile("sub\t%5,%1\n\t" "sbb\t1*8(%6),%2\n\t" "sbb\t2*8(%6),%3\n\t" "sbb\t3*8(%6),%4" : "=@ccc"(cf), "+r"(q), "+r"(r), "+r"(s), "+r"(t) : "r"(b[i] + c), "r"(b + i) : "memory", "cc"); d[i + 0] = q; d[i + 1] = r; d[i + 2] = s; d[i + 3] = t; } #endif for (; i < n; ++i) SBB(d[i], a[i], b[i], c, c); return c; } /** * \brief Perform an unsigned addition of MPIs: X = |A| + |B| * * \param X The destination MPI. This must point to an initialized MPI. * \param A The first summand. This must point to an initialized MPI. * \param B The second summand. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_add_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; size_t i, j; unsigned char cf; const mbedtls_mpi *T; mbedtls_mpi_uint c, tmp; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(A); MPI_VALIDATE_RET(B); if (X == B) T = A, A = X, B = T; if (X != A) MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, A)); X->s = 1; /* always positive b/c unsigned addition */ j = mbedtls_mpi_limbs(B); MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, j)); c = mpi_add_hlp(X->p, B->p, j); for (; c; ++j) { if (j >= X->n) MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, j + 1)); X->p[j] += c; c = X->p[j] < c; } cleanup: return ret; } static int mpi_sub_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B, size_t Bn) { int ret; size_t n, m; unsigned char cf; n = Bn; if (n > A->n) return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; /* B >= (2^ciL)^n > A */ if (X != A) { if (X->n < A->n) { if ((ret = mbedtls_mpi_grow(X, A->n))) return ret; } else if (X->n > A->n) { mbedtls_mpi_zeroize(X->p + A->n, X->n - A->n); } if ((m = A->n - n)) memcpy(X->p + n, A->p + n, m * ciL); } /* * X should always be positive as a result of unsigned subtractions. */ X->s = 1; cf = mpi_sub_hlp(X->p, A->p, B->p, n); if (cf) { /* Propagate the carry to the first nonzero limb of X. */ for (; n < A->n && !A->p[n]; n++) { /* --X->p[n]; */ X->p[n] = A->p[n] - 1; } /* If we ran out of space for the carry, it means that the result * is negative. */ if (n == X->n) return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; --X->p[n]; } return 0; } /** * \brief Perform an unsigned subtraction of MPIs: X = |A| - |B| * * \param X The destination MPI. This must point to an initialized MPI. * \param A The minuend. This must point to an initialized MPI. * \param B The subtrahend. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is greater than \p A. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_sub_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) { size_t n, m; unsigned char cf; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(A); MPI_VALIDATE_RET(B); if (X != A && !B->n) return mbedtls_mpi_copy(X, A); /* wut */ return mpi_sub_abs(X, A, B, mbedtls_mpi_limbs(B)); } /** * \brief Perform a signed addition of MPIs: X = A + B * * \param X The destination MPI. This must point to an initialized MPI. * \param A The first summand. This must point to an initialized MPI. * \param B The second summand. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_add_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) { int ret, s; size_t i, j; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(A); MPI_VALIDATE_RET(B); s = A->s; if (A->s * B->s < 0) { if (mpi_cmp_abs(A, B, &i, &j) >= 0) { MBEDTLS_MPI_CHK(mpi_sub_abs(X, A, B, j)); X->s = s; } else { MBEDTLS_MPI_CHK(mpi_sub_abs(X, B, A, i)); X->s = -s; } } else { MBEDTLS_MPI_CHK(mbedtls_mpi_add_abs(X, A, B)); X->s = s; } cleanup: return ret; } /** * \brief Perform a signed subtraction of MPIs: X = A - B * * \param X The destination MPI. This must point to an initialized MPI. * \param A The minuend. This must point to an initialized MPI. * \param B The subtrahend. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_sub_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) { int ret, s; size_t i, j; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(A); MPI_VALIDATE_RET(B); s = A->s; if (A->s * B->s > 0) { if (mpi_cmp_abs(A, B, &i, &j) >= 0) { MBEDTLS_MPI_CHK(mpi_sub_abs(X, A, B, j)); X->s = s; } else { MBEDTLS_MPI_CHK(mpi_sub_abs(X, B, A, i)); X->s = -s; } } else { MBEDTLS_MPI_CHK(mbedtls_mpi_add_abs(X, A, B)); X->s = s; } cleanup: return ret; } /** * \brief Performs signed addition of MPI and integer: X = A + b * * \param X The destination MPI. This must point to an initialized MPI. * \param A The first summand. This must point to an initialized MPI. * \param b The second summand. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a allocation failed. * \return Another negative error code on different kinds of * failure. */ int mbedtls_mpi_add_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b) { mbedtls_mpi _B; mbedtls_mpi_uint p[1]; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(A); p[0] = (b < 0) ? -b : b; _B.s = (b < 0) ? -1 : 1; _B.n = 1; _B.p = p; return mbedtls_mpi_add_mpi(X, A, &_B); } /** * \brief Perform a signed subtraction of an MPI and an integer: * X = A - b * * \param X The destination MPI. This must point to an initialized MPI. * \param A The minuend. This must point to an initialized MPI. * \param b The subtrahend. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_sub_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b) { mbedtls_mpi _B; mbedtls_mpi_uint p[1]; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(A); p[0] = (b < 0) ? -b : b; _B.s = (b < 0) ? -1 : 1; _B.n = 1; _B.p = p; return mbedtls_mpi_sub_mpi(X, A, &_B); } /* * Unsigned integer divide - double mbedtls_mpi_uint dividend, u1/u0, and * mbedtls_mpi_uint divisor, d */ static inline mbedtls_mpi_uint mbedtls_int_div_int(mbedtls_mpi_uint u1, mbedtls_mpi_uint u0, mbedtls_mpi_uint d, mbedtls_mpi_uint *r) { if (d && u1 < d) { #ifdef __x86_64__ mbedtls_mpi_uint quo, rem; asm("div\t%2" : "=a"(quo), "=d"(rem) : "r"(d), "0"(u0), "1"(u1) : "cc"); if (r) *r = rem; return quo; #elif defined(MBEDTLS_HAVE_UDBL) mbedtls_t_udbl dividend, quotient; 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) *r = (mbedtls_mpi_uint)(dividend - (quotient * d)); return (mbedtls_mpi_uint)quotient; #else size_t s; mbedtls_mpi_uint radix = (mbedtls_mpi_uint)1 << biH; 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; /* * 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_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) *r = (rAX * radix + u0_lsw - q0 * d) >> s; quotient = q1 * radix + q0; return quotient; #endif } else { if (r) *r = ~0; return ~0; } } static inline void Multiply2x1(uint64_t a[3], uint64_t b) { uint128_t x; uint64_t l, h; x = a[0]; x *= b; l = x; h = x >> 64; x = a[1]; x *= b; x += h + ((a[0] = l) < 0); l = x; h = x >> 64; a[2] = h + ((a[1] = l) < 0); } static inline bool GreaterThan3x3(uint64_t a[3], uint64_t b[3]) { if (a[2] > b[2]) return true; if (a[2] < b[2]) return false; if (a[1] > b[1]) return true; if (a[1] < b[1]) return false; return a[0] > b[0]; } /** * \brief Perform a division with remainder of two MPIs: * A = Q * B + R * * \param Q The destination MPI for the quotient. * This may be \c NULL if the value of the * quotient is not needed. * \param R The destination MPI for the remainder value. * This may be \c NULL if the value of the * remainder is not needed. * \param A The dividend. This must point to an initialized MPi. * \param B The divisor. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_div_mpi(mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; size_t i, n, t, k, Xn, Yn; mbedtls_mpi X, Y, Z, T1, T2; mbedtls_mpi_uint TP2[3]; MPI_VALIDATE_RET(A); MPI_VALIDATE_RET(B); if (mbedtls_mpi_is_zero(B)) 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) MBEDTLS_MPI_CHK(mbedtls_mpi_lset(Q, 0)); if (R) 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, 80)); /* we need left pad hard below */ 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 (mpi_cmp_abs(&X, &Y, &Xn, &Yn) >= 0) { Z.p[n - t]++; MBEDTLS_MPI_CHK(mpi_sub_abs(&X, &X, &Y, Yn)); } 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] = ~0; 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]--; T1.p[0] = (t < 1) ? 0 : Y.p[t - 1]; T1.p[1] = Y.p[t]; Multiply2x1(T1.p, Z.p[i - t - 1]); } while (GreaterThan3x3(T1.p, T2.p)); 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 (X.s < 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) { MBEDTLS_MPI_CHK(mbedtls_mpi_copy(Q, &Z)); Q->s = A->s * B->s; } if (R) { mbedtls_mpi_shift_r(&X, k); X.s = A->s; MBEDTLS_MPI_CHK(mbedtls_mpi_copy(R, &X)); if (mbedtls_mpi_is_zero(R)) 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; } /** * \brief Perform a division with remainder of an MPI by an integer: * A = Q * b + R * * \param Q The destination MPI for the quotient. * This may be \c NULL if the value of the * quotient is not needed. * \param R The destination MPI for the remainder value. * This may be \c NULL if the value of the * remainder is not needed. * \param A The dividend. This must point to an initialized MPi. * \param b The divisor. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed. * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. * \return Another negative error code on different kinds of failure. */ 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]; MPI_VALIDATE_RET(A); p[0] = (b < 0) ? -b : b; _B.s = (b < 0) ? -1 : 1; _B.n = 1; _B.p = p; return mbedtls_mpi_div_mpi(Q, R, A, &_B); } /** * \brief Perform a modular reduction. R = A mod B * * \param R The destination MPI for the residue value. * This must point to an initialized MPI. * \param A The MPI to compute the residue of. * This must point to an initialized MPI. * \param B The base of the modular reduction. * This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p B equals zero. * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p B is negative. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_mod_mpi(mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B) { size_t i, j; int ret = MBEDTLS_ERR_THIS_CORRUPTION; MPI_VALIDATE_RET(R); MPI_VALIDATE_RET(A); MPI_VALIDATE_RET(B); if (B->s < 0) return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; MBEDTLS_MPI_CHK(mbedtls_mpi_div_mpi(NULL, R, A, B)); while (R->s < 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; } /** * \brief Perform a modular reduction with respect to an integer. * r = A mod b * * \param r The address at which to store the residue. * This must not be \c NULL. * \param A The MPI to compute the residue of. * This must point to an initialized MPi. * \param b The integer base of the modular reduction. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if \p b equals zero. * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if \p b is negative. * \return Another negative error code on different kinds of failure. */ 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; MPI_VALIDATE_RET(r); MPI_VALIDATE_RET(A); if (!b) return MBEDTLS_ERR_MPI_DIVISION_BY_ZERO; if (b < 0) return MBEDTLS_ERR_MPI_NEGATIVE_VALUE; /* * handle trivial cases */ if (b == 1) { *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) y = b - y; *r = y; return 0; } /* * Fast Montgomery initialization (thanks to Tom St Denis) */ static void mpi_montg_init(mbedtls_mpi_uint *mm, const mbedtls_mpi *N) { mbedtls_mpi_uint x, m0 = N->p[0]; unsigned int i; x = m0; x += ((m0 + 2) & 4) << 1; for (i = biL; i >= 8; i /= 2) x *= 2 - m0 * x; *mm = -x; } /** * Montgomery multiplication: A = A * B * R^-1 mod N (HAC 14.36) * * \param[in,out] A One of the numbers to multiply. * It must have at least as many limbs as N * (A->n >= N->n), and any limbs beyond n are ignored. * On successful completion, A contains the result of * the multiplication A * B * R^-1 mod N where * R = (2^ciL)^n. * \param[in] B One of the numbers to multiply. * It must be nonzero and must not have more limbs than N * (B->n <= N->n). * \param[in] N The modulo. N must be odd. * \param mm The value calculated by `mpi_montg_init(&mm, N)`. * This is -N^-1 mod 2^ciL. * \param[in,out] T A bignum for temporary storage. * It must be at least twice the limb size of N plus 2 * (T->n >= 2 * (N->n + 1)). * Its initial content is unused and * its final content is indeterminate. * Note that unlike the usual convention in the library * for `const mbedtls_mpi*`, the content of T can change. */ static void mpi_montmul(mbedtls_mpi *A, const mbedtls_mpi *B, const mbedtls_mpi *N, mbedtls_mpi_uint mm, const mbedtls_mpi *T) { size_t i, n, m; mbedtls_mpi_uint u0, u1, *d, *Ap, *Bp, *Np; mbedtls_mpi_zeroize(T->p, T->n); d = T->p; n = N->n; m = (B->n < n) ? B->n : n; Ap = A->p; Bp = B->p; Np = N->p; for (i = 0; i < n; i++) { /* * T = (T + u0*B + u1*N) / 2^biL */ u0 = Ap[i]; u1 = (d[0] + u0 * Bp[0]) * mm; mbedtls_mpi_mul_hlp(m, Bp, d, u0); mbedtls_mpi_mul_hlp(n, Np, d, u1); *d++ = u0; d[n + 1] = 0; } /* At this point, d is either the desired result or the desired result * plus N. We now potentially subtract N, avoiding leaking whether the * subtraction is performed through side channels. */ /* Copy the n least significant limbs of d to A, so that * A = d if d < N (recall that N has n limbs). */ memcpy(Ap, d, n * ciL); /* If d >= N then we want to set A to d - N. To prevent timing attacks, * do the calculation without using conditional tests. */ /* Set d to d0 + (2^biL)^n - N where d0 is the current value of d. */ d[n] += 1; d[n] -= mpi_sub_hlp(d, d, Np, n); /* If d0 < N then d < (2^biL)^n * so d[n] == 0 and we want to keep A as it is. * If d0 >= N then d >= (2^biL)^n, and d <= (2^biL)^n + N < 2 * (2^biL)^n * so d[n] == 1 and we want to set A to the result of the subtraction * which is d - (2^biL)^n, i.e. the n least significant limbs of d. * This exactly corresponds to a conditional assignment. */ for (i = 0; i < n; ++i) { Ap[i] = Select(d[i], Ap[i], -d[n]); } } /* * Montgomery reduction: A = A * R^-1 mod N * * See mpi_montmul() regarding constraints and guarantees on the parameters. */ static void mpi_montred(mbedtls_mpi *A, const mbedtls_mpi *N, mbedtls_mpi_uint mm, const mbedtls_mpi *T) { mbedtls_mpi U; mbedtls_mpi_uint z = 1; U.n = U.s = (int)z; U.p = &z; mpi_montmul(A, &U, N, mm, T); } /** * \brief Perform a sliding-window exponentiation: X = A^E mod N * * \param X The destination MPI. This must point to an initialized MPI. * \param A The base of the exponentiation. * This must point to an initialized MPI. * \param E The exponent MPI. This must point to an initialized MPI. * \param N The base for the modular reduction. This must point to an * initialized MPI. * \param _RR A helper MPI depending solely on \p N which can be used to * speed-up multiple modular exponentiations for the same value * of \p N. This may be \c NULL. If it is not \c NULL, it must * point to an initialized MPI. If it hasn't been used after * the call to mbedtls_mpi_init(), this function will compute * the helper value and store it in \p _RR for reuse on * subsequent calls to this function. Otherwise, the function * will assume that \p _RR holds the helper value set by a * previous call to mbedtls_mpi_exp_mod(), and reuse it. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \c N is negative or * even, or if \c E is negative. * \return Another negative error code on different kinds of failures. * */ int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; size_t wbits, wsize, one = 1; size_t i, j, nblimbs; size_t bufsize, nbits; mbedtls_mpi_uint ei, mm, state; mbedtls_mpi RR, T, W[1 << MBEDTLS_MPI_WINDOW_SIZE], Apos; int neg; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(A); MPI_VALIDATE_RET(E); MPI_VALIDATE_RET(N); if (mbedtls_mpi_cmp_int(N, 0) <= 0 || !(N->p[0] & 1)) return MBEDTLS_ERR_MPI_BAD_INPUT_DATA; if (E->s < 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; /* * Init temps and window size */ mpi_montg_init(&mm, N); mbedtls_mpi_init(&RR); mbedtls_mpi_init(&T); mbedtls_mpi_init(&Apos); mbedtls_platform_zeroize(W, sizeof(W)); i = mbedtls_mpi_bitlen(E); wsize = (i > 671) ? 6 : (i > 239) ? 5 : (i > 79) ? 4 : (i > 23) ? 3 : 1; #if (MBEDTLS_MPI_WINDOW_SIZE < 6) if (wsize > MBEDTLS_MPI_WINDOW_SIZE) wsize = MBEDTLS_MPI_WINDOW_SIZE; #endif j = N->n + 1; MBEDTLS_MPI_CHK(mbedtls_mpi_grow(X, j)); MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[1], j)); MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&T, j * 2)); /* * Compensate for negative A (and correct at the end) */ neg = (A->s == -1); if (neg) { MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&Apos, A)); Apos.s = 1; A = &Apos; } /* * If 1st call, pre-compute R^2 mod N */ if (!_RR || !_RR->p) { MBEDTLS_MPI_CHK(mbedtls_mpi_lset(&RR, 1)); MBEDTLS_MPI_CHK(mbedtls_mpi_shift_l(&RR, N->n * 2 * biL)); MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&RR, &RR, N)); if (_RR) memcpy(_RR, &RR, sizeof(mbedtls_mpi)); } else { memcpy(&RR, _RR, sizeof(mbedtls_mpi)); } /* * W[1] = A * R^2 * R^-1 mod N = A * R mod N */ if (mbedtls_mpi_cmp_mpi(A, N) >= 0) MBEDTLS_MPI_CHK(mbedtls_mpi_mod_mpi(&W[1], A, N)); else MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[1], A)); mpi_montmul(&W[1], &RR, N, mm, &T); /* * X = R^2 * R^-1 mod N = R mod N */ MBEDTLS_MPI_CHK(mbedtls_mpi_copy(X, &RR)); mpi_montred(X, N, mm, &T); if (wsize > 1) { /* * W[1 << (wsize - 1)] = W[1] ^ (wsize - 1) */ j = one << (wsize - 1); MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[j], N->n + 1)); MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[j], &W[1])); for (i = 0; i < wsize - 1; i++) mpi_montmul(&W[j], &W[j], N, mm, &T); /* * W[i] = W[i - 1] * W[1] */ for (i = j + 1; i < (one << wsize); i++) { MBEDTLS_MPI_CHK(mbedtls_mpi_grow(&W[i], N->n + 1)); MBEDTLS_MPI_CHK(mbedtls_mpi_copy(&W[i], &W[i - 1])); mpi_montmul(&W[i], &W[1], N, mm, &T); } } nblimbs = E->n; bufsize = 0; nbits = 0; wbits = 0; state = 0; while (1) { if (!bufsize) { if (!nblimbs) break; nblimbs--; bufsize = sizeof(mbedtls_mpi_uint) << 3; } bufsize--; ei = (E->p[nblimbs] >> bufsize) & 1; /* * skip leading 0s */ if (ei == 0 && state == 0) continue; if (ei == 0 && state == 1) { /* * out of window, square X */ mpi_montmul(X, X, N, mm, &T); continue; } /* * add ei to current window */ state = 2; nbits++; wbits |= (ei << (wsize - nbits)); if (nbits == wsize) { /* * X = X^wsize R^-1 mod N */ for (i = 0; i < wsize; i++) mpi_montmul(X, X, N, mm, &T); /* * X = X * W[wbits] R^-1 mod N */ mpi_montmul(X, &W[wbits], N, mm, &T); state--; nbits = 0; wbits = 0; } } /* * process the remaining bits */ for (i = 0; i < nbits; i++) { mpi_montmul(X, X, N, mm, &T); wbits <<= 1; if ((wbits & (one << wsize))) mpi_montmul(X, &W[1], N, mm, &T); } /* * X = A^E * R * R^-1 mod N = A^E mod N */ mpi_montred(X, N, mm, &T); if (neg && E->n && (E->p[0] & 1)) { X->s = -1; MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(X, N, X)); } cleanup: for (i = (one << (wsize - 1)); i < (one << wsize); i++) mbedtls_mpi_free(&W[i]); mbedtls_mpi_free(&W[1]); mbedtls_mpi_free(&T); mbedtls_mpi_free(&Apos); if (!_RR || !_RR->p) mbedtls_mpi_free(&RR); return ret; } static inline int Compare(const mbedtls_mpi *X, const mbedtls_mpi *Y, size_t i, size_t j) { if (!i && !j) return 0; 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; } /** * \brief Compute the greatest common divisor: G = gcd(A, B) * * \param G The destination MPI. This must point to an initialized MPI. * \param A The first operand. This must point to an initialized MPI. * \param B The second operand. This must point to an initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on different kinds of failure. */ int mbedtls_mpi_gcd(mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; mbedtls_mpi TA, TB; size_t lz, lzt, i, j; MPI_VALIDATE_RET(G); MPI_VALIDATE_RET(A); MPI_VALIDATE_RET(B); 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); if (lzt < lz) lz = lzt; mbedtls_mpi_shift_r(&TA, lz); mbedtls_mpi_shift_r(&TB, lz); TA.s = TB.s = 1; i = mbedtls_mpi_bitlen(&TA); j = mbedtls_mpi_bitlen(&TB); while (!mbedtls_mpi_is_zero(&TA)) { mbedtls_mpi_shift_r(&TA, mbedtls_mpi_lsb(&TA)); mbedtls_mpi_shift_r(&TB, mbedtls_mpi_lsb(&TB)); if (mpi_cmp_abs(&TA, &TB, &i, &j) >= 0) { MBEDTLS_MPI_CHK(mpi_sub_abs(&TA, &TA, &TB, j)); mbedtls_mpi_shift_r(&TA, 1); } else { MBEDTLS_MPI_CHK(mpi_sub_abs(&TB, &TB, &TA, i)); mbedtls_mpi_shift_r(&TB, 1); } } 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; } /** * \brief Fill an MPI with a number of random bytes. * * \param X The destination MPI. This must point to an initialized MPI. * \param size The number of random bytes to generate. * \param f_rng The RNG function to use. This must not be \c NULL. * \param p_rng The RNG parameter to be passed to \p f_rng. This may be * \c NULL if \p f_rng doesn't need a context argument. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return Another negative error code on failure. * * \note The bytes obtained from the RNG are interpreted * as a big-endian representation of an MPI; this can * be relevant in applications like deterministic ECDSA. */ 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_THIS_CORRUPTION; size_t const limbs = CHARS_TO_LIMBS(size); size_t const overhead = (limbs * ciL) - size; unsigned char *Xp; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(f_rng); MBEDTLS_MPI_CHK(mbedtls_mpi_resize(X, limbs)); MBEDTLS_MPI_CHK(mbedtls_mpi_lset(X, 0)); Xp = (unsigned char *)X->p; MBEDTLS_MPI_CHK(f_rng(p_rng, Xp + overhead, size)); mpi_bigendian_to_host(X->p, limbs); cleanup: return ret; } /** * \brief Compute the modular inverse: X = A^-1 mod N * * \param X The destination MPI. This must point to an initialized MPI. * \param A The MPI to calculate the modular inverse of. This must point * to an initialized MPI. * \param N The base of the modular inversion. This must point to an * initialized MPI. * * \return \c 0 if successful. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p N is less than * or equal to one. * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p has no modular inverse * with respect to \p N. */ int mbedtls_mpi_inv_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N) { int ret = MBEDTLS_ERR_THIS_CORRUPTION; mbedtls_mpi G, TA, TU, U1, U2, TB, TV, V1, V2; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(A); MPI_VALIDATE_RET(N); 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_is_one(&G)) { 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)) { mbedtls_mpi_shift_r(&TU, 1); if ((U1.p[0] & 1) || (U2.p[0] & 1)) { MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&U1, &U1, &TB)); MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&U2, &U2, &TA)); } mbedtls_mpi_shift_r(&U1, 1); mbedtls_mpi_shift_r(&U2, 1); } while (!(TV.p[0] & 1)) { mbedtls_mpi_shift_r(&TV, 1); if ((V1.p[0] & 1) || (V2.p[0] & 1)) { MBEDTLS_MPI_CHK(mbedtls_mpi_add_mpi(&V1, &V1, &TB)); MBEDTLS_MPI_CHK(mbedtls_mpi_sub_mpi(&V2, &V2, &TA)); } mbedtls_mpi_shift_r(&V1, 1); 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_is_zero(&TU)); while (V1.s < 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) static const short kSmallPrime[] = { 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 211, 223, 227, 229, 233, 239, 241, 251, 257, 263, 269, 271, 277, 281, 283, 293, 307, 311, 313, 317, 331, 337, 347, 349, 353, 359, 367, 373, 379, 383, 389, 397, 401, 409, 419, 421, 431, 433, 439, 443, 449, 457, 461, 463, 467, 479, 487, 491, 499, 503, 509, 521, 523, 541, 547, 557, 563, 569, 571, 577, 587, 593, 599, 601, 607, 613, 617, 619, 631, 641, 643, 647, 653, 659, 661, 673, 677, 683, 691, 701, 709, 719, 727, 733, 739, 743, 751, 757, 761, 769, 773, 787, 797, 809, 811, 821, 823, 827, 829, 839, 853, 857, 859, 863, 877, 881, 883, 887, 907, 911, 919, 929, 937, 941, 947, 953, 967, 971, 977, 983, 991, 997, }; static struct Divisor kSmallDivisor[ARRAYLEN(kSmallPrime)]; static bool IsDivisible( const mbedtls_mpi_uint *Ap, size_t An, mbedtls_mpi_sint b, struct Divisor d ) { size_t i; mbedtls_mpi_uint x, y, z; MBEDTLS_ASSERT(b >= 3); for (i = An, y = 0; i > 0; i--) { x = Ap[i - 1]; y = (y << biH) | (x >> biH); z = Divide(y, d); y -= z * b; x <<= biH; y = (y << biH) | (x >> biH); z = Divide(y, d); y -= z * b; } return !y; } /* * 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, n; static bool once; if (!(X->p[0] & 1)) return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; n = mbedtls_mpi_limbs(X); if (!once) { for (i = 0; i < ARRAYLEN(kSmallPrime); ++i) kSmallDivisor[i] = GetDivisor(kSmallPrime[i]); once = true; } for (i = 0; i < ARRAYLEN(kSmallPrime); i++) { if (n == 1 && mbedtls_mpi_cmp_int(X, kSmallPrime[i]) <= 0) return 1; if (IsDivisible(X->p, X->n, kSmallPrime[i], kSmallDivisor[i])) return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; } 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; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(f_rng); 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_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) || mbedtls_mpi_is_one(&A)) continue; j = 1; while (j < s && mbedtls_mpi_cmp_mpi(&A, &W)) { /* * 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_is_one(&A)) break; j++; } /* * not prime if A != |X| - 1 or A == 1 */ if (mbedtls_mpi_cmp_mpi(&A, &W) || mbedtls_mpi_is_one(&A)) { 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; } /** * \brief Miller-Rabin primality test. * * \warning If \p X is potentially generated by an adversary, for * example when validating cryptographic parameters that * you didn't generate yourself and that are supposed to * be prime, then \p rounds should be at least the half * of the security strength of the cryptographic * algorithm. On the other hand, if \p X is chosen * uniformly or non-adversially (as is the case when * mbedtls_mpi_gen_prime calls this function), then \p * rounds can be much lower. * * \param X The MPI to check for primality. * This must point to an initialized MPI. * \param rounds The number of bases to perform the Miller-Rabin primality * test for. The probability of returning 0 on a composite is * at most 2-2*\p rounds. * \param f_rng The RNG function to use. This must not be \c NULL. * \param p_rng The RNG parameter to be passed to \p f_rng. * This may be \c NULL if \p f_rng doesn't use * a context parameter. * * \return \c 0 if successful, i.e. \p X is probably prime. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a allocation failed. * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime. * \return Another negative error code on other failures. */ 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_THIS_CORRUPTION; mbedtls_mpi XX; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(f_rng); XX.s = 1; XX.n = X->n; XX.p = X->p; if (mbedtls_mpi_is_zero(&XX) || mbedtls_mpi_is_one(&XX)) return MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; if (!mbedtls_mpi_cmp_int(&XX, 2)) return 0; if ((ret = mpi_check_small_factors(&XX))) { if (ret == 1) return 0; return ret; } return mpi_miller_rabin(&XX, rounds, f_rng, p_rng); } /** * \brief Generate a prime number. * * 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. * * \param X The destination MPI to store the generated prime in. * This must point to an initialized MPi. * \param nbits The required size of the destination MPI in bits. * This must be between \c 3 and #MBEDTLS_MPI_MAX_BITS. * \param flags A mask of flags of type #mbedtls_mpi_gen_prime_flag_t. * \param f_rng The RNG function to use. This must not be \c NULL. * \param p_rng The RNG parameter to be passed to \p f_rng. * This may be \c NULL if \p f_rng doesn't use * a context parameter. * * \return \c 0 if successful, in which case \p X holds a * probably prime number. * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a allocation failed. * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `nbits` is not * between \c 3 and #MBEDTLS_MPI_MAX_BITS. */ int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags, int (*f_rng)(void *, unsigned char *, size_t), void *p_rng) { int ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE; size_t k, n; int rounds; mbedtls_mpi_uint r; mbedtls_mpi Y; MPI_VALIDATE_RET(X); MPI_VALIDATE_RET(f_rng); 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)) { /* * 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] < 0xb504f333f9de6485ULL /* ceil(2^63.5) */) continue; k = n * biL; if (k > nbits) mbedtls_mpi_shift_r(X, k - nbits); X->p[0] |= 1; if (!(flags & MBEDTLS_MPI_GEN_PRIME_FLAG_DH)) { ret = mbedtls_mpi_is_prime_ext(X, rounds, f_rng, p_rng); if (ret != MBEDTLS_ERR_MPI_NOT_ACCEPTABLE) goto cleanup; } else { /* * An 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_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)) && !(ret = mpi_check_small_factors(&Y)) && !(ret = mpi_miller_rabin(X, rounds, f_rng, p_rng)) && !(ret = mpi_miller_rabin(&Y, rounds, f_rng, p_rng))) 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}}; /** * \brief Checkup routine * * \return 0 if successful, or 1 if the test failed */ 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) mbedtls_printf(" MPI test #1 (mul_mpi): "); if (mbedtls_mpi_cmp_mpi(&X, &U)) { if (verbose) mbedtls_printf("failed\n"); ret = 1; goto cleanup; } if (verbose) 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) mbedtls_printf(" MPI test #2 (div_mpi): "); if (mbedtls_mpi_cmp_mpi(&X, &U) || mbedtls_mpi_cmp_mpi(&Y, &V)) { if (verbose) mbedtls_printf("failed\n"); ret = 1; goto cleanup; } if (verbose) 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) mbedtls_printf(" MPI test #3 (exp_mod): "); if (mbedtls_mpi_cmp_mpi(&X, &U)) { if (verbose) mbedtls_printf("failed\n"); ret = 1; goto cleanup; } if (verbose) 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) mbedtls_printf(" MPI test #4 (inv_mod): "); if (mbedtls_mpi_cmp_mpi(&X, &U)) { if (verbose) mbedtls_printf("failed\n"); ret = 1; goto cleanup; } if (verbose) mbedtls_printf("passed\n"); if (verbose) 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])) { if (verbose) mbedtls_printf("failed at %d\n", i); ret = 1; goto cleanup; } } if (verbose) mbedtls_printf("passed\n"); cleanup: if (ret && verbose) 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) mbedtls_printf("\n"); return ret; } #endif /* MBEDTLS_SELF_TEST */ #endif /* MBEDTLS_BIGNUM_C */