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bignum.h File Reference
Multi-precision integer library. More...
Go to the source code of this file.
Data Structures | |
| struct | mbedtls_mpi |
| MPI structure. More... | |
Functions | |
| void | mbedtls_mpi_init (mbedtls_mpi *X) |
| Initialize one MPI (make internal references valid) This just makes it ready to be set or freed, but does not define a value for the MPI. | |
| void | mbedtls_mpi_free (mbedtls_mpi *X) |
| Unallocate one MPI. | |
| int | mbedtls_mpi_grow (mbedtls_mpi *X, size_t nblimbs) |
| Enlarge to the specified number of limbs. | |
| int | mbedtls_mpi_shrink (mbedtls_mpi *X, size_t nblimbs) |
| Resize down, keeping at least the specified number of limbs. | |
| int | mbedtls_mpi_copy (mbedtls_mpi *X, const mbedtls_mpi *Y) |
| Copy the contents of Y into X. | |
| void | mbedtls_mpi_swap (mbedtls_mpi *X, mbedtls_mpi *Y) |
| Swap the contents of X and Y. | |
| int | mbedtls_mpi_safe_cond_assign (mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign) |
| Safe conditional assignement X = Y if assign is 1. | |
| int | mbedtls_mpi_safe_cond_swap (mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char assign) |
| Safe conditional swap X <-> Y if swap is 1. | |
| int | mbedtls_mpi_lset (mbedtls_mpi *X, mbedtls_mpi_sint z) |
| Set value from integer. | |
| int | mbedtls_mpi_get_bit (const mbedtls_mpi *X, size_t pos) |
| Get a specific bit from X. | |
| int | mbedtls_mpi_set_bit (mbedtls_mpi *X, size_t pos, unsigned char val) |
| Set a bit of X to a specific value of 0 or 1. | |
| size_t | mbedtls_mpi_lsb (const mbedtls_mpi *X) |
| Return the number of zero-bits before the least significant '1' bit. | |
| size_t | mbedtls_mpi_bitlen (const mbedtls_mpi *X) |
| Return the number of bits up to and including the most significant '1' bit'. | |
| size_t | mbedtls_mpi_size (const mbedtls_mpi *X) |
| Return the total size in bytes. | |
| int | mbedtls_mpi_read_string (mbedtls_mpi *X, int radix, const char *s) |
| Import from an ASCII string. | |
| int | mbedtls_mpi_write_string (const mbedtls_mpi *X, int radix, char *buf, size_t buflen, size_t *olen) |
| Export into an ASCII string. | |
| int | mbedtls_mpi_read_file (mbedtls_mpi *X, int radix, FILE *fin) |
| Read MPI from a line in an opened file. | |
| int | mbedtls_mpi_write_file (const char *p, const mbedtls_mpi *X, int radix, FILE *fout) |
| Write X into an opened file, or stdout if fout is NULL. | |
| int | mbedtls_mpi_read_binary (mbedtls_mpi *X, const unsigned char *buf, size_t buflen) |
| Import X from unsigned binary data, big endian. | |
| int | mbedtls_mpi_write_binary (const mbedtls_mpi *X, unsigned char *buf, size_t buflen) |
| Export X into unsigned binary data, big endian. | |
| int | mbedtls_mpi_shift_l (mbedtls_mpi *X, size_t count) |
| Left-shift: X <<= count. | |
| int | mbedtls_mpi_shift_r (mbedtls_mpi *X, size_t count) |
| Right-shift: X >>= count. | |
| int | mbedtls_mpi_cmp_abs (const mbedtls_mpi *X, const mbedtls_mpi *Y) |
| Compare unsigned values. | |
| int | mbedtls_mpi_cmp_mpi (const mbedtls_mpi *X, const mbedtls_mpi *Y) |
| Compare signed values. | |
| int | mbedtls_mpi_cmp_int (const mbedtls_mpi *X, mbedtls_mpi_sint z) |
| Compare signed values. | |
| int | mbedtls_mpi_add_abs (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) |
| Unsigned addition: X = |A| + |B|. | |
| int | mbedtls_mpi_sub_abs (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) |
| Unsigned subtraction: X = |A| - |B|. | |
| int | mbedtls_mpi_add_mpi (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) |
| Signed addition: X = A + B. | |
| int | mbedtls_mpi_sub_mpi (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) |
| Signed subtraction: X = A - B. | |
| int | mbedtls_mpi_add_int (mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b) |
| Signed addition: X = A + b. | |
| int | mbedtls_mpi_sub_int (mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b) |
| Signed subtraction: X = A - b. | |
| int | mbedtls_mpi_mul_mpi (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B) |
| Baseline multiplication: X = A * B. | |
| int | mbedtls_mpi_mul_int (mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b) |
| Baseline multiplication: X = A * b. | |
| int | mbedtls_mpi_div_mpi (mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B) |
| Division by mbedtls_mpi: A = Q * B + R. | |
| int | mbedtls_mpi_div_int (mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A, mbedtls_mpi_sint b) |
| Division by int: A = Q * b + R. | |
| int | mbedtls_mpi_mod_mpi (mbedtls_mpi *R, const mbedtls_mpi *A, const mbedtls_mpi *B) |
| Modulo: R = A mod B. | |
| int | mbedtls_mpi_mod_int (mbedtls_mpi_uint *r, const mbedtls_mpi *A, mbedtls_mpi_sint b) |
| Modulo: r = A mod b. | |
| int | mbedtls_mpi_exp_mod (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR) |
| Sliding-window exponentiation: X = A^E mod N. | |
| int | mbedtls_mpi_fill_random (mbedtls_mpi *X, size_t size, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng) |
| Fill an MPI X with size bytes of random. | |
| int | mbedtls_mpi_gcd (mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B) |
| Greatest common divisor: G = gcd(A, B) | |
| int | mbedtls_mpi_inv_mod (mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N) |
| Modular inverse: X = A^-1 mod N. | |
| int | mbedtls_mpi_is_prime (const mbedtls_mpi *X, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng) |
| Miller-Rabin primality test. | |
| int | mbedtls_mpi_gen_prime (mbedtls_mpi *X, size_t nbits, int dh_flag, int(*f_rng)(void *, unsigned char *, size_t), void *p_rng) |
| Prime number generation. | |
| int | mbedtls_mpi_self_test (int verbose) |
| Checkup routine. | |
Detailed Description
Multi-precision integer library.
Definition in file bignum.h.
Function Documentation
| int mbedtls_mpi_add_abs | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | A, | ||
| const mbedtls_mpi * | B | ||
| ) |
| int mbedtls_mpi_add_int | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | A, | ||
| mbedtls_mpi_sint | b | ||
| ) |
| int mbedtls_mpi_add_mpi | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | A, | ||
| const mbedtls_mpi * | B | ||
| ) |
| size_t mbedtls_mpi_bitlen | ( | const mbedtls_mpi * | X ) |
| int mbedtls_mpi_cmp_abs | ( | const mbedtls_mpi * | X, |
| const mbedtls_mpi * | Y | ||
| ) |
| int mbedtls_mpi_cmp_int | ( | const mbedtls_mpi * | X, |
| mbedtls_mpi_sint | z | ||
| ) |
| int mbedtls_mpi_cmp_mpi | ( | const mbedtls_mpi * | X, |
| const mbedtls_mpi * | Y | ||
| ) |
| int mbedtls_mpi_copy | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | Y | ||
| ) |
| int mbedtls_mpi_div_int | ( | mbedtls_mpi * | Q, |
| mbedtls_mpi * | R, | ||
| const mbedtls_mpi * | A, | ||
| mbedtls_mpi_sint | b | ||
| ) |
Division by int: A = Q * b + R.
- Parameters:
-
Q Destination MPI for the quotient R Destination MPI for the rest value A Left-hand MPI b Integer to divide by
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0
- Note:
- Either Q or R can be NULL.
| int mbedtls_mpi_div_mpi | ( | mbedtls_mpi * | Q, |
| mbedtls_mpi * | R, | ||
| const mbedtls_mpi * | A, | ||
| const mbedtls_mpi * | B | ||
| ) |
Division by mbedtls_mpi: A = Q * B + R.
- Parameters:
-
Q Destination MPI for the quotient R Destination MPI for the rest value A Left-hand MPI B Right-hand MPI
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0
- Note:
- Either Q or R can be NULL.
| int mbedtls_mpi_exp_mod | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | A, | ||
| const mbedtls_mpi * | E, | ||
| const mbedtls_mpi * | N, | ||
| mbedtls_mpi * | _RR | ||
| ) |
Sliding-window exponentiation: X = A^E mod N.
- Parameters:
-
X Destination MPI A Left-hand MPI E Exponent MPI N Modular MPI _RR Speed-up MPI used for recalculations
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is negative or even or if E is negative
- Note:
- _RR is used to avoid re-computing R*R mod N across multiple calls, which speeds up things a bit. It can be set to NULL if the extra performance is unneeded.
| int mbedtls_mpi_fill_random | ( | mbedtls_mpi * | X, |
| size_t | size, | ||
| int(*)(void *, unsigned char *, size_t) | f_rng, | ||
| void * | p_rng | ||
| ) |
Fill an MPI X with size bytes of random.
- Parameters:
-
X Destination MPI size Size in bytes f_rng RNG function p_rng RNG parameter
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
- Note:
- The bytes obtained from the PRNG are interpreted as a big-endian representation of an MPI; this can be relevant in applications like deterministic ECDSA.
| void mbedtls_mpi_free | ( | mbedtls_mpi * | X ) |
| int mbedtls_mpi_gcd | ( | mbedtls_mpi * | G, |
| const mbedtls_mpi * | A, | ||
| const mbedtls_mpi * | B | ||
| ) |
| int mbedtls_mpi_gen_prime | ( | mbedtls_mpi * | X, |
| size_t | nbits, | ||
| int | dh_flag, | ||
| int(*)(void *, unsigned char *, size_t) | f_rng, | ||
| void * | p_rng | ||
| ) |
Prime number generation.
- Parameters:
-
X Destination MPI nbits Required size of X in bits ( 3 <= nbits <= MBEDTLS_MPI_MAX_BITS ) dh_flag If 1, then (X-1)/2 will be prime too f_rng RNG function p_rng RNG parameter
- Returns:
- 0 if successful (probably prime), MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
| int mbedtls_mpi_get_bit | ( | const mbedtls_mpi * | X, |
| size_t | pos | ||
| ) |
| int mbedtls_mpi_grow | ( | mbedtls_mpi * | X, |
| size_t | nblimbs | ||
| ) |
| void mbedtls_mpi_init | ( | mbedtls_mpi * | X ) |
| int mbedtls_mpi_inv_mod | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | A, | ||
| const mbedtls_mpi * | N | ||
| ) |
Modular inverse: X = A^-1 mod N.
- Parameters:
-
X Destination MPI A Left-hand MPI N Right-hand MPI
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_BAD_INPUT_DATA if N is <= 1, MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if A has no inverse mod N.
| int mbedtls_mpi_is_prime | ( | const mbedtls_mpi * | X, |
| int(*)(void *, unsigned char *, size_t) | f_rng, | ||
| void * | p_rng | ||
| ) |
| size_t mbedtls_mpi_lsb | ( | const mbedtls_mpi * | X ) |
| int mbedtls_mpi_lset | ( | mbedtls_mpi * | X, |
| mbedtls_mpi_sint | z | ||
| ) |
| int mbedtls_mpi_mod_int | ( | mbedtls_mpi_uint * | r, |
| const mbedtls_mpi * | A, | ||
| mbedtls_mpi_sint | b | ||
| ) |
Modulo: r = A mod b.
- Parameters:
-
r Destination mbedtls_mpi_uint A Left-hand MPI b Integer to divide by
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if b == 0, MBEDTLS_ERR_MPI_NEGATIVE_VALUE if b < 0
| int mbedtls_mpi_mod_mpi | ( | mbedtls_mpi * | R, |
| const mbedtls_mpi * | A, | ||
| const mbedtls_mpi * | B | ||
| ) |
Modulo: R = A mod B.
- Parameters:
-
R Destination MPI for the rest value A Left-hand MPI B Right-hand MPI
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if B == 0, MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B < 0
| int mbedtls_mpi_mul_int | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | A, | ||
| mbedtls_mpi_uint | b | ||
| ) |
| int mbedtls_mpi_mul_mpi | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | A, | ||
| const mbedtls_mpi * | B | ||
| ) |
| int mbedtls_mpi_read_binary | ( | mbedtls_mpi * | X, |
| const unsigned char * | buf, | ||
| size_t | buflen | ||
| ) |
| int mbedtls_mpi_read_file | ( | mbedtls_mpi * | X, |
| int | radix, | ||
| FILE * | fin | ||
| ) |
Read MPI from a line in an opened file.
- Parameters:
-
X Destination MPI radix Input numeric base fin Input file handle
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer is too small or a MBEDTLS_ERR_MPI_XXX error code
- Note:
- On success, this function advances the file stream to the end of the current line or to EOF.
The function returns 0 on an empty line.
Leading whitespaces are ignored, as is a '0x' prefix for radix 16.
| int mbedtls_mpi_read_string | ( | mbedtls_mpi * | X, |
| int | radix, | ||
| const char * | s | ||
| ) |
| int mbedtls_mpi_safe_cond_assign | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | Y, | ||
| unsigned char | assign | ||
| ) |
Safe conditional assignement X = Y if assign is 1.
- Parameters:
-
X MPI to conditionally assign to Y Value to be assigned assign 1: perform the assignment, 0: keep X's original value
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
- 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).
| int mbedtls_mpi_safe_cond_swap | ( | mbedtls_mpi * | X, |
| mbedtls_mpi * | Y, | ||
| unsigned char | assign | ||
| ) |
Safe conditional swap X <-> Y if swap is 1.
- Parameters:
-
X First mbedtls_mpi value Y Second mbedtls_mpi value assign 1: perform the swap, 0: keep X and Y's original values
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
- 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).
| int mbedtls_mpi_self_test | ( | int | verbose ) |
| int mbedtls_mpi_set_bit | ( | mbedtls_mpi * | X, |
| size_t | pos, | ||
| unsigned char | val | ||
| ) |
Set a bit of X to a specific value of 0 or 1.
- Note:
- Will grow X if necessary to set a bit to 1 in a not yet existing limb. Will not grow if bit should be set to 0
- Parameters:
-
X MPI to use pos Zero-based index of the bit in X val The value to set the bit to (0 or 1)
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed, MBEDTLS_ERR_MPI_BAD_INPUT_DATA if val is not 0 or 1
| int mbedtls_mpi_shift_l | ( | mbedtls_mpi * | X, |
| size_t | count | ||
| ) |
| int mbedtls_mpi_shift_r | ( | mbedtls_mpi * | X, |
| size_t | count | ||
| ) |
| int mbedtls_mpi_shrink | ( | mbedtls_mpi * | X, |
| size_t | nblimbs | ||
| ) |
| size_t mbedtls_mpi_size | ( | const mbedtls_mpi * | X ) |
| int mbedtls_mpi_sub_abs | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | A, | ||
| const mbedtls_mpi * | B | ||
| ) |
| int mbedtls_mpi_sub_int | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | A, | ||
| mbedtls_mpi_sint | b | ||
| ) |
| int mbedtls_mpi_sub_mpi | ( | mbedtls_mpi * | X, |
| const mbedtls_mpi * | A, | ||
| const mbedtls_mpi * | B | ||
| ) |
| void mbedtls_mpi_swap | ( | mbedtls_mpi * | X, |
| mbedtls_mpi * | Y | ||
| ) |
| int mbedtls_mpi_write_binary | ( | const mbedtls_mpi * | X, |
| unsigned char * | buf, | ||
| size_t | buflen | ||
| ) |
Export X into unsigned binary data, big endian.
Always fills the whole buffer, which will start with zeros if the number is smaller.
- Parameters:
-
X Source MPI buf Output buffer buflen Output buffer size
- Returns:
- 0 if successful, MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
| int mbedtls_mpi_write_file | ( | const char * | p, |
| const mbedtls_mpi * | X, | ||
| int | radix, | ||
| FILE * | fout | ||
| ) |
Write X into an opened file, or stdout if fout is NULL.
- Parameters:
-
p Prefix, can be NULL X Source MPI radix Output numeric base fout Output file handle (can be NULL)
- Returns:
- 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
- Note:
- Set fout == NULL to print X on the console.
| int mbedtls_mpi_write_string | ( | const mbedtls_mpi * | X, |
| int | radix, | ||
| char * | buf, | ||
| size_t | buflen, | ||
| size_t * | olen | ||
| ) |
Export into an ASCII string.
- Parameters:
-
X Source MPI radix Output numeric base buf Buffer to write the string to buflen Length of buf olen Length of the string written, including final NUL byte
- Returns:
- 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code. *olen is always updated to reflect the amount of data that has (or would have) been written.
- Note:
- Call this function with buflen = 0 to obtain the minimum required buffer size in *olen.
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