File bignum.h
Multiprecision integer library.
Defines

MBEDTLS_ERR_MPI_FILE_IO_ERROR
An error occurred while reading from or writing to a file.

MBEDTLS_ERR_MPI_BAD_INPUT_DATA
Bad input parameters to function.

MBEDTLS_ERR_MPI_INVALID_CHARACTER
There is an invalid character in the digit string.

MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL
The buffer is too small to write to.

MBEDTLS_ERR_MPI_NEGATIVE_VALUE
The input arguments are negative or result in illegal output.

MBEDTLS_ERR_MPI_DIVISION_BY_ZERO
The input argument for division is zero, which is not allowed.

MBEDTLS_ERR_MPI_NOT_ACCEPTABLE
The input arguments are not acceptable.

MBEDTLS_ERR_MPI_ALLOC_FAILED
Memory allocation failed.

MBEDTLS_MPI_CHK(f)

MBEDTLS_MPI_MAX_LIMBS

MBEDTLS_MPI_MAX_BITS
Maximum number of bits for usable MPIs.

MBEDTLS_MPI_MAX_BITS_SCALE100

MBEDTLS_LN_2_DIV_LN_10_SCALE100

MBEDTLS_MPI_RW_BUFFER_SIZE

MBEDTLS_HAVE_INT32

MBEDTLS_MPI_UINT_MAX

MBEDTLS_MPI_INIT
Typedefs

typedef int32_t mbedtls_mpi_sint
The signed type corresponding to mbedtls_mpi_uint.
This is always an signed integer type with no padding bits. The size is platformdependent.

typedef uint32_t mbedtls_mpi_uint
The type of machine digits in a bignum, called limbs.
This is always an unsigned integer type with no padding bits. The size is platformdependent.

typedef struct mbedtls_mpi mbedtls_mpi
MPI structure.
Enums

enum mbedtls_mpi_gen_prime_flag_t
Flags for mbedtls_mpi_gen_prime()
Each of these flags is a constraint on the result X returned by mbedtls_mpi_gen_prime().
Values:

enumerator MBEDTLS_MPI_GEN_PRIME_FLAG_DH
(X1)/2 is prime too

enumerator MBEDTLS_MPI_GEN_PRIME_FLAG_LOW_ERR
lower error rate from 2^{80} to 2^{128}

enumerator MBEDTLS_MPI_GEN_PRIME_FLAG_DH
Functions

void mbedtls_mpi_init(mbedtls_mpi *X)
Initialize an MPI context.
This makes the MPI ready to be set or freed, but does not define a value for the MPI.
 Parameters:
X – The MPI context to initialize. This must not be
NULL
.

void mbedtls_mpi_free(mbedtls_mpi *X)
This function frees the components of an MPI context.
 Parameters:
X – The MPI context to be cleared. This may be
NULL
, in which case this function is a noop. If it is notNULL
, it must point to an initialized MPI.

int mbedtls_mpi_grow(mbedtls_mpi *X, size_t nblimbs)
Enlarge an MPI to the specified number of limbs.
Note
This function does nothing if the MPI is already large enough.
 Parameters:
X – The MPI to grow. It must be initialized.
nblimbs – The target number of limbs.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
 Returns:
Another negative error code on other kinds of failure.

int mbedtls_mpi_shrink(mbedtls_mpi *X, size_t nblimbs)
This function resizes an MPI downwards, keeping at least the specified number of limbs.
If
X
is smaller thannblimbs
, it is resized up instead. Parameters:
X – The MPI to shrink. This must point to an initialized MPI.
nblimbs – The minimum number of limbs to keep.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed (this can only happen when resizing up).
 Returns:
Another negative error code on other kinds of failure.

int mbedtls_mpi_copy(mbedtls_mpi *X, const mbedtls_mpi *Y)
Make a copy of an MPI.
Note
The limbbuffer in the destination MPI is enlarged if necessary to hold the value in the source MPI.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
Y – The source MPI. This must point to an initialized MPI.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
 Returns:
Another negative error code on other kinds of failure.

void mbedtls_mpi_swap(mbedtls_mpi *X, mbedtls_mpi *Y)
Swap the contents of two MPIs.
 Parameters:
X – The first MPI. It must be initialized.
Y – The second MPI. It must be initialized.

int mbedtls_mpi_safe_cond_assign(mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned char assign)
Perform a safe conditional copy of MPI which doesn’t reveal whether the condition was true or not.
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).Warning
If
assign
is neither 0 nor 1, the result of this function is indeterminate, and the resulting value inX
might be neither its original value nor the value inY
. Parameters:
X – The MPI to conditionally assign to. This must point to an initialized MPI.
Y – The MPI to be assigned from. This must point to an initialized MPI.
assign – The condition deciding whether to perform the assignment or not. Must be either 0 or 1:
1
: Perform the assignmentX = Y
.0
: Keep the original value ofX
.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
 Returns:
Another negative error code on other kinds of failure.

int mbedtls_mpi_safe_cond_swap(mbedtls_mpi *X, mbedtls_mpi *Y, unsigned char swap)
Perform a safe conditional swap which doesn’t reveal whether the condition was true or not.
Note
This function is equivalent to if( swap ) mbedtls_mpi_swap( X, Y ); except that it avoids leaking any information about whether the swap was done or not (the above code may leak information through branch prediction and/or memory access patterns analysis).
Warning
If
swap
is neither 0 nor 1, the result of this function is indeterminate, and bothX
andY
might end up with values different to either of the original ones. Parameters:
X – The first MPI. This must be initialized.
Y – The second MPI. This must be initialized.
swap – The condition deciding whether to perform the swap or not. Must be either 0 or 1:
1
: Swap the values ofX
andY
.0
: Keep the original values ofX
andY
.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
 Returns:
Another negative error code on other kinds of failure.

int mbedtls_mpi_lset(mbedtls_mpi *X, mbedtls_mpi_sint z)
Store integer value in MPI.
 Parameters:
X – The MPI to set. This must be initialized.
z – The value to use.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
 Returns:
Another negative error code on other kinds of failure.

int mbedtls_mpi_get_bit(const mbedtls_mpi *X, size_t pos)
Get a specific bit from an MPI.
 Parameters:
X – The MPI to query. This must be initialized.
pos – Zerobased index of the bit to query.
 Returns:
0
or1
on success, depending on whether bitpos
ofX
is unset or set. Returns:
A negative error code on failure.

int mbedtls_mpi_set_bit(mbedtls_mpi *X, size_t pos, unsigned char val)
Modify a specific bit in an MPI.
Note
This function will grow the target MPI if necessary to set a bit to
1
in a not yet existing limb. It will not grow if the bit should be set to0
. Parameters:
X – The MPI to modify. This must be initialized.
pos – Zerobased index of the bit to modify.
val – The desired value of bit
pos:
0
or1
.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
 Returns:
Another negative error code on other kinds of failure.

size_t mbedtls_mpi_lsb(const mbedtls_mpi *X)
Return the number of bits of value
0
before the least significant bit of value1
.Note
This is the same as the zerobased index of the least significant bit of value
1
. Parameters:
X – The MPI to query.
 Returns:
The number of bits of value
0
before the least significant bit of value1
inX
.

size_t mbedtls_mpi_bitlen(const mbedtls_mpi *X)
Return the number of bits up to and including the most significant bit of value
1
.Note
This is same as the onebased index of the most significant bit of value
1
. Parameters:
X – The MPI to query. This must point to an initialized MPI.
 Returns:
The number of bits up to and including the most significant bit of value
1
.

size_t mbedtls_mpi_size(const mbedtls_mpi *X)
Return the total size of an MPI value in bytes.
Note
The value returned by this function may be less than the number of bytes used to store
X
internally. This happens if and only if there are trailing bytes of value zero. Parameters:
X – The MPI to use. This must point to an initialized MPI.
 Returns:
The least number of bytes capable of storing the absolute value of
X
.

int mbedtls_mpi_read_string(mbedtls_mpi *X, int radix, const char *s)
Import an MPI from an ASCII string.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
radix – The numeric base of the input string.
s – Nullterminated string buffer.
 Returns:
0
if successful. Returns:
A negative error code on failure.

int mbedtls_mpi_write_string(const mbedtls_mpi *X, int radix, char *buf, size_t buflen, size_t *olen)
Export an MPI to an ASCII string.
Note
You can call this function with
buflen == 0
to obtain the minimum required buffer size in*olen
. Parameters:
X – The source MPI. This must point to an initialized MPI.
radix – The numeric base of the output string.
buf – The buffer to write the string to. This must be writable buffer of length
buflen
Bytes.buflen – The available size in Bytes of
buf
.olen – The address at which to store the length of the string written, including the final
NULL
byte. This must not beNULL
.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the target buffer
buf
is too small to hold the value ofX
in the desired base. In this case,*olen
is nonetheless updated to contain the size ofbuf
required for a successful call. Returns:
Another negative error code on different kinds of failure.

int mbedtls_mpi_read_file(mbedtls_mpi *X, int radix, FILE *fin)
Read an MPI from a line in an opened file.
The function returns
0
on an empty line.Leading whitespaces are ignored, as is a ‘0x’ prefix for radix
16
.Note
On success, this function advances the file stream to the end of the current line or to EOF.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
radix – The numeric base of the string representation used in the source line.
fin – The input file handle to use. This must not be
NULL
.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if the file read buffer is too small.
 Returns:
Another negative error code on failure.

int mbedtls_mpi_write_file(const char *p, const mbedtls_mpi *X, int radix, FILE *fout)
Export an MPI into an opened file.
 Parameters:
p – A string prefix to emit prior to the MPI data. For example, this might be a label, or “0x” when printing in base
16
. This may beNULL
if no prefix is needed.X – The source MPI. This must point to an initialized MPI.
radix – The numeric base to be used in the emitted string.
fout – The output file handle. This may be
NULL
, in which case the output is written tostdout
.
 Returns:
0
if successful. Returns:
A negative error code on failure.

int mbedtls_mpi_read_binary(mbedtls_mpi *X, const unsigned char *buf, size_t buflen)
Import an MPI from unsigned big endian binary data.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
buf – The input buffer. This must be a readable buffer of length
buflen
Bytes.buflen – The length of the input buffer
buf
in Bytes.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
 Returns:
Another negative error code on different kinds of failure.

int mbedtls_mpi_read_binary_le(mbedtls_mpi *X, const unsigned char *buf, size_t buflen)
Import X from unsigned binary data, little endian.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
buf – The input buffer. This must be a readable buffer of length
buflen
Bytes.buflen – The length of the input buffer
buf
in Bytes.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
 Returns:
Another negative error code on different kinds of failure.

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 – The source MPI. This must point to an initialized MPI.
buf – The output buffer. This must be a writable buffer of length
buflen
Bytes.buflen – The size of the output buffer
buf
in Bytes.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if
buf
isn’t large enough to hold the value ofX
. Returns:
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)
Export X into unsigned binary data, little endian. Always fills the whole buffer, which will end with zeros if the number is smaller.
 Parameters:
X – The source MPI. This must point to an initialized MPI.
buf – The output buffer. This must be a writable buffer of length
buflen
Bytes.buflen – The size of the output buffer
buf
in Bytes.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if
buf
isn’t large enough to hold the value ofX
. Returns:
Another negative error code on different kinds of failure.

int mbedtls_mpi_shift_l(mbedtls_mpi *X, size_t count)
Perform a leftshift on an MPI: X <<= count.
 Parameters:
X – The MPI to shift. This must point to an initialized MPI. The MPI pointed by
X
may be resized to fit the resulting number.count – The number of bits to shift by.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
Another negative error code on different kinds of failure.

int mbedtls_mpi_shift_r(mbedtls_mpi *X, size_t count)
Perform a rightshift on an MPI: X >>= count.
 Parameters:
X – The MPI to shift. This must point to an initialized MPI.
count – The number of bits to shift by.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
Another negative error code on different kinds of failure.

int mbedtls_mpi_cmp_abs(const mbedtls_mpi *X, const mbedtls_mpi *Y)
Compare the absolute values of two MPIs.
 Parameters:
X – The lefthand MPI. This must point to an initialized MPI.
Y – The righthand MPI. This must point to an initialized MPI.
 Returns:
1
ifX
is greater thanY
. Returns:
1
ifX
is lesser thanY
. Returns:
0
ifX
is equal toY
.

int mbedtls_mpi_cmp_mpi(const mbedtls_mpi *X, const mbedtls_mpi *Y)
Compare two MPIs.
 Parameters:
X – The lefthand MPI. This must point to an initialized MPI.
Y – The righthand MPI. This must point to an initialized MPI.
 Returns:
1
ifX
is greater thanY
. Returns:
1
ifX
is lesser thanY
. Returns:
0
ifX
is equal toY
.

int mbedtls_mpi_lt_mpi_ct(const mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned *ret)
Check if an MPI is less than the other in constant time.
 Parameters:
X – The lefthand MPI. This must point to an initialized MPI with the same allocated length as Y.
Y – The righthand MPI. This must point to an initialized MPI with the same allocated length as X.
ret – The result of the comparison:
1
ifX
is less thanY
.0
ifX
is greater than or equal toY
.
 Returns:
0 on success.
 Returns:
MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the allocated length of the two input MPIs is not the same.

int mbedtls_mpi_cmp_int(const mbedtls_mpi *X, mbedtls_mpi_sint z)
Compare an MPI with an integer.
 Parameters:
X – The lefthand MPI. This must point to an initialized MPI.
z – The integer value to compare
X
to.
 Returns:
1
ifX
is greater thanz
. Returns:
1
ifX
is lesser thanz
. Returns:
0
ifX
is equal toz
.

int mbedtls_mpi_add_abs(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
Perform an unsigned addition of MPIs: X = A + B.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
A – The first summand. This must point to an initialized MPI.
B – The second summand. This must point to an initialized MPI.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
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)
Perform an unsigned subtraction of MPIs: X = A  B.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
A – The minuend. This must point to an initialized MPI.
B – The subtrahend. This must point to an initialized MPI.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_NEGATIVE_VALUE if
B
is greater thanA
. Returns:
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)
Perform a signed addition of MPIs: X = A + B.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
A – The first summand. This must point to an initialized MPI.
B – The second summand. This must point to an initialized MPI.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
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)
Perform a signed subtraction of MPIs: X = A  B.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
A – The minuend. This must point to an initialized MPI.
B – The subtrahend. This must point to an initialized MPI.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
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)
Perform a signed addition of an MPI and an integer: X = A + b.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
A – The first summand. This must point to an initialized MPI.
b – The second summand.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
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)
Perform a signed subtraction of an MPI and an integer: X = A  b.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
A – The minuend. This must point to an initialized MPI.
b – The subtrahend.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
Another negative error code on different kinds of failure.

int mbedtls_mpi_mul_mpi(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B)
Perform a multiplication of two MPIs: X = A * B.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
A – The first factor. This must point to an initialized MPI.
B – The second factor. This must point to an initialized MPI.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
Another negative error code on different kinds of failure.

int mbedtls_mpi_mul_int(mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b)
Perform a multiplication of an MPI with an unsigned integer: X = A * b.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
A – The first factor. This must point to an initialized MPI.
b – The second factor.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
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)
Perform a division with remainder of two MPIs: A = Q * B + R.
 Parameters:
Q – The destination MPI for the quotient. This may be
NULL
if the value of the quotient is not needed. This must not alias A or B.R – The destination MPI for the remainder value. This may be
NULL
if the value of the remainder is not needed. This must not alias A or B.A – The dividend. This must point to an initialized MPI.
B – The divisor. This must point to an initialized MPI.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
 Returns:
MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if
B
equals zero. Returns:
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)
Perform a division with remainder of an MPI by an integer: A = Q * b + R.
 Parameters:
Q – The destination MPI for the quotient. This may be
NULL
if the value of the quotient is not needed. This must not alias A.R – The destination MPI for the remainder value. This may be
NULL
if the value of the remainder is not needed. This must not alias A.A – The dividend. This must point to an initialized MPi.
b – The divisor.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
 Returns:
MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if
b
equals zero. Returns:
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)
Perform a modular reduction. R = A mod B.
 Parameters:
R – The destination MPI for the residue value. This must point to an initialized MPI.
A – The MPI to compute the residue of. This must point to an initialized MPI.
B – The base of the modular reduction. This must point to an initialized MPI.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if
B
equals zero. Returns:
MBEDTLS_ERR_MPI_NEGATIVE_VALUE if
B
is negative. Returns:
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)
Perform a modular reduction with respect to an integer. r = A mod b.
 Parameters:
r – The address at which to store the residue. This must not be
NULL
.A – The MPI to compute the residue of. This must point to an initialized MPi.
b – The integer base of the modular reduction.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if
b
equals zero. Returns:
MBEDTLS_ERR_MPI_NEGATIVE_VALUE if
b
is negative. Returns:
Another negative error code on different kinds of failure.

int mbedtls_mpi_exp_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *prec_RR)
Perform a modular exponentiation: X = A^E mod N.
 Parameters:
X – The destination MPI. This must point to an initialized MPI. This must not alias E or N.
A – The base of the exponentiation. This must point to an initialized MPI.
E – The exponent MPI. This must point to an initialized MPI.
N – The base for the modular reduction. This must point to an initialized MPI.
prec_RR – A helper MPI depending solely on
N
which can be used to speedup multiple modular exponentiations for the same value ofN
. This may beNULL
. If it is notNULL
, 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 inprec_RR
for reuse on subsequent calls to this function. Otherwise, the function will assume thatprec_RR
holds the helper value set by a previous call to mbedtls_mpi_exp_mod(), and reuse it.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
MBEDTLS_ERR_MPI_BAD_INPUT_DATA if
N
is negative or even, or ifE
is negative. Returns:
Another negative error code on different kinds of failures.

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 with a number of random bytes.
Note
The bytes obtained from the RNG are interpreted as a bigendian representation of an MPI; this can be relevant in applications like deterministic ECDSA.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
size – The number of random bytes to generate.
f_rng – The RNG function to use. This must not be
NULL
.p_rng – The RNG parameter to be passed to
f_rng
. This may beNULL
iff_rng
doesn’t need a context argument.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
Another negative error code on failure.

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)
Generate a random number uniformly in a range.
This function generates a random number between
min
inclusive andN
exclusive.The procedure complies with RFC 6979 §3.3 (deterministic ECDSA) when the RNG is a suitably parametrized instance of HMAC_DRBG and
min
is1
.Note
There are
N  min
possible outputs. The lower boundmin
can be reached, but the upper boundN
cannot. Parameters:
X – The destination MPI. This must point to an initialized MPI.
min – The minimum value to return. It must be nonnegative.
N – The upper bound of the range, exclusive. In other words, this is one plus the maximum value to return.
N
must be strictly larger thanmin
.f_rng – The RNG function to use. This must not be
NULL
.p_rng – The RNG parameter to be passed to
f_rng
.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
MBEDTLS_ERR_MPI_BAD_INPUT_DATA if
min
orN
is invalid or if they are incompatible. Returns:
MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was unable to find a suitable value within a limited number of attempts. This has a negligible probability if
N
is significantly larger thanmin
, which is the case for all usual cryptographic applications. Returns:
Another negative error code on failure.

int mbedtls_mpi_gcd(mbedtls_mpi *G, const mbedtls_mpi *A, const mbedtls_mpi *B)
Compute the greatest common divisor: G = gcd(A, B)
 Parameters:
G – The destination MPI. This must point to an initialized MPI.
A – The first operand. This must point to an initialized MPI.
B – The second operand. This must point to an initialized MPI.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
Another negative error code on different kinds of failure.

int mbedtls_mpi_inv_mod(mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *N)
Compute the modular inverse: X = A^1 mod N.
 Parameters:
X – The destination MPI. This must point to an initialized MPI.
A – The MPI to calculate the modular inverse of. This must point to an initialized MPI.
N – The base of the modular inversion. This must point to an initialized MPI.
 Returns:
0
if successful. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
MBEDTLS_ERR_MPI_BAD_INPUT_DATA if
N
is less than or equal to one. Returns:
MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if
A
has no modular inverse with respect toN
.

int mbedtls_mpi_is_prime_ext(const mbedtls_mpi *X, int rounds, int (*f_rng)(void*, unsigned char*, size_t), void *p_rng)
MillerRabin primality test.
Warning
If
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, thenrounds
should be at least the half of the security strength of the cryptographic algorithm. On the other hand, ifX
is chosen uniformly or nonadversarially (as is the case when mbedtls_mpi_gen_prime calls this function), thenrounds
can be much lower. Parameters:
X – The MPI to check for primality. This must point to an initialized MPI.
rounds – The number of bases to perform the MillerRabin primality test for. The probability of returning 0 on a composite is at most 2^{2* }.
f_rng – The RNG function to use. This must not be
NULL
.p_rng – The RNG parameter to be passed to
f_rng
. This may beNULL
iff_rng
doesn’t use a context parameter.
 Returns:
0
if successful, i.e.X
is probably prime. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if
X
is not prime. Returns:
Another negative error code on other kinds of failure.

int mbedtls_mpi_gen_prime(mbedtls_mpi *X, size_t nbits, int flags, int (*f_rng)(void*, unsigned char*, size_t), void *p_rng)
Generate a prime number.
 Parameters:
X – The destination MPI to store the generated prime in. This must point to an initialized MPi.
nbits – The required size of the destination MPI in bits. This must be between
3
and MBEDTLS_MPI_MAX_BITS.flags – A mask of flags of type mbedtls_mpi_gen_prime_flag_t.
f_rng – The RNG function to use. This must not be
NULL
.p_rng – The RNG parameter to be passed to
f_rng
. This may beNULL
iff_rng
doesn’t use a context parameter.
 Returns:
0
if successful, in which caseX
holds a probably prime number. Returns:
MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
 Returns:
MBEDTLS_ERR_MPI_BAD_INPUT_DATA if
nbits
is not between3
and MBEDTLS_MPI_MAX_BITS.

int mbedtls_mpi_self_test(int verbose)
Checkup routine.
 Returns:
0 if successful, or 1 if the test failed

struct mbedtls_mpi
 #include <bignum.h>
MPI structure.
Public Members

mbedtls_mpi_uint *private_p
Pointer to limbs.
This may be
NULL
ifn
is 0.

signed short private_s
Sign: 1 if the mpi is negative, 1 otherwise.
The number 0 must be represented with
s = +1
. Although many library functions treat alllimbszero as equivalent to a valid representation of 0 regardless of the sign bit, there are exceptions, so bignum functions and external callers must always sets
to +1 for the number zero.Note that this implies that calloc() or
... = {0}
does not create a valid MPI representation. You must call mbedtls_mpi_init().

unsigned short private_n
Total number of limbs in
p
.

mbedtls_mpi_uint *private_p