diff --git a/include/mbedtls/bignum.h b/include/mbedtls/bignum.h
index 40cfab49a..d8de4a375 100644
--- a/include/mbedtls/bignum.h
+++ b/include/mbedtls/bignum.h
@@ -186,96 +186,111 @@ typedef struct mbedtls_mpi
mbedtls_mpi;
/**
- * \brief Initialize one MPI (make internal references valid)
- * This just makes it ready to be set or freed,
+ * \brief Initialize an MPI context.
+ *
+ * This makes the MPI ready to be set or freed,
* but does not define a value for the MPI.
*
- * \param X One MPI to initialize.
+ * \param X The MPI context to initialize. Must not be \c NULL.
*/
void mbedtls_mpi_init( mbedtls_mpi *X );
/**
- * \brief Unallocate one MPI
+ * \brief Clear an MPI context.
*
- * \param X One MPI to unallocate.
+ * \param X The MPI context to be cleared. May be \c NULL,
+ * in which case this function is a no-op.
*/
void mbedtls_mpi_free( mbedtls_mpi *X );
/**
- * \brief Enlarge to the specified number of limbs
+ * \brief Enlarge an MPI to the specified number of limbs.
*
- * This function does nothing if the MPI is already large enough.
+ * \note This function does nothing if the MPI is
+ * already large enough.
*
- * \param X MPI to grow
- * \param nblimbs The target number of limbs
+ * \param X The MPI to grow. Must point to an initialized MPI.
+ * \param nblimbs The target number of limbs.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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 );
/**
- * \brief Resize down, keeping at least the specified number of limbs
+ * \brief Resize down, keeping at least the specified number of limbs.
*
* If \c X is smaller than \c nblimbs, it is resized up
* instead.
*
- * \param X MPI to shrink
- * \param nblimbs The minimum number of limbs to keep
+ * \param X The MPI to shrink. Must point to an initialized MPI.
+ * \param nblimbs The minimum number of limbs to keep.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \return \c 0 if successful.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
* (this 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 );
/**
- * \brief Copy the contents of Y into X
+ * \brief Make a copy of an MPI.
*
- * \param X Destination MPI. It is enlarged if necessary.
- * \param Y Source MPI.
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param Y The source MPI.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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 );
/**
- * \brief Swap the contents of X and Y
+ * \brief Swap the contents of two MPIs.
*
- * \param X First MPI value
- * \param Y Second MPI value
+ * \param X The first MPI. Must not be \c NULL.
+ * \param Y The second MPI. Must not be \c NULL.
*/
void mbedtls_mpi_swap( mbedtls_mpi *X, mbedtls_mpi *Y );
/**
- * \brief Safe conditional assignement X = Y if assign is 1
+ * \brief Safe conditional copy of MPI which doesn't
+ * reveal whether the conditional was true or not.
*
- * \param X MPI to conditionally assign to
- * \param Y Value to be assigned
- * \param assign 1: perform the assignment, 0: keep X's original value
- *
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ * \param X The MPI to conditionally assign to.
+ * \param Y The MPI to be assigned from.
+ * \param assign The conditional 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 );
+ * `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 );
/**
- * \brief Safe conditional swap X <-> Y if swap is 1
+ * \brief Safe conditional swap which doesn't
+ * reveal whether the conditional was true or not.
*
- * \param X First mbedtls_mpi value
- * \param Y Second mbedtls_mpi value
- * \param assign 1: perform the swap, 0: keep X and Y's original values
- *
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
+ * \param X The first MPI.
+ * \param Y The second MPI.
+ * \param assign The conditional 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 );
@@ -283,415 +298,506 @@ int mbedtls_mpi_safe_cond_assign( mbedtls_mpi *X, const mbedtls_mpi *Y, unsigned
* 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 assign );
/**
- * \brief Set value from integer
+ * \brief Store integer value in MPI.
*
- * \param X MPI to set
- * \param z Value to use
+ * \param X The MPI to set.
+ * \param z The value to use.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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 );
/**
- * \brief Get a specific bit from X
+ * \brief Get a specific bit from an MPI.
*
- * \param X MPI to use
- * \param pos Zero-based index of the bit in X
+ * \param X The MPI to query.
+ * \param pos Zero-based index of the bit to query.
*
- * \return Either a 0 or a 1
+ * \return \c 0 or \c 1 on success, depending on whether bit \c pos
+ * of \c X is unset resp. set.
+ * \return A negative error code on failure.
*/
int mbedtls_mpi_get_bit( const mbedtls_mpi *X, size_t pos );
/**
- * \brief Set a bit of X to a specific value of 0 or 1
+ * \brief Modify a specific bit in an MPI.
*
- * \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
+ * \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 MPI to use
- * \param pos Zero-based index of the bit in X
- * \param val The value to set the bit to (0 or 1)
+ * \param X The MPI to modify.
+ * \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 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
+ * \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 );
/**
- * \brief Return the number of zero-bits before the least significant
- * '1' bit
+ * \brief Return the number of zero-bits before the
+ * least significant 1-bit
*
- * Note: Thus also the zero-based index of the least significant '1' bit
+ * \note This is the same as the zero-based index of
+ * the least significant '1' bit.
*
- * \param X MPI to use
+ * \param X The MPI to query.
+ *
+ * \return The number of zero-bits before the least significant
+ * 1-bit in \p X.
*/
size_t mbedtls_mpi_lsb( const mbedtls_mpi *X );
/**
* \brief Return the number of bits up to and including the most
- * significant '1' bit'
+ * significant 1-bit.
*
- * Note: Thus also the one-based index of the most significant '1' bit
+ * * \note This is same as the one-based index of the most
+ * significant 1-bit.
*
- * \param X MPI to use
+ * \param X The MPI to query. Must point to an initialized MPI.
+ *
+ * \return The number of bits up to and including the most
+ * significant 1-bit.
*/
size_t mbedtls_mpi_bitlen( const mbedtls_mpi *X );
/**
- * \brief Return the total size in bytes
+ * \brief Return the total size an MPI value in bytes.
*
- * \param X MPI to use
+ * \param X The MPI to use. 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 zero-bytes.
+ *
+ * \return The least number of bytes capable of storing
+ * the absolute value of \p X.
*/
size_t mbedtls_mpi_size( const mbedtls_mpi *X );
/**
- * \brief Import from an ASCII string
+ * \brief Import an MPI from an ASCII string.
*
- * \param X Destination MPI
- * \param radix Input numeric base
- * \param s Null-terminated string buffer
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param radix The numeric base of the input string.
+ * \param s Null-terminated string buffer.
*
- * \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
+ * \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 );
/**
- * \brief Export into an ASCII string
+ * \brief Export an MPI into an ASCII string.
*
- * \param X Source MPI
- * \param radix Output numeric base
- * \param buf Buffer to write the string to
- * \param buflen Length of buf
- * \param olen Length of the string written, including final NUL byte
+ * \param X The source MPI. Must point to an initialized MPI.
+ * \param radix The numeric base of the output string.
+ * \param buf Buffer to write the string to. Must be writable of
+ * length \p buflen Bytes. May be \c NULL if `buflen == 0`.
+ * \param buflen The available size in Bytes of \p buf.
+ * \param olen Address at which to store the length of the string written,
+ * including final \c NULL byte. Must not be \c NULL.
*
- * \return 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`.
*
- * \note 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 );
#if defined(MBEDTLS_FS_IO)
/**
- * \brief Read MPI from a line in an opened file
+ * \brief Read an MPI from a line in an opened file.
*
- * \param X Destination MPI
- * \param radix Input numeric base
- * \param fin Input file handle
- *
- * \return 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
+ * \param X The destination MPI. 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. 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 0 on an empty line.
+ * The function returns \c 0 on an empty line.
*
* Leading whitespaces are ignored, as is a
- * '0x' prefix for radix 16.
+ * '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 );
/**
- * \brief Write X into an opened file, or stdout if fout is NULL
+ * \brief Export an MPI into an opened file.
*
- * \param p Prefix, can be NULL
- * \param X Source MPI
- * \param radix Output numeric base
- * \param fout Output file handle (can be NULL)
+ * \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 16. May be \c NULL if no prefix
+ * is needed.
+ * \param X The source MPI. Must point to an initialized MPI.
+ * \param radix The numeric base to be used in the emitted string.
+ * \param fout The output file handle. May be \c NULL, in which case
+ * the output is written to `stdout`.
*
- * \return 0 if successful, or a MBEDTLS_ERR_MPI_XXX error code
- *
- * \note Set fout == NULL to print X on the console.
+ * \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 mbedtls_mpi_write_file( const char *p, const mbedtls_mpi *X,
+ int radix, FILE *fout );
#endif /* MBEDTLS_FS_IO */
/**
- * \brief Import X from unsigned binary data, big endian
+ * \brief Import an MPI from unsigned big endian binary data.
*
- * \param X Destination MPI
- * \param buf Input buffer
- * \param buflen Input buffer size
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param buf The input buffer. Must be a readable buffer of length
+ * \p buflen Bytes.
+ * \param buflen The length of the input buffer \p p in Bytes.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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 *buf, size_t buflen );
+int mbedtls_mpi_read_binary( mbedtls_mpi *X, const unsigned char *buf,
+ size_t buflen );
/**
- * \brief Export X into unsigned binary data, big endian.
- * Always fills the whole buffer, which will start with zeros
- * if the number is smaller.
+ * \brief Export an MPI into unsigned big endian binary data
+ * of fixed size.
*
- * \param X Source MPI
- * \param buf Output buffer
- * \param buflen Output buffer size
+ * \param X The source MPI. Must point to an initialized MPI.
+ * \param buf The output buffer. Must be a writable buffer of length
+ * \p buflen Bytes.
+ * \param buflen The size of the output buffer \p buf in Bytes.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if buf isn't large enough
+ * \return \c 0 if successful.
+ * \return #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
+ * large enoguh 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 );
+int mbedtls_mpi_write_binary( const mbedtls_mpi *X, unsigned char *buf,
+ size_t buflen );
/**
- * \brief Left-shift: X <<= count
+ * \brief Perform a left-shift on an MPI: X <<= count
*
- * \param X MPI to shift
- * \param count Amount to shift
+ * \param X The MPI to shift. Must point to an initialized MPI.
+ * \param count The amount to shift, in bits.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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_shift_l( mbedtls_mpi *X, size_t count );
/**
- * \brief Right-shift: X >>= count
+ * \brief Perform a right-shift on an MPI: X >>= count
*
- * \param X MPI to shift
- * \param count Amount to shift
+ * \param X The MPI to shift. Must point to an initialized MPI.
+ * \param count The amount to shift, in bits.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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_shift_r( mbedtls_mpi *X, size_t count );
/**
- * \brief Compare unsigned values
+ * \brief Compare the absolute values of two MPIs.
*
- * \param X Left-hand MPI
- * \param Y Right-hand MPI
+ * \param X The left-hand MPI. Must point to an initialized MPI.
+ * \param Y The right-hand MPI. Must point to an initialized MPI.
*
- * \return 1 if |X| is greater than |Y|,
- * -1 if |X| is lesser than |Y| or
- * 0 if |X| is equal to |Y|
+ * \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 than `|Y|`.
*/
int mbedtls_mpi_cmp_abs( const mbedtls_mpi *X, const mbedtls_mpi *Y );
/**
- * \brief Compare signed values
+ * \brief Compare two MPIs.
*
- * \param X Left-hand MPI
- * \param Y Right-hand MPI
+ * \param X The left-hand MPI. Must point to an initialized MPI.
+ * \param Y The right-hand MPI. Must point to an initialized MPI.
*
- * \return 1 if X is greater than Y,
- * -1 if X is lesser than Y or
- * 0 if X is equal to Y
+ * \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 than `Y`.
*/
int mbedtls_mpi_cmp_mpi( const mbedtls_mpi *X, const mbedtls_mpi *Y );
/**
- * \brief Compare signed values
+ * \brief Compare an MPI with an integer.
*
- * \param X Left-hand MPI
- * \param z The integer value to compare to
+ * \param X The left-hand MPI. Must point to an initialized MPI.
+ * \param z The integer value to compare \p X to.
*
- * \return 1 if X is greater than z,
- * -1 if X is lesser than z or
- * 0 if X is equal to z
+ * \return \c 1 if `X` is greater than `z`.
+ * \return \c -1 if `X` is lesser than `z`.
+ * \return \c 0 if `X` is equal than `z`.
*/
int mbedtls_mpi_cmp_int( const mbedtls_mpi *X, mbedtls_mpi_sint z );
/**
- * \brief Unsigned addition: X = |A| + |B|
+ * \brief Perform an unsigned addition of MPIs: X = |A| + |B|
*
- * \param X Destination MPI
- * \param A Left-hand MPI
- * \param B Right-hand MPI
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param A The first summand. Must point to an initialized MPI.
+ * \param B The second summand. Must point to an initialized MPI.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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 mbedtls_mpi_add_abs( mbedtls_mpi *X, const mbedtls_mpi *A,
+ const mbedtls_mpi *B );
/**
- * \brief Unsigned subtraction: X = |A| - |B|
+ * \brief Perform an unsigned subtraction of MPIs: X = |A| - |B|
*
- * \param X Destination MPI
- * \param A Left-hand MPI
- * \param B Right-hand MPI
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param A The minuend. Must point to an initialized MPI.
+ * \param B The subtrahend. 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.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_NEGATIVE_VALUE if B is greater than A
*/
-int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
+int mbedtls_mpi_sub_abs( mbedtls_mpi *X, const mbedtls_mpi *A,
+ const mbedtls_mpi *B );
/**
- * \brief Signed addition: X = A + B
+ * \brief Perform a signed addition of MPIs: X = A + B
*
- * \param X Destination MPI
- * \param A Left-hand MPI
- * \param B Right-hand MPI
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param A The first summand. Must point to an initialized MPI.
+ * \param B The second summand. Must point to an initialized MPI.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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 mbedtls_mpi_add_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
+ const mbedtls_mpi *B );
/**
- * \brief Signed subtraction: X = A - B
+ * \brief Perform a signed subtraction of MPIs: X = A - B
*
- * \param X Destination MPI
- * \param A Left-hand MPI
- * \param B Right-hand MPI
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param A The minuend. Must point to an initialized MPI.
+ * \param B The subtrahend. Must point to an initialized MPI.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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 mbedtls_mpi_sub_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
+ const mbedtls_mpi *B );
/**
- * \brief Signed addition: X = A + b
+ * \brief Perform a signed addition of an MPI and an integer: X = A + b
*
- * \param X Destination MPI
- * \param A Left-hand MPI
- * \param b The integer value to add
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param A The first summand. Must point to an initialized MPI.
+ * \param b The second summand.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_sint b );
+int mbedtls_mpi_add_int( mbedtls_mpi *X, const mbedtls_mpi *A,
+ mbedtls_mpi_sint b );
/**
- * \brief Signed subtraction: X = A - b
+ * \brief Perform a signed subtraction of an MPI and an integer:
+ * X = A - b
*
- * \param X Destination MPI
- * \param A Left-hand MPI
- * \param b The integer value to subtract
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param A The minuend. Must point to an initialized MPI.
+ * \param B The subtrahend.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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 );
+int mbedtls_mpi_sub_int( mbedtls_mpi *X, const mbedtls_mpi *A,
+ mbedtls_mpi_sint b );
/**
- * \brief Baseline multiplication: X = A * B
+ * \brief Perform a multiplication of two MPIs: X = A * B
*
- * \param X Destination MPI
- * \param A Left-hand MPI
- * \param B Right-hand MPI
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param A The first factor. Must point to an initialized MPI.
+ * \param B The second factor. 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.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
-int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *B );
+int mbedtls_mpi_mul_mpi( mbedtls_mpi *X, const mbedtls_mpi *A,
+ const mbedtls_mpi *B );
/**
- * \brief Baseline multiplication: X = A * b
+ * \brief Perform a multiplication of an MPI with an unsigned integer:
+ * X = A * b
*
- * \param X Destination MPI
- * \param A Left-hand MPI
- * \param b The unsigned integer value to multiply with
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param A The first factor. Must point to an initialized MPI.
+ * \param b The second factor.
*
- * \note b is unsigned
+ * \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.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
*/
-int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A, mbedtls_mpi_uint b );
+int mbedtls_mpi_mul_int( mbedtls_mpi *X, const mbedtls_mpi *A,
+ mbedtls_mpi_uint b );
/**
- * \brief Division by mbedtls_mpi: A = Q * B + R
+ * \brief Perform a division with remainder of two MPIs:
+ * A = Q * B + R
*
- * \param Q Destination MPI for the quotient
- * \param R Destination MPI for the rest value
- * \param A Left-hand MPI
- * \param B Right-hand MPI
+ * \param Q The destination MPI for the quotient.
+ * May be \c NULL is the value of the quotient is not needed.
+ * \param R The destination MPI for the remainder value.
+ * May be \c NULL if the value of the remainder is not needed.
+ * \param A The divident. Must point to an initialized MPi.
+ * \param B The divisor. Must point to an initialized MPI.
*
- * \return 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.
+ * \return \c 0 if successful.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
+ * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if `B == 0`.
+ * \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 mbedtls_mpi_div_mpi( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
+ const mbedtls_mpi *B );
/**
- * \brief Division by int: A = Q * b + R
+ * \brief Perform a division with remainder of an MPI by an integer:
+ * A = Q * b + R
*
- * \param Q Destination MPI for the quotient
- * \param R Destination MPI for the rest value
- * \param A Left-hand MPI
- * \param b Integer to divide by
+ * \param Q The destination MPI for the quotient.
+ * May be \c NULL is the value of the quotient is not needed.
+ * \param R The destination MPI for the remainder value.
+ * May be \c NULL if the value of the remainder is not needed.
+ * \param A The divident. Must point to an initialized MPi.
+ * \param b The divisor.
*
- * \return 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.
+ * \return \c 0 if successful.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed.
+ * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if `b == 0`.
+ * \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 );
+int mbedtls_mpi_div_int( mbedtls_mpi *Q, mbedtls_mpi *R, const mbedtls_mpi *A,
+ mbedtls_mpi_sint b );
/**
- * \brief Modulo: R = A mod B
+ * \brief Perform a modular reduction. R = A mod B
*
- * \param R Destination MPI for the rest value
- * \param A Left-hand MPI
- * \param B Right-hand MPI
+ * \param R The destination MPI for the residue value.
+ * Must point to an initialized MPI.
+ * \param A The MPI to compute the residue of.
+ * Must point to an initialized MPI.
+ * \param B The base of the modular reduction.
+ * 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 `B == 0`.
+ * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if `B < 0`.
+ * \return Another negative error code on different kinds of failure.
*
- * \return 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 );
+int mbedtls_mpi_mod_mpi( mbedtls_mpi *R, const mbedtls_mpi *A,
+ const mbedtls_mpi *B );
/**
- * \brief Modulo: r = A mod b
+ * \brief Perform a modular reduction with respect to an integer.
+ * r = A mod b
*
- * \param r Destination mbedtls_mpi_uint
- * \param A Left-hand MPI
- * \param b Integer to divide by
+ * \param r The address at which to store the residue.
+ * Must not be \c NULL.
+ * \param A The MPI to compute the residue of.
+ * Must point to an initialized MPi.
+ * \param b The integer base of the modular reduction.
*
- * \return 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
+ * \return \c 0 if successful.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
+ * \return #MBEDTLS_ERR_MPI_DIVISION_BY_ZERO if `b == 0`.
+ * \return #MBEDTLS_ERR_MPI_NEGATIVE_VALUE if `b < 0`.
+ * \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 );
+int mbedtls_mpi_mod_int( mbedtls_mpi_uint *r, const mbedtls_mpi *A,
+ mbedtls_mpi_sint b );
/**
- * \brief Sliding-window exponentiation: X = A^E mod N
+ * \brief Perform a sliding-window exponentiation: X = A^E mod N
*
- * \param X Destination MPI
- * \param A Left-hand MPI
- * \param E Exponent MPI
- * \param N Modular MPI
- * \param _RR Speed-up MPI used for recalculations
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param A The base of the exponentiation.
+ * Must point to an initialized MPI.
+ * \param E The exponent MPI. Must point to an initialized MPI.
+ * \param N The base for the modular reduction. 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. May be \c NULL. If it is not \c NULL, it must point
+ * an initialized MPI. If it is freshly initialized, i.e. not
+ * 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 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
+ * \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.
*
- * \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_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi *E, const mbedtls_mpi *N, mbedtls_mpi *_RR );
+int mbedtls_mpi_exp_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
+ const mbedtls_mpi *E, const mbedtls_mpi *N,
+ mbedtls_mpi *_RR );
/**
- * \brief Fill an MPI X with size bytes of random
+ * \brief Fill an MPI with a number of random bytes.
*
- * \param X Destination MPI
- * \param size Size in bytes
- * \param f_rng RNG function
- * \param p_rng RNG parameter
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param size The number of random bytes to generate.
+ * \param f_rng The RNG function to use. Must not be \c NULL.
+ * \param p_rng The RNG parameter to be passed to \p f_rng. May be \c NULL
+ * if \p f_rng doesn't need a context argument.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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 PRNG are interpreted
+ * \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.
*/
@@ -700,30 +806,36 @@ int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
void *p_rng );
/**
- * \brief Greatest common divisor: G = gcd(A, B)
+ * \brief Compute the greatest common divisor: G = gcd(A, B)
*
- * \param G Destination MPI
- * \param A Left-hand MPI
- * \param B Right-hand MPI
+ * \param G The destination MPI. Must point to an initialized MPI.
+ * \param A The first operand. Must point to an initialized MPI.
+ * \param A The second operand. Must point to an initialized MPI.
*
- * \return 0 if successful,
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed
+ * \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 mbedtls_mpi_gcd( mbedtls_mpi *G, const mbedtls_mpi *A,
+ const mbedtls_mpi *B );
/**
- * \brief Modular inverse: X = A^-1 mod N
+ * \brief Compute the modular inverse: X = A^-1 mod N
*
- * \param X Destination MPI
- * \param A Left-hand MPI
- * \param N Right-hand MPI
+ * \param X The destination MPI. Must point to an initialized MPI.
+ * \param A The MPI to calculate the modular inverse of. Must point
+ * to an initialized MPI.
+ * \param N The base of the modular inversion. Must point to an
+ * initialized MPI.
*
- * \return 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.
+ * \return \c 0 if successful.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
+ * \return #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if `N <= 1`.
+ * \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 mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A,
+ const mbedtls_mpi *N );
#if !defined(MBEDTLS_DEPRECATED_REMOVED)
#if defined(MBEDTLS_DEPRECATED_WARNING)
@@ -732,19 +844,22 @@ int mbedtls_mpi_inv_mod( mbedtls_mpi *X, const mbedtls_mpi *A, const mbedtls_mpi
#define MBEDTLS_DEPRECATED
#endif
/**
- * \brief Miller-Rabin primality test with error probability of
- * 2-80
+ * \brief Perform a Miller-Rabin primality test with error
+ * probability of 2-80.
*
* \deprecated Superseded by mbedtls_mpi_is_prime_ext() which allows
* specifying the number of Miller-Rabin rounds.
*
- * \param X MPI to check
- * \param f_rng RNG function
- * \param p_rng RNG parameter
+ * \param X The MPI to check for primality.
+ * Must point to an initialized MPI.
+ * \param f_rng The RNG function to use. Must not be \c NULL.
+ * \param p_rng The RNG parameter to be passed to \p f_rng.
+ * May be \c NULL if \p f_rng doesn't use a context parameter.
*
- * \return 0 if successful (probably prime),
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
- * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
+ * \return \c 0 if successful, i.e. \p X is probably prime.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
+ * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
+ * \return Another negative error code on other kinds of failure.
*/
MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
int (*f_rng)(void *, unsigned char *, size_t),
@@ -764,16 +879,19 @@ MBEDTLS_DEPRECATED int mbedtls_mpi_is_prime( const mbedtls_mpi *X,
* case when mbedtls_mpi_gen_prime calls this function), then
* \p rounds can be much lower.
*
- * \param X MPI to check
- * \param rounds Number of bases to perform Miller-Rabin primality test for.
- * The probability of returning 0 on a composite is at most
- * 2-2*\p rounds.
- * \param f_rng RNG function
- * \param p_rng RNG parameter
+ * \param X The MPI to check for primality.
+ * 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. Must not be \c NULL.
+ * \param p_rng The RNG parameter to be passed to \p f_rng.
+ * May be \c NULL if \p f_rng doesn't use a context parameter.
*
- * \return 0 if successful (probably prime),
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
- * MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if X is not prime
+ * \return \c 0 if successful, i.e. \p X is probably prime.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
+ * \return #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if \p X is not prime.
+ * \return Another negative error code on other kinds of failure.
*/
int mbedtls_mpi_is_prime_ext( const mbedtls_mpi *X, int rounds,
int (*f_rng)(void *, unsigned char *, size_t),
@@ -790,18 +908,22 @@ typedef enum {
} mbedtls_mpi_gen_prime_flag_t;
/**
- * \brief Prime number generation
+ * \brief Generate a prime number.
*
- * \param X Destination MPI
- * \param nbits Required size of X in bits
- * ( 3 <= nbits <= MBEDTLS_MPI_MAX_BITS )
- * \param flags Mask of flags of type #mbedtls_mpi_gen_prime_flag_t
- * \param f_rng RNG function
- * \param p_rng RNG parameter
+ * \param X The destination MPI to store the generated prime in.
+ * Must point to an initialized MPi.
+ * \param nbits The required size of the destination MPI in bits.
+ * 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. Must not be \c NULL.
+ * \param p_rng The RNG parameter to be passed to \p f_rng.
+ * May be \c NULL if \p f_rng doesn't use a context parameter.
*
- * \return 0 if successful (probably prime),
- * MBEDTLS_ERR_MPI_ALLOC_FAILED if memory allocation failed,
- * MBEDTLS_ERR_MPI_BAD_INPUT_DATA if nbits is < 3
+ * \return \c 0 if successful, in which case \p X holds a probably
+ * probably prime number.
+ * \return #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory 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),