diff --git a/library/bignum_mod.h b/library/bignum_mod.h
index f8c71d0..d2f6cee 100644
--- a/library/bignum_mod.h
+++ b/library/bignum_mod.h
@@ -220,29 +220,29 @@
 /** \brief  Multiply two residues, returning the residue modulo the specified
  *          modulus.
  *
- * \note Currenty handles the case when `m->int_rep` is
+ * \note Currently handles the case when `N->int_rep` is
  * MBEDTLS_MPI_MOD_REP_MONTGOMERY.
  *
- * The size of the operation is determined by \p N. \p A and \p B must have
- * the same number of limbs as \p N.
+ * The size of the operation is determined by \p N. \p A, \p B and \p X must
+ * all be associated with the modulus \p N and must all have the same number
+ * of limbs as \p N.
  *
  * \p X may be aliased to \p A or \p B, or even both, but may not overlap
  * either otherwise. They may not alias \p N (since they must be in canonical
  * form, they cannot == \p N).
  *
- * \param[out] X        The address of the result MPI.
- *                      This must be initialized. Must have enough limbs to
- *                      store the full value of the result.
+ * \param[out] X        The address of the result MPI. Must have the same
+ *                      number of limbs as \p N.
  *                      On successful completion, \p X contains the result of
  *                      the multiplication `A * B * R^-1` mod N where
- *                      `R = 2^(biL *N->limbs)`.
- * \param[in]  A        The address of the first MPI. This must be initialized.
- * \param[in]  B        The address of the second MPI. This must be initialized.
+ *                      `R = 2^(biL * N->limbs)`.
+ * \param[in]  A        The address of the first MPI.
+ * \param[in]  B        The address of the second MPI.
  * \param[in]  N        The address of the modulus. Used to perform a modulo
  *                      operation on the result of the multiplication.
  *
  * \return      \c 0 if successful.
- * \return      #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if all the parameters does not
+ * \return      #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if all the parameters do not
  *              have the same number of limbs or \p N is invalid.
  * \return      #MBEDTLS_ERR_MPI_ALLOC_FAILED on memory-allocation failure.
  */