diff --git a/library/bignum_mod_raw.h b/library/bignum_mod_raw.h
index f8638a63ed..05c46b96b4 100644
--- a/library/bignum_mod_raw.h
+++ b/library/bignum_mod_raw.h
@@ -173,21 +173,31 @@ void mbedtls_mpi_mod_raw_sub( mbedtls_mpi_uint *X,
 /** \brief  Multiply two MPIs, returning the residue modulo the specified
  *          modulus.
  *
- * 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.
+ * \note Currently handles the case when `m->int_rep` is
+ * MBEDTLS_MPI_MOD_REP_MONTGOMERY.
+ *
+ * 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.
+ * 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[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.
+ * \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.
+ * \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 subtraction.
- * \param[in]  T        The address of an MPI used by the multiplication
- *                      as a temp variable.
+ *                      operation on the result of the multiplication.
+ * \param[in,out] T     Temporary storage of size at least 2 * AN_limbs + 1
+ *                      limbs. Its initial content is unused and
+ *                      its final content is indeterminate.
+ *                      It must not alias or otherwise overlap any of the
+ *                      other parameters.
  */
 void mbedtls_mpi_mod_raw_mul( mbedtls_mpi_uint *X,
                               const mbedtls_mpi_uint *A,