diff --git a/library/bignum_core.c b/library/bignum_core.c
index c015fc7..606765a 100644
--- a/library/bignum_core.c
+++ b/library/bignum_core.c
@@ -129,7 +129,7 @@
     return( mpi_bigendian_to_host_c( x ) );
 }
 
-void mbedtls_mpi_core_bigendian_to_host( mbedtls_mpi_uint * const X,
+void mbedtls_mpi_core_bigendian_to_host( mbedtls_mpi_uint *X,
                                          size_t limbs )
 {
     mbedtls_mpi_uint *cur_limb_left;
diff --git a/library/bignum_core.h b/library/bignum_core.h
index 397f79a..8266cec 100644
--- a/library/bignum_core.h
+++ b/library/bignum_core.h
@@ -44,8 +44,8 @@
  *
  * \note This function returns 0 if all the limbs of \p X are 0.
  *
- * \param X     The address of the MPI.
- * \param nx    The number of limbs of \p X.
+ * \param[in] X     The address of the MPI.
+ * \param nx        The number of limbs of \p X.
  *
  * \return      The number of bits in \p X.
  */
@@ -54,10 +54,10 @@
 /** Convert a big-endian byte array aligned to the size of mbedtls_mpi_uint
  * into the storage form used by mbedtls_mpi.
  *
- * \param X     The address of the MPI.
- * \param limbs The number of limbs of \p X.
+ * \param[in,out] X     The address of the MPI.
+ * \param limbs         The number of limbs of \p X.
  */
-void mbedtls_mpi_core_bigendian_to_host( mbedtls_mpi_uint * const X,
+void mbedtls_mpi_core_bigendian_to_host( mbedtls_mpi_uint *X,
                                          size_t limbs );
 
 /** Import X from unsigned binary data, little endian.
@@ -65,10 +65,10 @@
  * The MPI needs to have enough limbs to store the full value (including any
  * most significant zero bytes in the input).
  *
- * \param X      The address of the MPI.
- * \param nx     The number of limbs of \p X.
- * \param buf    The input buffer to import from.
- * \param buflen The length in bytes of \p buf.
+ * \param[out] X    The address of the MPI.
+ * \param nx        The number of limbs of \p X.
+ * \param[in] buf   The input buffer to import from.
+ * \param buflen    The length in bytes of \p buf.
  *
  * \return       \c 0 if successful.
  * \return       #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p X isn't
@@ -84,12 +84,12 @@
  * The MPI needs to have enough limbs to store the full value (including any
  * most significant zero bytes in the input).
  *
- * \param X      The address of the MPI.
- *               May only be #NULL if \nx is 0 and \p buflen is 0.
- * \param nx     The number of limbs of \p X.
- * \param buf    The input buffer to import from.
- *               May only be #NULL if \p buflen is 0.
- * \param buflen The length in bytes of \p buf.
+ * \param[out] X    The address of the MPI.
+ *                  May only be #NULL if \nx is 0 and \p buflen is 0.
+ * \param nx        The number of limbs of \p X.
+ * \param[in] buf   The input buffer to import from.
+ *                  May only be #NULL if \p buflen is 0.
+ * \param buflen    The length in bytes of \p buf.
  *
  * \return       \c 0 if successful.
  * \return       #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p X isn't
@@ -106,10 +106,10 @@
  *       value held in \p X fits in the buffer (that is, if enough of the most
  *       significant bytes of \p X are 0).
  *
- * \param X      The address of the MPI.
- * \param nx     The number of limbs of \p X.
- * \param buf    The output buffer to export to.
- * \param buflen The length in bytes of \p buf.
+ * \param[in] X     The address of the MPI.
+ * \param nx        The number of limbs of \p X.
+ * \param[out] buf  The output buffer to export to.
+ * \param buflen    The length in bytes of \p buf.
  *
  * \return       \c 0 if successful.
  * \return       #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
@@ -126,10 +126,10 @@
  *       value held in \p X fits in the buffer (that is, if enough of the most
  *       significant bytes of \p X are 0).
  *
- * \param X      The address of the MPI.
- * \param nx     The number of limbs of \p X.
- * \param buf    The output buffer to export to.
- * \param buflen The length in bytes of \p buf.
+ * \param[in] X     The address of the MPI.
+ * \param nx        The number of limbs of \p X.
+ * \param[out] buf  The output buffer to export to.
+ * \param buflen    The length in bytes of \p buf.
  *
  * \return       \c 0 if successful.
  * \return       #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
diff --git a/library/bignum_mod.c b/library/bignum_mod.c
index 4382bf8..5678ca0 100644
--- a/library/bignum_mod.c
+++ b/library/bignum_mod.c
@@ -43,7 +43,7 @@
 #include "constant_time_internal.h"
 
 int mbedtls_mpi_mod_residue_setup( mbedtls_mpi_mod_residue *r,
-                                   mbedtls_mpi_mod_modulus *m,
+                                   const mbedtls_mpi_mod_modulus *m,
                                    mbedtls_mpi_uint *p,
                                    size_t pn )
 {
diff --git a/library/bignum_mod.h b/library/bignum_mod.h
index d2ba73e..3fbedbf 100644
--- a/library/bignum_mod.h
+++ b/library/bignum_mod.h
@@ -67,22 +67,23 @@
 
 /** Setup a residue structure.
  *
- * \param r     The address of residue to setup. The size is determined by \p m.
- *              (In particular, it must have at least as many limbs as the
- *              modulus \p m.)
- * \param m     The address of the modulus related to \p r.
- * \param p     The address of the limb array storing the value of \p r. The
- *              memory pointed to by \p p will be used by \p r and must not be
- *              modified in any way until after mbedtls_mpi_mod_residue_release()
- *              is called.
- * \param pn    The number of limbs of \p p.
+ * \param[out] r    The address of residue to setup. The size is determined by
+ *                  \p m.
+ *                  (In particular, it must have at least as many limbs as the
+ *                  modulus \p m.)
+ * \param[in] m     The address of the modulus related to \p r.
+ * \param[in] p     The address of the limb array storing the value of \p r.
+ *                  The memory pointed to by \p p will be used by \p r and must
+ *                  not be modified in any way until after
+ *                  mbedtls_mpi_mod_residue_release() is called.
+ * \param pn        The number of limbs of \p p.
  *
  * \return      \c 0 if successful.
  * \return      #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p pn is less than the limbs
  *              in \p m or if \p p is not less than \p m.
  */
 int mbedtls_mpi_mod_residue_setup( mbedtls_mpi_mod_residue *r,
-                                   mbedtls_mpi_mod_modulus *m,
+                                   const mbedtls_mpi_mod_modulus *m,
                                    mbedtls_mpi_uint *p,
                                    size_t pn );
 
@@ -94,22 +95,22 @@
  * This function invalidates \p r and it must not be used until after
  * mbedtls_mpi_mod_residue_setup() is called on it again.
  *
- * \param r     The address of residue to release.
+ * \param[out] r     The address of residue to release.
  */
 void mbedtls_mpi_mod_residue_release( mbedtls_mpi_mod_residue *r );
 
 /** Initialize a modulus structure.
  *
- * \param m     The address of a modulus.
+ * \param[out] m     The address of a modulus.
  */
 void mbedtls_mpi_mod_modulus_init( mbedtls_mpi_mod_modulus *m );
 
 /** Setup a modulus structure.
  *
- * \param m         The address of the modulus structure to populate.
- * \param p         The address of the limb array storing the value of \p m. The
- *                  memory pointed to by \p p will be used by \p m and must not
- *                  be modified in any way until after
+ * \param[out] m    The address of the modulus structure to populate.
+ * \param[in] p     The address of the limb array storing the value of \p m.
+ *                  The memory pointed to by \p p will be used by \p m and must
+ *                  not be modified in any way until after
  *                  mbedtls_mpi_mod_modulus_free() is called.
  * \param pn        The number of limbs of \p p.
  * \param ext_rep   The external representation to be used for residues
@@ -135,7 +136,7 @@
  *          mbedtls_mpi_mod_modulus_setup() only removes the reference to it,
  *          making it safe to free or to use it again.
  *
- * \param m     The address of a modulus.
+ * \param[in,out] m     The address of a modulus.
  */
 void mbedtls_mpi_mod_modulus_free( mbedtls_mpi_mod_modulus *m );
 
diff --git a/library/bignum_mod_raw.c b/library/bignum_mod_raw.c
index c4a3eb8..334965d 100644
--- a/library/bignum_mod_raw.c
+++ b/library/bignum_mod_raw.c
@@ -42,8 +42,8 @@
 #include "constant_time_internal.h"
 
 int mbedtls_mpi_mod_raw_read( mbedtls_mpi_uint *X,
-                              mbedtls_mpi_mod_modulus *m,
-                              unsigned char *buf,
+                              const mbedtls_mpi_mod_modulus *m,
+                              const unsigned char *buf,
                               size_t buflen )
 {
     int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
@@ -74,8 +74,8 @@
     return( ret );
 }
 
-int mbedtls_mpi_mod_raw_write( mbedtls_mpi_uint *X,
-                               mbedtls_mpi_mod_modulus *m,
+int mbedtls_mpi_mod_raw_write( const mbedtls_mpi_uint *X,
+                               const mbedtls_mpi_mod_modulus *m,
                                unsigned char *buf,
                                size_t buflen )
 {
diff --git a/library/bignum_mod_raw.h b/library/bignum_mod_raw.h
index e8c2a7d..b4ef83d 100644
--- a/library/bignum_mod_raw.h
+++ b/library/bignum_mod_raw.h
@@ -38,12 +38,12 @@
  * The MPI needs to have enough limbs to store the full value (including any
  * most significant zero bytes in the input).
  *
- * \param X      The address of the MPI. The size is determined by \p m. (In
- *               particular, it must have at least as many limbs as the modulus
- *               \p m.)
- * \param m      The address of the modulus related to \p X.
- * \param buf    The input buffer to import from.
- * \param buflen The length in bytes of \p buf.
+ * \param[out] X    The address of the MPI. The size is determined by \p m. (In
+ *                  particular, it must have at least as many limbs as the
+ *                  modulus \p m.)
+ * \param[in] m     The address of the modulus related to \p X.
+ * \param[in] buf   The input buffer to import from.
+ * \param buflen    The length in bytes of \p buf.
  *
  * \return       \c 0 if successful.
  * \return       #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p X isn't
@@ -52,18 +52,18 @@
  *               of \p m is invalid or \p X is not less than \p m.
  */
 int mbedtls_mpi_mod_raw_read( mbedtls_mpi_uint *X,
-                              mbedtls_mpi_mod_modulus *m,
-                              unsigned char *buf,
+                              const mbedtls_mpi_mod_modulus *m,
+                              const unsigned char *buf,
                               size_t buflen );
 
 /** Export X into unsigned binary data.
  *
- * \param X      The address of the MPI. The size is determined by \p m. (In
- *               particular, it must have at least as many limbs as the modulus
- *               \p m.)
- * \param m      The address of the modulus related to \p X.
- * \param buf    The output buffer to export to.
- * \param buflen The length in bytes of \p buf.
+ * \param[in] X     The address of the MPI. The size is determined by \p m. (In
+ *                  particular, it must have at least as many limbs as the modulus
+ *                  \p m.)
+ * \param[in] m     The address of the modulus related to \p X.
+ * \param[out] buf  The output buffer to export to.
+ * \param buflen    The length in bytes of \p buf.
  *
  * \return       \c 0 if successful.
  * \return       #MBEDTLS_ERR_MPI_BUFFER_TOO_SMALL if \p buf isn't
@@ -71,8 +71,8 @@
  * \return       #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if the external representation
  *               of \p m is invalid.
  */
-int mbedtls_mpi_mod_raw_write( mbedtls_mpi_uint *X,
-                               mbedtls_mpi_mod_modulus *m,
+int mbedtls_mpi_mod_raw_write( const mbedtls_mpi_uint *X,
+                               const mbedtls_mpi_mod_modulus *m,
                                unsigned char *buf,
                                size_t buflen );