diff --git a/library/bignum_mod.h b/library/bignum_mod.h
index 11b4e980f0..f089f650ef 100644
--- a/library/bignum_mod.h
+++ b/library/bignum_mod.h
@@ -2,6 +2,63 @@
  *  Modular bignum functions
  *
  * This module implements operations on integers modulo some fixed modulus.
+ *
+ * The functions in this module obey the following conventions unless
+ * explicitly indicated otherwise:
+ *
+ * - **Modulus parameters**: the modulus is passed as a pointer to a structure
+ *   of type #mbedtls_mpi_mod_modulus. The structure must be set up with an
+ *   array of limbs storing the bignum value of the modulus. The modulus must
+ *   be odd and is assumed to have no leading zeroes. The modulus is usually
+ *   named \c N and is usually input-only. Functions which take a parameter
+ *   of type \c const #mbedtls_mpi_mod_modulus* must not modify its value.
+ * - **Bignum parameters**: Bignums are passed as pointers to an array of
+ *   limbs or to a #mbedtls_mpi_mod_residue structure. A limb has the type
+ *   #mbedtls_mpi_uint. Residues must be initialized before use, and must be
+ *   associated with the modulus \c N. Unless otherwise specified:
+ *     - Bignum parameters called \c A, \c B, ... are inputs and are not
+ *       modified by the function. Functions which take a parameter of
+ *       type \c const #mbedtls_mpi_mod_residue* must not modify its value.
+ *     - Bignum parameters called \c X, \c Y, ... are outputs or input-output.
+ *       The initial bignum value of output-only parameters is ignored, but
+ *       they must be set up and associated with the modulus \c N. Some
+ *       functions (typically constant-flow) require that the limbs in an
+ *       output residue are initialized.
+ *     - Bignum parameters called \c p are inputs used to set up a modulus or
+ *       residue. These must be pointers to an array of limbs.
+ *     - \c T is a temporary storage area. The initial content of such a
+ *       parameter is ignored and the final content is unspecified.
+ *     - Some functions use different names, such as \c r for the residue.
+ * - **Bignum sizes**: bignum sizes are always expressed in limbs. Both
+ *   #mbedtls_mpi_mod_modulus and #mbedtls_mpi_mod_residue have a \c limbs
+ *   member storing its size. All bignum parameters must have the same
+ *   number of limbs as the modulus. All bignum sizes must be at least 1 and
+ *   must be significantly less than #SIZE_MAX. The behavior if a size is 0 is
+ *   undefined.
+ * - **Bignum representation**: the representation of inputs and outputs is
+ *   specified by the \c int_rep field of the modulus.
+ * - **Parameter ordering**: for bignum parameters, outputs come before inputs.
+ *   The modulus is passed after residues. Temporaries come last.
+ * - **Aliasing**: in general, output bignums may be aliased to one or more
+ *   inputs. Modulus values may not be aliased to any other parameter. Outputs
+ *   may not be aliased to one another. Temporaries may not be aliased to any
+ *   other parameter.
+ * - **Overlap**: apart from aliasing of residue pointers (where two residue
+ *   arguments are equal pointers), overlap is not supported and may result
+ *   in undefined behavior.
+ * - **Error handling**: functions generally check compatibility of input
+ *   sizes. Most functions will not check that input values are in canonical
+ *   form (i.e. that \c A < \c N), this is only checked during setup of a
+ *   residue structure.
+ * - **Modular representatives**: all functions expect inputs to be in the
+ *   range [0, \c N - 1] and guarantee outputs in the range [0, \c N - 1].
+ *   Residues are set up with an associated modulus, and operations are only
+ *   guaranteed to work if the modulus is associated with all residue
+ *   parameters. If a residue is passed with a modulus other than the one it
+ *   is associated with, then it may be out of range. If an input is out of
+ *   range, outputs are fully unspecified, though bignum values out of range
+ *   should not cause buffer overflows (beware that this is not extensively
+ *   tested).
  */
 
 /*
diff --git a/library/bignum_mod_raw.h b/library/bignum_mod_raw.h
index f9968ba748..e6237b3593 100644
--- a/library/bignum_mod_raw.h
+++ b/library/bignum_mod_raw.h
@@ -11,6 +11,51 @@
  * the wrong size. The functions in bignum_mod.h provide a higher-level
  * interface that includes protections against accidental misuse, at the
  * expense of code size and sometimes more cumbersome memory management.
+ *
+ * The functions in this module obey the following conventions unless
+ * explicitly indicated otherwise:
+ * - **Modulus parameters**: the modulus is passed as a pointer to a structure
+ *   of type #mbedtls_mpi_mod_modulus. The structure must be set up with an
+ *   array of limbs storing the bignum value of the modulus. The modulus must
+ *   be odd and is assumed to have no leading zeroes. The modulus is usually
+ *   named \c N and is usually input-only.
+ * - **Bignum parameters**: Bignums are passed as pointers to an array of
+ *   limbs. A limb has the type #mbedtls_mpi_uint. Unless otherwise specified:
+ *     - Bignum parameters called \c A, \c B, ... are inputs, and are not
+ *       modified by the function.
+ *     - Bignum parameters called \c X, \c Y are outputs or input-output.
+ *       The initial content of output-only parameters is ignored.
+ *     - \c T is a temporary storage area. The initial content of such a
+ *       parameter is ignored and the final content is unspecified.
+ * - **Bignum sizes**: bignum sizes are usually expressed by the \c limbs
+ *   member of the modulus argument. All bignum parameters must have the same
+ *   number of limbs as the modulus. All bignum sizes must be at least 1 and
+ *   must be significantly less than #SIZE_MAX. The behavior if a size is 0 is
+ *   undefined.
+ * - **Bignum representation**: the representation of inputs and outputs is
+ *   specified by the \c int_rep field of the modulus for arithmetic
+ *   functions. Utility functions may allow for different representation.
+ * - **Parameter ordering**: for bignum parameters, outputs come before inputs.
+ *   The modulus is passed after other bignum input parameters. Temporaries
+ *   come last.
+ * - **Aliasing**: in general, output bignums may be aliased to one or more
+ *   inputs. Modulus values may not be aliased to any other parameter. Outputs
+ *   may not be aliased to one another. Temporaries may not be aliased to any
+ *   other parameter.
+ * - **Overlap**: apart from aliasing of limb array pointers (where two
+ *   arguments are equal pointers), overlap is not supported and may result
+ *   in undefined behavior.
+ * - **Error handling**: This is a low-level module. Functions generally do not
+ *   try to protect against invalid arguments such as nonsensical sizes or
+ *   null pointers. Note that passing bignums with a different size than the
+ *   modulus may lead to buffer overflows. Some functions which allocate
+ *   memory or handle reading/writing of bignums will return an error if
+ *   memory allocation fails or if buffer sizes are invalid.
+ * - **Modular representatives**: all functions expect inputs to be in the
+ *   range [0, \c N - 1] and guarantee outputs in the range [0, \c N - 1]. If
+ *   an input is out of range, outputs are fully unspecified, though bignum
+ *   values out of range should not cause buffer overflows (beware that this is
+ *   not extensively tested).
  */
 
 /*