diff --git a/include/mbedtls/ecdsa.h b/include/mbedtls/ecdsa.h
index 4057828..86f4944 100644
--- a/include/mbedtls/ecdsa.h
+++ b/include/mbedtls/ecdsa.h
@@ -118,7 +118,8 @@
  * \brief           This function computes the ECDSA signature of a
  *                  previously-hashed message.
  *
- * \note            The deterministic version is usually preferred.
+ * \note            The deterministic version implemented in
+ *                  mbedtls_ecdsa_sign_det() is usually preferred.
  *
  * \note            If the bitlength of the message hash is larger than the
  *                  bitlength of the group order, then the hash is truncated
@@ -128,14 +129,22 @@
  *
  * \see             ecp.h
  *
- * \param grp       The ECP group.
- * \param r         The first output integer.
- * \param s         The second output integer.
- * \param d         The private signing key.
- * \param buf       The message hash.
- * \param blen      The length of \p buf.
- * \param f_rng     The RNG function.
- * \param p_rng     The RNG context.
+ * \param grp       The context for the elliptic curve to use.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param r         The MPI context in which to store the first part
+ *                  the signature. This must be initialized.
+ * \param s         The MPI context in which to store the second part
+ *                  the signature. This must be initialized.
+ * \param d         The private signing key. This must be initialized.
+ * \param buf       The content to be signed. This is usually the hash of
+ *                  the original data to be signed. This must be a readable
+ *                  buffer of length \p blen Bytes. It may be \c NULL if
+ *                  \p blen is zero.
+ * \param blen      The length of \p buf in Bytes.
+ * \param f_rng     The RNG function. This must not be \c NULL.
+ * \param p_rng     The RNG context to be passed to \p f_rng. This may be
+ *                  \c NULL if \p f_rng doesn't need a context parameter.
  *
  * \return          \c 0 on success.
  * \return          An \c MBEDTLS_ERR_ECP_XXX
@@ -162,21 +171,29 @@
  *
  * \see             ecp.h
  *
- * \param grp       The ECP group.
- * \param r         The first output integer.
- * \param s         The second output integer.
- * \param d         The private signing key.
- * \param buf       The message hash.
- * \param blen      The length of \p buf.
- * \param md_alg    The MD algorithm used to hash the message.
+ * \param grp       The context for the elliptic curve to use.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param r         The MPI context in which to store the first part
+ *                  the signature. This must be initialized.
+ * \param s         The MPI context in which to store the second part
+ *                  the signature. This must be initialized.
+ * \param d         The private signing key. This must be initialized
+ *                  and setup, for example through mbedtls_ecp_gen_privkey().
+ * \param buf       The hashed content to be signed. This must be a readable
+ *                  buffer of length \p blen Bytes. It may be \c NULL if
+ *                  \p blen is zero.
+ * \param blen      The length of \p buf in Bytes.
+ * \param md_alg    The hash algorithm used to hash the original data.
  *
  * \return          \c 0 on success.
  * \return          An \c MBEDTLS_ERR_ECP_XXX or \c MBEDTLS_MPI_XXX
  *                  error code on failure.
  */
-int mbedtls_ecdsa_sign_det( mbedtls_ecp_group *grp, mbedtls_mpi *r, mbedtls_mpi *s,
-                    const mbedtls_mpi *d, const unsigned char *buf, size_t blen,
-                    mbedtls_md_type_t md_alg );
+int mbedtls_ecdsa_sign_det( mbedtls_ecp_group *grp, mbedtls_mpi *r,
+                            mbedtls_mpi *s, const mbedtls_mpi *d,
+                            const unsigned char *buf, size_t blen,
+                            mbedtls_md_type_t md_alg );
 #endif /* MBEDTLS_ECDSA_DETERMINISTIC */
 
 /**
@@ -191,12 +208,19 @@
  *
  * \see             ecp.h
  *
- * \param grp       The ECP group.
- * \param buf       The message hash.
- * \param blen      The length of \p buf.
- * \param Q         The public key to use for verification.
+ * \param grp       The ECP group to use.
+ *                  This must be initialized and have group parameters
+ *                  set, for example through mbedtls_ecp_group_load().
+ * \param buf       The hashed content that was signed. This must be a readable
+ *                  buffer of length \p blen Bytes. It may be \c NULL if
+ *                  \p blen is zero.
+ * \param blen      The length of \p buf in Bytes.
+ * \param Q         The public key to use for verification. This must be
+ *                  initialized and setup.
  * \param r         The first integer of the signature.
+ *                  This must be initialized.
  * \param s         The second integer of the signature.
+ *                  This must be initialized.
  *
  * \return          \c 0 on success.
  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if the signature
@@ -205,8 +229,9 @@
  *                  error code on failure for any other reason.
  */
 int mbedtls_ecdsa_verify( mbedtls_ecp_group *grp,
-                  const unsigned char *buf, size_t blen,
-                  const mbedtls_ecp_point *Q, const mbedtls_mpi *r, const mbedtls_mpi *s);
+                          const unsigned char *buf, size_t blen,
+                          const mbedtls_ecp_point *Q, const mbedtls_mpi *r,
+                          const mbedtls_mpi *s);
 
 /**
  * \brief           This function computes the ECDSA signature and writes it
@@ -223,11 +248,6 @@
  *                  of the Digital Signature Algorithm (DSA) and Elliptic
  *                  Curve Digital Signature Algorithm (ECDSA)</em>.
  *
- * \note            The \p sig buffer must be at least twice as large as the
- *                  size of the curve used, plus 9. For example, 73 Bytes if
- *                  a 256-bit curve is used. A buffer length of
- *                  #MBEDTLS_ECDSA_MAX_LEN is always safe.
- *
  * \note            If the bitlength of the message hash is larger than the
  *                  bitlength of the group order, then the hash is truncated as
  *                  defined in <em>Standards for Efficient Cryptography Group
@@ -236,20 +256,32 @@
  *
  * \see             ecp.h
  *
- * \param ctx       The ECDSA context.
+ * \param ctx       The ECDSA context to use. This must be initialized
+ *                  and have a group and private key bound to it, for example
+ *                  via mbedtls_ecdsa_genkey() or mbedtls_ecdsa_from_keypair().
  * \param md_alg    The message digest that was used to hash the message.
- * \param hash      The message hash.
- * \param hlen      The length of the hash.
- * \param sig       The buffer that holds the signature.
- * \param slen      The length of the signature written.
- * \param f_rng     The RNG function.
- * \param p_rng     The RNG context.
+ * \param hash      The message hash to be signed. This must be a readable
+ *                  buffer of length \p blen Bytes.
+ * \param hlen      The length of the hash \p hash in Bytes.
+ * \param sig       The buffer to which to write the signature. This must be a
+ *                  writable buffer of length at least twice as large as the
+ *                  size of the curve used, plus 9. For example, 73 Bytes if
+ *                  a 256-bit curve is used. A buffer length of
+ *                  #MBEDTLS_ECDSA_MAX_LEN is always safe.
+ * \param slen      The address at which to store the actual length of
+ *                  the signature written. Must not be \c NULL.
+ * \param f_rng     The RNG function. This must not be \c NULL if
+ *                  #MBEDTLS_ECDSA_DETERMINISTIC is unset. Otherwise,
+ *                  it is unused and may be set to \c NULL.
+ * \param p_rng     The RNG context to be passed to \p f_rng. This may be
+ *                  \c NULL if \p f_rng is \c NULL or doesn't use a context.
  *
  * \return          \c 0 on success.
  * \return          An \c MBEDTLS_ERR_ECP_XXX, \c MBEDTLS_ERR_MPI_XXX or
  *                  \c MBEDTLS_ERR_ASN1_XXX error code on failure.
  */
-int mbedtls_ecdsa_write_signature( mbedtls_ecdsa_context *ctx, mbedtls_md_type_t md_alg,
+int mbedtls_ecdsa_write_signature( mbedtls_ecdsa_context *ctx,
+                                   mbedtls_md_type_t md_alg,
                            const unsigned char *hash, size_t hlen,
                            unsigned char *sig, size_t *slen,
                            int (*f_rng)(void *, unsigned char *, size_t),
@@ -265,15 +297,28 @@
  *                  but it can return early and restart according to the limit
  *                  set with \c mbedtls_ecp_set_max_ops() to reduce blocking.
  *
- * \param ctx       The ECDSA context.
+ * \param ctx       The ECDSA context to use. This must be initialized
+ *                  and have a group and private key bound to it, for example
+ *                  via mbedtls_ecdsa_genkey() or mbedtls_ecdsa_from_keypair().
  * \param md_alg    The message digest that was used to hash the message.
- * \param hash      The message hash.
- * \param hlen      The length of the hash.
- * \param sig       The buffer that holds the signature.
- * \param slen      The length of the signature written.
- * \param f_rng     The RNG function.
- * \param p_rng     The RNG context.
- * \param rs_ctx    The restart context (NULL disables restart).
+ * \param hash      The message hash to be signed. This must be a readable
+ *                  buffer of length \p blen Bytes.
+ * \param hlen      The length of the hash \p hash in Bytes.
+ * \param sig       The buffer to which to write the signature. This must be a
+ *                  writable buffer of length at least twice as large as the
+ *                  size of the curve used, plus 9. For example, 73 Bytes if
+ *                  a 256-bit curve is used. A buffer length of
+ *                  #MBEDTLS_ECDSA_MAX_LEN is always safe.
+ * \param slen      The address at which to store the actual length of
+ *                  the signature written. Must not be \c NULL.
+ * \param f_rng     The RNG function. This must not be \c NULL if
+ *                  #MBEDTLS_ECDSA_DETERMINISTIC is unset. Otherwise,
+ *                  it is unused and may be set to \c NULL.
+ * \param p_rng     The RNG context to be passed to \p f_rng. This may be
+ *                  \c NULL if \p f_rng is \c NULL or doesn't use a context.
+ * \param rs_ctx    The restart context to use. This may be \c NULL to disable
+ *                  restarting. If it is not \c NULL, it must point to an
+ *                  initialized restart context.
  *
  * \return          \c 0 on success.
  * \return          #MBEDTLS_ERR_ECP_IN_PROGRESS if maximum number of
@@ -309,11 +354,6 @@
  * \warning         It is not thread-safe to use the same context in
  *                  multiple threads.
  *
- * \note            The \p sig buffer must be at least twice as large as the
- *                  size of the curve used, plus 9. For example, 73 Bytes if a
- *                  256-bit curve is used. A buffer length of
- *                  #MBEDTLS_ECDSA_MAX_LEN is always safe.
- *
  * \note            If the bitlength of the message hash is larger than the
  *                  bitlength of the group order, then the hash is truncated as
  *                  defined in <em>Standards for Efficient Cryptography Group
@@ -325,12 +365,20 @@
  * \deprecated      Superseded by mbedtls_ecdsa_write_signature() in
  *                  Mbed TLS version 2.0 and later.
  *
- * \param ctx       The ECDSA context.
- * \param hash      The message hash.
- * \param hlen      The length of the hash.
- * \param sig       The buffer that holds the signature.
- * \param slen      The length of the signature written.
- * \param md_alg    The MD algorithm used to hash the message.
+ * \param ctx       The ECDSA context to use. This must be initialized
+ *                  and have a group and private key bound to it, for example
+ *                  via mbedtls_ecdsa_genkey() or mbedtls_ecdsa_from_keypair().
+ * \param hash      The message hash to be signed. This must be a readable
+ *                  buffer of length \p blen Bytes.
+ * \param hlen      The length of the hash \p hash in Bytes.
+ * \param sig       The buffer to which to write the signature. This must be a
+ *                  writable buffer of length at least twice as large as the
+ *                  size of the curve used, plus 9. For example, 73 Bytes if
+ *                  a 256-bit curve is used. A buffer length of
+ *                  #MBEDTLS_ECDSA_MAX_LEN is always safe.
+ * \param slen      The address at which to store the actual length of
+ *                  the signature written. Must not be \c NULL.
+ * \param md_alg    The message digest that was used to hash the message.
  *
  * \return          \c 0 on success.
  * \return          An \c MBEDTLS_ERR_ECP_XXX, \c MBEDTLS_ERR_MPI_XXX or
@@ -355,11 +403,14 @@
  *
  * \see             ecp.h
  *
- * \param ctx       The ECDSA context.
- * \param hash      The message hash.
- * \param hlen      The size of the hash.
- * \param sig       The signature to read and verify.
- * \param slen      The size of \p sig.
+ * \param ctx       The ECDSA context to use. This must be initialized
+ *                  and have a group and public key bound to it.
+ * \param hash      The message hash that was signed. This must be a readable
+ *                  buffer of length \p size Bytes.
+ * \param hlen      The size of the hash \p hash.
+ * \param sig       The signature to read and verify. This must be a readable
+ *                  buffer of length \p slen Bytes.
+ * \param slen      The size of \p sig in Bytes.
  *
  * \return          \c 0 on success.
  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if signature is invalid.
@@ -382,12 +433,17 @@
  *                  but it can return early and restart according to the limit
  *                  set with \c mbedtls_ecp_set_max_ops() to reduce blocking.
  *
- * \param ctx       The ECDSA context.
- * \param hash      The message hash.
- * \param hlen      The size of the hash.
- * \param sig       The signature to read and verify.
- * \param slen      The size of \p sig.
- * \param rs_ctx    The restart context (NULL disables restart).
+ * \param ctx       The ECDSA context to use. This must be initialized
+ *                  and have a group and public key bound to it.
+ * \param hash      The message hash that was signed. This must be a readable
+ *                  buffer of length \p size Bytes.
+ * \param hlen      The size of the hash \p hash.
+ * \param sig       The signature to read and verify. This must be a readable
+ *                  buffer of length \p slen Bytes.
+ * \param slen      The size of \p sig in Bytes.
+ * \param rs_ctx    The restart context to use. This may be \c NULL to disable
+ *                  restarting. If it is not \c NULL, it must point to an
+ *                  initialized restart context.
  *
  * \return          \c 0 on success.
  * \return          #MBEDTLS_ERR_ECP_BAD_INPUT_DATA if signature is invalid.
@@ -409,10 +465,12 @@
  * \see            ecp.h
  *
  * \param ctx      The ECDSA context to store the keypair in.
+ *                 This must be initialized.
  * \param gid      The elliptic curve to use. One of the various
  *                 \c MBEDTLS_ECP_DP_XXX macros depending on configuration.
- * \param f_rng    The RNG function.
- * \param p_rng    The RNG context.
+ * \param f_rng    The RNG function to use. This must not be \c NULL.
+ * \param p_rng    The RNG context to be passed to \p f_rng. This may be
+ *                 \c NULL if \p f_rng doesn't need a context argument.
  *
  * \return         \c 0 on success.
  * \return         An \c MBEDTLS_ERR_ECP_XXX code on failure.
@@ -425,36 +483,51 @@
  *
  * \see             ecp.h
  *
- * \param ctx       The ECDSA context to set.
- * \param key       The EC key to use.
+ * \param ctx       The ECDSA context to set. This must be initialized.
+ * \param key       The EC key to use. This must be initialized and hold
+ *                  a private-public key pair or a public key. In the former
+ *                  case, the ECDSA context may be used for signature creation
+ *                  after this call. In the latter case, it may be used for
+ *                  signature verification.
  *
  * \return          \c 0 on success.
  * \return          An \c MBEDTLS_ERR_ECP_XXX code on failure.
  */
-int mbedtls_ecdsa_from_keypair( mbedtls_ecdsa_context *ctx, const mbedtls_ecp_keypair *key );
+int mbedtls_ecdsa_from_keypair( mbedtls_ecdsa_context *ctx,
+                                const mbedtls_ecp_keypair *key );
 
 /**
  * \brief           This function initializes an ECDSA context.
  *
  * \param ctx       The ECDSA context to initialize.
+ *                  This must not be \c NULL.
  */
 void mbedtls_ecdsa_init( mbedtls_ecdsa_context *ctx );
 
 /**
  * \brief           This function frees an ECDSA context.
  *
- * \param ctx       The ECDSA context to free.
+ * \param ctx       The ECDSA context to free. This may be \c NULL,
+ *                  in which case this function does nothing. If it
+ *                  is not \c NULL, it must be initialized.
  */
 void mbedtls_ecdsa_free( mbedtls_ecdsa_context *ctx );
 
 #if defined(MBEDTLS_ECP_RESTARTABLE)
 /**
- * \brief           Initialize a restart context
+ * \brief           Initialize a restart context.
+ *
+ * \param ctx       The restart context to initialize.
+ *                  This must not be \c NULL.
  */
 void mbedtls_ecdsa_restart_init( mbedtls_ecdsa_restart_ctx *ctx );
 
 /**
- * \brief           Free the components of a restart context
+ * \brief           Free the components of a restart context.
+ *
+ * \param ctx       The restart context to free. This may be \c NULL,
+ *                  in which case this function does nothing. If it
+ *                  is not \c NULL, it must be initialized.
  */
 void mbedtls_ecdsa_restart_free( mbedtls_ecdsa_restart_ctx *ctx );
 #endif /* MBEDTLS_ECP_RESTARTABLE */