diff --git a/include/mbedtls/x509_crt.h b/include/mbedtls/x509_crt.h
index d383168d2..5c5509c79 100644
--- a/include/mbedtls/x509_crt.h
+++ b/include/mbedtls/x509_crt.h
@@ -1108,16 +1108,13 @@ void mbedtls_x509write_crt_free( mbedtls_x509write_cert *ctx );
  * \param ctx       certificate to write away
  * \param buf       buffer to write to
  * \param size      size of the buffer
- * \param f_rng     RNG function (for signature, see note)
+ * \param f_rng     RNG function. This must not be \c NULL.
  * \param p_rng     RNG parameter
  *
  * \return          length of data written if successful, or a specific
  *                  error code
  *
- * \note            f_rng may be NULL if RSA is used for signature and the
- *                  signature is made offline (otherwise f_rng is desirable
- *                  for countermeasures against timing attacks).
- *                  ECDSA signatures always require a non-NULL f_rng.
+ * \note            \p f_rng is used for the signature operation.
  */
 int mbedtls_x509write_crt_der( mbedtls_x509write_cert *ctx, unsigned char *buf, size_t size,
                        int (*f_rng)(void *, unsigned char *, size_t),
@@ -1130,15 +1127,12 @@ int mbedtls_x509write_crt_der( mbedtls_x509write_cert *ctx, unsigned char *buf,
  * \param ctx       certificate to write away
  * \param buf       buffer to write to
  * \param size      size of the buffer
- * \param f_rng     RNG function (for signature, see note)
+ * \param f_rng     RNG function. This must not be \c NULL.
  * \param p_rng     RNG parameter
  *
  * \return          0 if successful, or a specific error code
  *
- * \note            f_rng may be NULL if RSA is used for signature and the
- *                  signature is made offline (otherwise f_rng is desirable
- *                  for countermeasures against timing attacks).
- *                  ECDSA signatures always require a non-NULL f_rng.
+ * \note            \p f_rng is used for the signature operation.
  */
 int mbedtls_x509write_crt_pem( mbedtls_x509write_cert *ctx, unsigned char *buf, size_t size,
                        int (*f_rng)(void *, unsigned char *, size_t),
diff --git a/include/mbedtls/x509_csr.h b/include/mbedtls/x509_csr.h
index 0a069df93..a0f1278e2 100644
--- a/include/mbedtls/x509_csr.h
+++ b/include/mbedtls/x509_csr.h
@@ -264,16 +264,13 @@ void mbedtls_x509write_csr_free( mbedtls_x509write_csr *ctx );
  * \param ctx       CSR to write away
  * \param buf       buffer to write to
  * \param size      size of the buffer
- * \param f_rng     RNG function (for signature, see note)
+ * \param f_rng     RNG function. This must not be \c NULL.
  * \param p_rng     RNG parameter
  *
  * \return          length of data written if successful, or a specific
  *                  error code
  *
- * \note            f_rng may be NULL if RSA is used for signature and the
- *                  signature is made offline (otherwise f_rng is desirable
- *                  for countermeasures against timing attacks).
- *                  ECDSA signatures always require a non-NULL f_rng.
+ * \note            \p f_rng is used for the signature operation.
  */
 int mbedtls_x509write_csr_der( mbedtls_x509write_csr *ctx, unsigned char *buf, size_t size,
                        int (*f_rng)(void *, unsigned char *, size_t),
@@ -287,15 +284,12 @@ int mbedtls_x509write_csr_der( mbedtls_x509write_csr *ctx, unsigned char *buf, s
  * \param ctx       CSR to write away
  * \param buf       buffer to write to
  * \param size      size of the buffer
- * \param f_rng     RNG function (for signature, see note)
+ * \param f_rng     RNG function. This must not be \c NULL.
  * \param p_rng     RNG parameter
  *
  * \return          0 if successful, or a specific error code
  *
- * \note            f_rng may be NULL if RSA is used for signature and the
- *                  signature is made offline (otherwise f_rng is desirable
- *                  for countermeasures against timing attacks).
- *                  ECDSA signatures always require a non-NULL f_rng.
+ * \note            \p f_rng is used for the signature operation.
  */
 int mbedtls_x509write_csr_pem( mbedtls_x509write_csr *ctx, unsigned char *buf, size_t size,
                        int (*f_rng)(void *, unsigned char *, size_t),