diff --git a/library/ecp_invasive.h b/library/ecp_invasive.h
index cfa12e9..16b7b61 100644
--- a/library/ecp_invasive.h
+++ b/library/ecp_invasive.h
@@ -171,9 +171,20 @@
 
 #if defined(MBEDTLS_ECP_DP_SECP192K1_ENABLED)
 
-/*
- * Fast quasi-reduction modulo p192k1 = 2^192 - R,
- * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x0100001119
+/** Fast quasi-reduction modulo p192k1 = 2^192 - R,
+ * with R = 2^32 + 2^12 + 2^8 + 2^7 + 2^6 + 2^3 + 1 = 0x01000011C9
+ *
+ * \param[in,out]   X       The address of the MPI to be converted.
+ *                          Must have exact limb size that stores a 384-bit MPI
+ *                          (double the bitlength of the modulus).
+ *                          Upon return holds the reduced value which is
+ *                          in range `0 <= X < 2 * N` (where N is the modulus).
+ *                          The bitlength of the reduced value is the same as
+ *                          that of the modulus (192 bits).
+ * \param[in]       X_limbs The length of \p X in limbs.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_ALLOC_FAILED if memory allocation failed.
  */
 MBEDTLS_STATIC_TESTABLE
 int mbedtls_ecp_mod_p192k1_raw(mbedtls_mpi_uint *X, size_t X_limbs);
@@ -182,6 +193,21 @@
 
 #if defined(MBEDTLS_ECP_DP_SECP224K1_ENABLED)
 
+/** Fast quasi-reduction modulo p224k1 = 2^224 - R,
+ * with R = 2^32 + 2^12 + 2^11 + 2^9 + 2^7 + 2^4 + 2 + 1 = 0x0100001A93
+ *
+ * \param[in,out]   X       The address of the MPI to be converted.
+ *                          Must have exact limb size that stores a 448-bit MPI
+ *                          (double the bitlength of the modulus).
+ *                          Upon return holds the reduced value which is
+ *                          in range `0 <= X < 2 * N` (where N is the modulus).
+ *                          The bitlength of the reduced value is the same as
+ *                          that of the modulus (224 bits).
+ * \param[in]       X_limbs The length of \p X in limbs.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_ALLOC_FAILED if memory allocation failed.
+ */
 MBEDTLS_STATIC_TESTABLE
 int mbedtls_ecp_mod_p224k1_raw(mbedtls_mpi_uint *X, size_t X_limbs);
 
@@ -189,6 +215,21 @@
 
 #if defined(MBEDTLS_ECP_DP_SECP256K1_ENABLED)
 
+/** Fast quasi-reduction modulo p256k1 = 2^256 - R,
+ * with R = 2^32 + 2^9 + 2^8 + 2^7 + 2^6 + 2^4 + 1 = 0x01000003D1
+ *
+ * \param[in,out]   X       The address of the MPI to be converted.
+ *                          Must have exact limb size that stores a 512-bit MPI
+ *                          (double the bitlength of the modulus).
+ *                          Upon return holds the reduced value which is
+ *                          in range `0 <= X < 2 * N` (where N is the modulus).
+ *                          The bitlength of the reduced value is the same as
+ *                          that of the modulus (256 bits).
+ * \param[in]       X_limbs The length of \p X in limbs.
+ *
+ * \return          \c 0 on success.
+ * \return          #MBEDTLS_ERR_ECP_ALLOC_FAILED if memory allocation failed.
+ */
 MBEDTLS_STATIC_TESTABLE
 int mbedtls_ecp_mod_p256k1_raw(mbedtls_mpi_uint *X, size_t X_limbs);