Improve DHM documentation

- Rephrase file/function/parameter/enum/define/error descriptions into full
  and clear sentences.
- Make sure to adhere to the Arm writing guidelines.
- Fix missing/incorrect Doxygen tags.
- Standardize terminology used within the file.
- Standardize defines documentation

GitHub PR: #1323
diff --git a/include/mbedtls/dhm.h b/include/mbedtls/dhm.h
index 8a28ffa..b1750f1 100644
--- a/include/mbedtls/dhm.h
+++ b/include/mbedtls/dhm.h
@@ -1,10 +1,18 @@
 /**
  * \file dhm.h
  *
- * \brief Diffie-Hellman-Merkle key exchange
+ * \brief Diffie-Hellman-Merkle key exchange.
+ *
+ * <em>RFC-3526: More Modular Exponential (MODP) Diffie-Hellman groups for
+ * Internet Key Exchange (IKE)</em> defines a number of standardized
+ * Diffie-Hellman groups for IKE.
+ *
+ * <em>RFC-5114: Additional Diffie-Hellman Groups for Use with IETF
+ * Standards</em> defines a number of standardized Diffie-Hellman
+ * groups that can be used.
  */
 /*
- *  Copyright (C) 2006-2015, ARM Limited, All Rights Reserved
+ *  Copyright (C) 2006-2018, Arm Limited (or its affiliates), All Rights Reserved
  *  SPDX-License-Identifier: Apache-2.0
  *
  *  Licensed under the Apache License, Version 2.0 (the "License"); you may
@@ -19,8 +27,9 @@
  *  See the License for the specific language governing permissions and
  *  limitations under the License.
  *
- *  This file is part of mbed TLS (https://tls.mbed.org)
+ *  This file is part of Mbed TLS (https://tls.mbed.org)
  */
+
 #ifndef MBEDTLS_DHM_H
 #define MBEDTLS_DHM_H
 
@@ -35,7 +44,7 @@
 /*
  * DHM Error codes
  */
-#define MBEDTLS_ERR_DHM_BAD_INPUT_DATA                    -0x3080  /**< Bad input parameters to function. */
+#define MBEDTLS_ERR_DHM_BAD_INPUT_DATA                    -0x3080  /**< Bad input parameters. */
 #define MBEDTLS_ERR_DHM_READ_PARAMS_FAILED                -0x3100  /**< Reading of the DHM parameters failed. */
 #define MBEDTLS_ERR_DHM_MAKE_PARAMS_FAILED                -0x3180  /**< Making of the DHM parameters failed. */
 #define MBEDTLS_ERR_DHM_READ_PUBLIC_FAILED                -0x3200  /**< Reading of the public values failed. */
@@ -43,22 +52,22 @@
 #define MBEDTLS_ERR_DHM_CALC_SECRET_FAILED                -0x3300  /**< Calculation of the DHM secret failed. */
 #define MBEDTLS_ERR_DHM_INVALID_FORMAT                    -0x3380  /**< The ASN.1 data is not formatted correctly. */
 #define MBEDTLS_ERR_DHM_ALLOC_FAILED                      -0x3400  /**< Allocation of memory failed. */
-#define MBEDTLS_ERR_DHM_FILE_IO_ERROR                     -0x3480  /**< Read/write of file failed. */
+#define MBEDTLS_ERR_DHM_FILE_IO_ERROR                     -0x3480  /**< Read or write of file failed. */
 #define MBEDTLS_ERR_DHM_HW_ACCEL_FAILED                   -0x3500  /**< DHM hardware accelerator failed. */
 
+
+ /* The following lists the source of the above groups in the standards:
+ * - RFC-3526 section 3: 2048-bit MODP Group
+ * - RFC-3526 section 4: 3072-bit MODP Group
+ * - RFC-3526 section 5: 4096-bit MODP Group
+ * - RFC-5114 section 2.2: 2048-bit MODP Group with 224-bit Prime Order Subgroup
+ * .
+ */
+
 /**
- * RFC 3526 defines a number of standardized Diffie-Hellman groups
- * for IKE.
- * RFC 5114 defines a number of standardized Diffie-Hellman groups
- * that can be used.
- *
- * Some are included here for convenience.
- *
- * Included are:
- *  RFC 3526 3.    2048-bit MODP Group
- *  RFC 3526 4.    3072-bit MODP Group
- *  RFC 3526 5.    4096-bit MODP Group
- *  RFC 5114 2.2.  2048-bit MODP Group with 224-bit Prime Order Subgroup
+ * The hexadecimal presentation of the prime underlying the 2048-bit MODP
+ * Group, as defined in <em>RFC-3526: More Modular Exponential (MODP)
+ * Diffie-Hellman groups for Internet Key Exchange (IKE)</em>.
  */
 #define MBEDTLS_DHM_RFC3526_MODP_2048_P               \
     "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1" \
@@ -73,8 +82,18 @@
     "DE2BCBF6955817183995497CEA956AE515D2261898FA0510" \
     "15728E5A8AACAA68FFFFFFFFFFFFFFFF"
 
+/**
+ * The hexadecimal presentation of the chosen generator of the 2048-bit MODP
+ * Group, as defined in <em>RFC-3526: More Modular Exponential (MODP)
+ * Diffie-Hellman groups for Internet Key Exchange (IKE)</em>.
+ */
 #define MBEDTLS_DHM_RFC3526_MODP_2048_G          "02"
 
+/**
+ * The hexadecimal presentation of the prime underlying the 3072-bit MODP
+ * Group, as defined in <em>RFC-3072: More Modular Exponential (MODP)
+ * Diffie-Hellman groups for Internet Key Exchange (IKE)</em>.
+ */
 #define MBEDTLS_DHM_RFC3526_MODP_3072_P               \
     "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1" \
     "29024E088A67CC74020BBEA63B139B22514A08798E3404DD" \
@@ -93,8 +112,18 @@
     "BBE117577A615D6C770988C0BAD946E208E24FA074E5AB31" \
     "43DB5BFCE0FD108E4B82D120A93AD2CAFFFFFFFFFFFFFFFF"
 
+/**
+ * The hexadecimal presentation of the chosen generator of the 3072-bit MODP
+ * Group, as defined in <em>RFC-3526: More Modular Exponential (MODP)
+ * Diffie-Hellman groups for Internet Key Exchange (IKE)</em>.
+ */
 #define MBEDTLS_DHM_RFC3526_MODP_3072_G          "02"
 
+/**
+ * The hexadecimal presentation of the prime underlying the 4096-bit MODP
+ * Group, as defined in <em>RFC-3526: More Modular Exponential (MODP)
+ * Diffie-Hellman groups for Internet Key Exchange (IKE)</em>.
+ */
 #define MBEDTLS_DHM_RFC3526_MODP_4096_P                \
     "FFFFFFFFFFFFFFFFC90FDAA22168C234C4C6628B80DC1CD1" \
     "29024E088A67CC74020BBEA63B139B22514A08798E3404DD" \
@@ -119,8 +148,19 @@
     "93B4EA988D8FDDC186FFB7DC90A6C08F4DF435C934063199" \
     "FFFFFFFFFFFFFFFF"
 
+/**
+ * The hexadecimal presentation of the chosen generator of the 4096-bit MODP
+ * Group, as defined in <em>RFC-3526: More Modular Exponential (MODP)
+ * Diffie-Hellman groups for Internet Key Exchange (IKE)</em>.
+ */
 #define MBEDTLS_DHM_RFC3526_MODP_4096_G          "02"
 
+/**
+ * The hexadecimal presentation of the prime underlying the
+ * 2048-bit MODP Group with 224-bit Prime Order Subgroup, as defined
+ * in <em>RFC-5114: Additional Diffie-Hellman Groups for Use with
+ * IETF Standards</em>.
+ */
 #define MBEDTLS_DHM_RFC5114_MODP_2048_P               \
     "AD107E1E9123A9D0D660FAA79559C51FA20D64E5683B9FD1" \
     "B54B1597B61D0A75E6FA141DF95A56DBAF9A3C407BA1DF15" \
@@ -134,6 +174,11 @@
     "C9B53DCF4BA80A29E3FB73C16B8E75B97EF363E2FFA31F71" \
     "CF9DE5384E71B81C0AC4DFFE0C10E64F"
 
+/**
+ * The hexadecimal presentation of the chosen generator of the 2048-bit MODP
+ * Group with 224-bit Prime Order Subgroup, as defined in <em>RFC-5114:
+ * Additional Diffie-Hellman Groups for Use with IETF Standards</em>.
+ */
 #define MBEDTLS_DHM_RFC5114_MODP_2048_G              \
     "AC4032EF4F2D9AE39DF30B5C8FFDAC506CDEBE7B89998CAF"\
     "74866A08CFE4FFE3A6824A4E10B9A6F0DD921F01A70C4AFA"\
@@ -152,59 +197,62 @@
 #endif
 
 /**
- * \brief          DHM context structure
+ * \brief          The DHM context structure.
  */
 typedef struct
 {
-    size_t len; /*!<  size(P) in chars  */
-    mbedtls_mpi P;      /*!<  prime modulus     */
-    mbedtls_mpi G;      /*!<  generator         */
-    mbedtls_mpi X;      /*!<  secret value      */
-    mbedtls_mpi GX;     /*!<  self = G^X mod P  */
-    mbedtls_mpi GY;     /*!<  peer = G^Y mod P  */
-    mbedtls_mpi K;      /*!<  key = GY^X mod P  */
-    mbedtls_mpi RP;     /*!<  cached R^2 mod P  */
-    mbedtls_mpi Vi;     /*!<  blinding value    */
-    mbedtls_mpi Vf;     /*!<  un-blinding value */
-    mbedtls_mpi pX;     /*!<  previous X        */
+    size_t len;         /*!<  The size of \p P in Bytes. */
+    mbedtls_mpi P;      /*!<  The prime modulus. */
+    mbedtls_mpi G;      /*!<  The generator. */
+    mbedtls_mpi X;      /*!<  Our secret value. */
+    mbedtls_mpi GX;     /*!<  Our public key = \c G^X mod \c P. */
+    mbedtls_mpi GY;     /*!<  The public key of the peer = \c G^Y mod \c P. */
+    mbedtls_mpi K;      /*!<  The shared secret = \c G^(XY) mod \c P. */
+    mbedtls_mpi RP;     /*!<  The cached value = \c R^2 mod \c P. */
+    mbedtls_mpi Vi;     /*!<  The blinding value. */
+    mbedtls_mpi Vf;     /*!<  The unblinding value. */
+    mbedtls_mpi pX;     /*!<  The previous \c X. */
 }
 mbedtls_dhm_context;
 
 /**
- * \brief          Initialize DHM context
+ * \brief          This function initializes the DHM context.
  *
- * \param ctx      DHM context to be initialized
+ * \param ctx      The DHM context to initialize.
  */
 void mbedtls_dhm_init( mbedtls_dhm_context *ctx );
 
 /**
- * \brief          Parse the ServerKeyExchange parameters
+ * \brief          This function parses the ServerKeyExchange parameters.
  *
- * \param ctx      DHM context
- * \param p        &(start of input buffer)
- * \param end      end of buffer
+ * \param ctx      The DHM context.
+ * \param p        The start of the input buffer.
+ * \param end      The end of the input buffer.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_DHM_XXX error code
+ * \return         \c 0 on success, or an \c MBEDTLS_ERR_DHM_XXX error code
+ *                 on failure.
  */
 int mbedtls_dhm_read_params( mbedtls_dhm_context *ctx,
                      unsigned char **p,
                      const unsigned char *end );
 
 /**
- * \brief          Setup and write the ServerKeyExchange parameters
+ * \brief          This function sets up and writes the ServerKeyExchange
+ *                 parameters.
  *
- * \param ctx      DHM context
- * \param x_size   private value size in bytes
- * \param output   destination buffer
- * \param olen     number of chars written
- * \param f_rng    RNG function
- * \param p_rng    RNG parameter
+ * \param ctx      The DHM context.
+ * \param x_size   The private value size in Bytes.
+ * \param olen     The number of characters written.
+ * \param output   The destination buffer.
+ * \param f_rng    The RNG function.
+ * \param p_rng    The RNG parameter.
  *
- * \note           This function assumes that ctx->P and ctx->G
- *                 have already been properly set (for example
- *                 using mbedtls_mpi_read_string or mbedtls_mpi_read_binary).
+ * \note           This function assumes that the \c ctx->P and \c ctx->G have
+ *                 already been properly set, for example, using
+ *                 mbedtls_mpi_read_string() or mbedtls_mpi_read_binary().
  *
- * \return         0 if successful, or an MBEDTLS_ERR_DHM_XXX error code
+ * \return         \c 0 on success, or an \c MBEDTLS_ERR_DHM_XXX error code
+ *                 on failure.
  */
 int mbedtls_dhm_make_params( mbedtls_dhm_context *ctx, int x_size,
                      unsigned char *output, size_t *olen,
@@ -212,28 +260,32 @@
                      void *p_rng );
 
 /**
- * \brief          Import the peer's public value G^Y
+ * \brief          This function imports the public value G^Y of the peer.
  *
- * \param ctx      DHM context
- * \param input    input buffer
- * \param ilen     size of buffer
+ * \param ctx      The DHM context.
+ * \param input    The input buffer.
+ * \param ilen     The size of the input buffer.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_DHM_XXX error code
+ * \return         \c 0 on success, or an \c MBEDTLS_ERR_DHM_XXX error code
+ *                 on failure.
  */
 int mbedtls_dhm_read_public( mbedtls_dhm_context *ctx,
                      const unsigned char *input, size_t ilen );
 
 /**
- * \brief          Create own private value X and export G^X
+ * \brief          This function creates its own private value \c X and
+ *                 exports \c G^X.
  *
- * \param ctx      DHM context
- * \param x_size   private value size in bytes
- * \param output   destination buffer
- * \param olen     must be at least equal to the size of P, ctx->len
- * \param f_rng    RNG function
- * \param p_rng    RNG parameter
+ * \param ctx      The DHM context.
+ * \param x_size   The private value size in Bytes.
+ * \param output   The destination buffer.
+ * \param olen     The length of the destination buffer. Must be at least
+                   equal to ctx->len (the size of \c P).
+ * \param f_rng    The RNG function.
+ * \param p_rng    The RNG parameter.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_DHM_XXX error code
+ * \return         \c 0 on success, or an \c MBEDTLS_ERR_DHM_XXX error code
+ *                 on failure.
  */
 int mbedtls_dhm_make_public( mbedtls_dhm_context *ctx, int x_size,
                      unsigned char *output, size_t olen,
@@ -241,22 +293,24 @@
                      void *p_rng );
 
 /**
- * \brief          Derive and export the shared secret (G^Y)^X mod P
+ * \brief               This function derives and exports the shared secret
+ *                      \c (G^Y)^X mod \c P.
  *
- * \param ctx      DHM context
- * \param output   destination buffer
- * \param output_size   size of the destination buffer
- * \param olen     on exit, holds the actual number of bytes written
- * \param f_rng    RNG function, for blinding purposes
- * \param p_rng    RNG parameter
+ * \param ctx           The DHM context.
+ * \param output        The destination buffer.
+ * \param output_size   The size of the destination buffer.
+ * \param olen          On exit, holds the actual number of Bytes written.
+ * \param f_rng         The RNG function, for blinding purposes.
+ * \param p_rng         The RNG parameter.
  *
- * \return         0 if successful, or an MBEDTLS_ERR_DHM_XXX error code
+ * \return         \c 0 on success, or an \c MBEDTLS_ERR_DHM_XXX error code
+ *                 on failure.
  *
- * \note           If non-NULL, f_rng is used to blind the input as
- *                 countermeasure against timing attacks. Blinding is
- *                 automatically used if and only if our secret value X is
- *                 re-used and costs nothing otherwise, so it is recommended
- *                 to always pass a non-NULL f_rng argument.
+ * \note           If non-NULL, \p f_rng is used to blind the input as
+ *                 a countermeasure against timing attacks. Blinding is used
+ *                 only if our secret value \p X is re-used and omitted
+ *                 otherwise. Therefore, we recommend always passing a
+ *                 non-NULL \p f_rng argument.
  */
 int mbedtls_dhm_calc_secret( mbedtls_dhm_context *ctx,
                      unsigned char *output, size_t output_size, size_t *olen,
@@ -264,23 +318,24 @@
                      void *p_rng );
 
 /**
- * \brief          Free and clear the components of a DHM key
+ * \brief          This function frees and clears the components of a DHM key.
  *
- * \param ctx      DHM context to free and clear
+ * \param ctx      The DHM context to free and clear.
  */
 void mbedtls_dhm_free( mbedtls_dhm_context *ctx );
 
 #if defined(MBEDTLS_ASN1_PARSE_C)
 /** \ingroup x509_module */
 /**
- * \brief          Parse DHM parameters in PEM or DER format
+ * \brief             This function parses DHM parameters in PEM or DER format.
  *
- * \param dhm      DHM context to be initialized
- * \param dhmin    input buffer
- * \param dhminlen size of the buffer
- *                 (including the terminating null byte for PEM data)
+ * \param dhm         The DHM context to initialize.
+ * \param dhmin       The input buffer.
+ * \param dhminlen    The size of the buffer, including the terminating null
+ *                    Byte for PEM data.
  *
- * \return         0 if successful, or a specific DHM or PEM error code
+ * \return            \c 0 on success, or a specific DHM or PEM error code
+ *                    on failure.
  */
 int mbedtls_dhm_parse_dhm( mbedtls_dhm_context *dhm, const unsigned char *dhmin,
                    size_t dhminlen );
@@ -288,12 +343,13 @@
 #if defined(MBEDTLS_FS_IO)
 /** \ingroup x509_module */
 /**
- * \brief          Load and parse DHM parameters
+ * \brief          This function loads and parses DHM parameters from a file.
  *
- * \param dhm      DHM context to be initialized
- * \param path     filename to read the DHM Parameters from
+ * \param dhm      The DHM context to load the parameters to.
+ * \param path     The filename to read the DHM parameters from.
  *
- * \return         0 if successful, or a specific DHM or PEM error code
+ * \return         \c 0 on success, or a specific DHM or PEM error code
+ *                 on failure.
  */
 int mbedtls_dhm_parse_dhmfile( mbedtls_dhm_context *dhm, const char *path );
 #endif /* MBEDTLS_FS_IO */
@@ -312,9 +368,9 @@
 #endif
 
 /**
- * \brief          Checkup routine
+ * \brief          The DMH checkup routine.
  *
- * \return         0 if successful, or 1 if the test failed
+ * \return         \c 0 on success, or \c 1 on failure.
  */
 int mbedtls_dhm_self_test( int verbose );
 
diff --git a/library/error.c b/library/error.c
index f602686..d9ad638 100644
--- a/library/error.c
+++ b/library/error.c
@@ -227,7 +227,7 @@
 
 #if defined(MBEDTLS_DHM_C)
         if( use_ret == -(MBEDTLS_ERR_DHM_BAD_INPUT_DATA) )
-            mbedtls_snprintf( buf, buflen, "DHM - Bad input parameters to function" );
+            mbedtls_snprintf( buf, buflen, "DHM - Bad input parameters" );
         if( use_ret == -(MBEDTLS_ERR_DHM_READ_PARAMS_FAILED) )
             mbedtls_snprintf( buf, buflen, "DHM - Reading of the DHM parameters failed" );
         if( use_ret == -(MBEDTLS_ERR_DHM_MAKE_PARAMS_FAILED) )
@@ -243,7 +243,7 @@
         if( use_ret == -(MBEDTLS_ERR_DHM_ALLOC_FAILED) )
             mbedtls_snprintf( buf, buflen, "DHM - Allocation of memory failed" );
         if( use_ret == -(MBEDTLS_ERR_DHM_FILE_IO_ERROR) )
-            mbedtls_snprintf( buf, buflen, "DHM - Read/write of file failed" );
+            mbedtls_snprintf( buf, buflen, "DHM - Read or write of file failed" );
         if( use_ret == -(MBEDTLS_ERR_DHM_HW_ACCEL_FAILED) )
             mbedtls_snprintf( buf, buflen, "DHM - DHM hardware accelerator failed" );
 #endif /* MBEDTLS_DHM_C */