diff --git a/ChangeLog.d/issue4176.txt b/ChangeLog.d/issue4176.txt
new file mode 100644
index 0000000000..ddca37f9be
--- /dev/null
+++ b/ChangeLog.d/issue4176.txt
@@ -0,0 +1,3 @@
+Bugfix
+   * Fix a resource leak in a test suite with an alternative AES
+     implementation. Fixes #4176.
diff --git a/ChangeLog.d/random-range.txt b/ChangeLog.d/random-range.txt
new file mode 100644
index 0000000000..dc35ec6c66
--- /dev/null
+++ b/ChangeLog.d/random-range.txt
@@ -0,0 +1,4 @@
+Security
+* Fix a bias in the generation of finite-field Diffie-Hellman-Merkle (DHM)
+  private keys and of blinding values for DHM and elliptic curves (ECP)
+  computations. Reported by FlorianF89 in #4245.
diff --git a/ChangeLog.d/winsock.txt b/ChangeLog.d/winsock.txt
new file mode 100644
index 0000000000..0b42e691c2
--- /dev/null
+++ b/ChangeLog.d/winsock.txt
@@ -0,0 +1,4 @@
+Bugfix
+   * Fix mbedtls_net_poll() and mbedtls_net_recv_timeout() often failing with
+     MBEDTLS_ERR_NET_POLL_FAILED on Windows. Fixes #4465.
+
diff --git a/library/dhm.c b/library/dhm.c
index d652cf0ac9..535b698ce6 100644
--- a/library/dhm.c
+++ b/library/dhm.c
@@ -130,22 +130,21 @@ static int dhm_read_bignum( mbedtls_mpi *X,
  */
 static int dhm_check_range( const mbedtls_mpi *param, const mbedtls_mpi *P )
 {
-    mbedtls_mpi L, U;
+    mbedtls_mpi U;
     int ret = 0;
 
-    mbedtls_mpi_init( &L ); mbedtls_mpi_init( &U );
+    mbedtls_mpi_init( &U );
 
-    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &L, 2 ) );
     MBEDTLS_MPI_CHK( mbedtls_mpi_sub_int( &U, P, 2 ) );
 
-    if( mbedtls_mpi_cmp_mpi( param, &L ) < 0 ||
+    if( mbedtls_mpi_cmp_int( param, 2 ) < 0 ||
         mbedtls_mpi_cmp_mpi( param, &U ) > 0 )
     {
         ret = MBEDTLS_ERR_DHM_BAD_INPUT_DATA;
     }
 
 cleanup:
-    mbedtls_mpi_free( &L ); mbedtls_mpi_free( &U );
+    mbedtls_mpi_free( &U );
     return( ret );
 }
 
@@ -181,38 +180,54 @@ int mbedtls_dhm_read_params( mbedtls_dhm_context *ctx,
 }
 
 /*
- * Setup and write the ServerKeyExchange parameters
+ * Pick a random R in the range [2, M-2] for blinding or key generation.
  */
-int mbedtls_dhm_make_params( mbedtls_dhm_context *ctx, int x_size,
-                     unsigned char *output, size_t *olen,
-                     int (*f_rng)(void *, unsigned char *, size_t),
-                     void *p_rng )
+static int dhm_random_below( mbedtls_mpi *R, const mbedtls_mpi *M,
+                int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
 {
-    int ret, count = 0;
-    size_t n1, n2, n3;
-    unsigned char *p;
-    DHM_VALIDATE_RET( ctx != NULL );
-    DHM_VALIDATE_RET( output != NULL );
-    DHM_VALIDATE_RET( olen != NULL );
-    DHM_VALIDATE_RET( f_rng != NULL );
+    int ret, count;
+    size_t m_size = mbedtls_mpi_size( M );
+    size_t m_bitlen = mbedtls_mpi_bitlen( M );
+
+    count = 0;
+    do
+    {
+        if( count++ > 30 )
+            return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( R, m_size, f_rng, p_rng ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( R, ( m_size * 8 ) - m_bitlen ) );
+    }
+    while( dhm_check_range( R, M ) != 0 );
+
+cleanup:
+    return( ret );
+}
+
+static int dhm_make_common( mbedtls_dhm_context *ctx, int x_size,
+                            int (*f_rng)(void *, unsigned char *, size_t),
+                            void *p_rng )
+{
+    int ret = 0;
 
     if( mbedtls_mpi_cmp_int( &ctx->P, 0 ) == 0 )
         return( MBEDTLS_ERR_DHM_BAD_INPUT_DATA );
+    if( x_size < 0 )
+        return( MBEDTLS_ERR_DHM_BAD_INPUT_DATA );
 
-    /*
-     * Generate X as large as possible ( < P )
-     */
-    do
+    if( (unsigned) x_size < mbedtls_mpi_size( &ctx->P ) )
     {
         MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &ctx->X, x_size, f_rng, p_rng ) );
-
-        while( mbedtls_mpi_cmp_mpi( &ctx->X, &ctx->P ) >= 0 )
-            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &ctx->X, 1 ) );
-
-        if( count++ > 10 )
-            return( MBEDTLS_ERR_DHM_MAKE_PARAMS_FAILED );
     }
-    while( dhm_check_range( &ctx->X, &ctx->P ) != 0 );
+    else
+    {
+        /* Generate X as large as possible ( <= P - 2 ) */
+        ret = dhm_random_below( &ctx->X, &ctx->P, f_rng, p_rng );
+        if( ret == MBEDTLS_ERR_MPI_NOT_ACCEPTABLE )
+            return( MBEDTLS_ERR_DHM_MAKE_PARAMS_FAILED );
+        if( ret != 0 )
+            return( ret );
+    }
 
     /*
      * Calculate GX = G^X mod P
@@ -223,8 +238,33 @@ int mbedtls_dhm_make_params( mbedtls_dhm_context *ctx, int x_size,
     if( ( ret = dhm_check_range( &ctx->GX, &ctx->P ) ) != 0 )
         return( ret );
 
+cleanup:
+    return( ret );
+}
+
+/*
+ * Setup and write the ServerKeyExchange parameters
+ */
+int mbedtls_dhm_make_params( mbedtls_dhm_context *ctx, int x_size,
+                     unsigned char *output, size_t *olen,
+                     int (*f_rng)(void *, unsigned char *, size_t),
+                     void *p_rng )
+{
+    int ret;
+    size_t n1, n2, n3;
+    unsigned char *p;
+    DHM_VALIDATE_RET( ctx != NULL );
+    DHM_VALIDATE_RET( output != NULL );
+    DHM_VALIDATE_RET( olen != NULL );
+    DHM_VALIDATE_RET( f_rng != NULL );
+
+    ret = dhm_make_common( ctx, x_size, f_rng, p_rng );
+    if( ret != 0 )
+        goto cleanup;
+
     /*
-     * export P, G, GX
+     * Export P, G, GX. RFC 5246 §4.4 states that "leading zero octets are
+     * not required". We omit leading zeros for compactness.
      */
 #define DHM_MPI_EXPORT( X, n )                                          \
     do {                                                                \
@@ -250,11 +290,9 @@ int mbedtls_dhm_make_params( mbedtls_dhm_context *ctx, int x_size,
     ctx->len = n1;
 
 cleanup:
-
-    if( ret != 0 )
+    if( ret != 0 && ret > -128 )
         return( MBEDTLS_ERR_DHM_MAKE_PARAMS_FAILED + ret );
-
-    return( 0 );
+    return( ret );
 }
 
 /*
@@ -306,7 +344,7 @@ int mbedtls_dhm_make_public( mbedtls_dhm_context *ctx, int x_size,
                      int (*f_rng)(void *, unsigned char *, size_t),
                      void *p_rng )
 {
-    int ret, count = 0;
+    int ret;
     DHM_VALIDATE_RET( ctx != NULL );
     DHM_VALIDATE_RET( output != NULL );
     DHM_VALIDATE_RET( f_rng != NULL );
@@ -314,62 +352,18 @@ int mbedtls_dhm_make_public( mbedtls_dhm_context *ctx, int x_size,
     if( olen < 1 || olen > ctx->len )
         return( MBEDTLS_ERR_DHM_BAD_INPUT_DATA );
 
-    if( mbedtls_mpi_cmp_int( &ctx->P, 0 ) == 0 )
-        return( MBEDTLS_ERR_DHM_BAD_INPUT_DATA );
-
-    /*
-     * generate X and calculate GX = G^X mod P
-     */
-    do
-    {
-        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &ctx->X, x_size, f_rng, p_rng ) );
-
-        while( mbedtls_mpi_cmp_mpi( &ctx->X, &ctx->P ) >= 0 )
-            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &ctx->X, 1 ) );
-
-        if( count++ > 10 )
-            return( MBEDTLS_ERR_DHM_MAKE_PUBLIC_FAILED );
-    }
-    while( dhm_check_range( &ctx->X, &ctx->P ) != 0 );
-
-    MBEDTLS_MPI_CHK( mbedtls_mpi_exp_mod( &ctx->GX, &ctx->G, &ctx->X,
-                          &ctx->P , &ctx->RP ) );
-
-    if( ( ret = dhm_check_range( &ctx->GX, &ctx->P ) ) != 0 )
-        return( ret );
+    ret = dhm_make_common( ctx, x_size, f_rng, p_rng );
+    if( ret == MBEDTLS_ERR_DHM_MAKE_PARAMS_FAILED )
+        return( MBEDTLS_ERR_DHM_MAKE_PUBLIC_FAILED );
+    if( ret != 0 )
+        goto cleanup;
 
     MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->GX, output, olen ) );
 
 cleanup:
-
-    if( ret != 0 )
+    if( ret != 0 && ret > -128 )
         return( MBEDTLS_ERR_DHM_MAKE_PUBLIC_FAILED + ret );
 
-    return( 0 );
-}
-
-/*
- * Pick a random R in the range [2, M) for blinding purposes
- */
-static int dhm_random_below( mbedtls_mpi *R, const mbedtls_mpi *M,
-                int (*f_rng)(void *, unsigned char *, size_t), void *p_rng )
-{
-    int ret, count;
-
-    count = 0;
-    do
-    {
-        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( R, mbedtls_mpi_size( M ), f_rng, p_rng ) );
-
-        while( mbedtls_mpi_cmp_mpi( R, M ) >= 0 )
-            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( R, 1 ) );
-
-        if( count++ > 10 )
-            return( MBEDTLS_ERR_MPI_NOT_ACCEPTABLE );
-    }
-    while( mbedtls_mpi_cmp_int( R, 1 ) <= 0 );
-
-cleanup:
     return( ret );
 }
 
@@ -420,7 +414,7 @@ static int dhm_update_blinding( mbedtls_dhm_context *ctx,
      * We need to generate blinding values from scratch
      */
 
-    /* Vi = random( 2, P-1 ) */
+    /* Vi = random( 2, P-2 ) */
     MBEDTLS_MPI_CHK( dhm_random_below( &ctx->Vi, &ctx->P, f_rng, p_rng ) );
 
     /* Vf = Vi^-X mod P
@@ -484,8 +478,9 @@ int mbedtls_dhm_calc_secret( mbedtls_dhm_context *ctx,
         MBEDTLS_MPI_CHK( mbedtls_mpi_mod_mpi( &ctx->K, &ctx->K, &ctx->P ) );
     }
 
+    /* Output the secret without any leading zero byte. This is mandatory
+     * for TLS per RFC 5246 §8.1.2. */
     *olen = mbedtls_mpi_size( &ctx->K );
-
     MBEDTLS_MPI_CHK( mbedtls_mpi_write_binary( &ctx->K, output, *olen ) );
 
 cleanup:
diff --git a/library/ecp.c b/library/ecp.c
index 9db6988838..285c3636a9 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -1738,18 +1738,17 @@ static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *p
     /* Generate l such that 1 < l < p */
     do
     {
-        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
-
-        while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
-            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
-
-        if( count++ > 10 )
+        if( count++ > 30 )
         {
             ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
             goto cleanup;
         }
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, ( p_size * 8 ) - grp->pbits ) );
     }
-    while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
+    while( ( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 ) ||
+           ( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 ) );
 
     /* Z = l * Z */
     MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &pt->Z,   &pt->Z,     &l  ) ); MOD_MUL( pt->Z );
@@ -2514,18 +2513,17 @@ static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P
     /* Generate l such that 1 < l < p */
     do
     {
-        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
-
-        while( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 )
-            MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, 1 ) );
-
-        if( count++ > 10 )
+        if( count++ > 30 )
         {
             ret = MBEDTLS_ERR_ECP_RANDOM_FAILED;
             goto cleanup;
         }
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &l, ( p_size * 8 ) - grp->pbits ) );
     }
-    while( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 );
+    while( ( mbedtls_mpi_cmp_int( &l, 1 ) <= 0 ) ||
+           ( mbedtls_mpi_cmp_mpi( &l, &grp->P ) >= 0 ) );
 
     MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->X, &P->X, &l ) ); MOD_MUL( P->X );
     MBEDTLS_MPI_CHK( mbedtls_mpi_mul_mpi( &P->Z, &P->Z, &l ) ); MOD_MUL( P->Z );
diff --git a/library/net_sockets.c b/library/net_sockets.c
index 3874783750..1e701a5000 100644
--- a/library/net_sockets.c
+++ b/library/net_sockets.c
@@ -166,6 +166,31 @@ static int net_prepare( void )
     return( 0 );
 }
 
+/*
+ * Return 0 if the file descriptor is valid, an error otherwise.
+ * If for_select != 0, check whether the file descriptor is within the range
+ * allowed for fd_set used for the FD_xxx macros and the select() function.
+ */
+static int check_fd( int fd, int for_select )
+{
+    if( fd < 0 )
+        return( MBEDTLS_ERR_NET_INVALID_CONTEXT );
+
+#if (defined(_WIN32) || defined(_WIN32_WCE)) && !defined(EFIX64) && \
+    !defined(EFI32)
+    (void) for_select;
+#else
+    /* A limitation of select() is that it only works with file descriptors
+     * that are strictly less than FD_SETSIZE. This is a limitation of the
+     * fd_set type. Error out early, because attempting to call FD_SET on a
+     * large file descriptor is a buffer overflow on typical platforms. */
+    if( for_select && fd >= FD_SETSIZE )
+        return( MBEDTLS_ERR_NET_POLL_FAILED );
+#endif
+
+    return( 0 );
+}
+
 /*
  * Initialize a context
  */
@@ -497,15 +522,9 @@ int mbedtls_net_poll( mbedtls_net_context *ctx, uint32_t rw, uint32_t timeout )
 
     int fd = ctx->fd;
 
-    if( fd < 0 )
-        return( MBEDTLS_ERR_NET_INVALID_CONTEXT );
-
-    /* A limitation of select() is that it only works with file descriptors
-     * that are strictly less than FD_SETSIZE. This is a limitation of the
-     * fd_set type. Error out early, because attempting to call FD_SET on a
-     * large file descriptor is a buffer overflow on typical platforms. */
-    if( fd >= FD_SETSIZE )
-        return( MBEDTLS_ERR_NET_POLL_FAILED );
+    ret = check_fd( fd, 1 );
+    if( ret != 0 )
+        return( ret );
 
 #if defined(__has_feature)
 #if __has_feature(memory_sanitizer)
@@ -584,8 +603,9 @@ int mbedtls_net_recv( void *ctx, unsigned char *buf, size_t len )
     int ret;
     int fd = ((mbedtls_net_context *) ctx)->fd;
 
-    if( fd < 0 )
-        return( MBEDTLS_ERR_NET_INVALID_CONTEXT );
+    ret = check_fd( fd, 0 );
+    if( ret != 0 )
+        return( ret );
 
     ret = (int) read( fd, buf, len );
 
@@ -623,15 +643,9 @@ int mbedtls_net_recv_timeout( void *ctx, unsigned char *buf,
     fd_set read_fds;
     int fd = ((mbedtls_net_context *) ctx)->fd;
 
-    if( fd < 0 )
-        return( MBEDTLS_ERR_NET_INVALID_CONTEXT );
-
-    /* A limitation of select() is that it only works with file descriptors
-     * that are strictly less than FD_SETSIZE. This is a limitation of the
-     * fd_set type. Error out early, because attempting to call FD_SET on a
-     * large file descriptor is a buffer overflow on typical platforms. */
-    if( fd >= FD_SETSIZE )
-        return( MBEDTLS_ERR_NET_POLL_FAILED );
+    ret = check_fd( fd, 1 );
+    if( ret != 0 )
+        return( ret );
 
     FD_ZERO( &read_fds );
     FD_SET( fd, &read_fds );
@@ -671,8 +685,9 @@ int mbedtls_net_send( void *ctx, const unsigned char *buf, size_t len )
     int ret;
     int fd = ((mbedtls_net_context *) ctx)->fd;
 
-    if( fd < 0 )
-        return( MBEDTLS_ERR_NET_INVALID_CONTEXT );
+    ret = check_fd( fd, 0 );
+    if( ret != 0 )
+        return( ret );
 
     ret = (int) write( fd, buf, len );
 
diff --git a/tests/suites/test_suite_aes.function b/tests/suites/test_suite_aes.function
index 23bf83d093..1b7e5dbb27 100644
--- a/tests/suites/test_suite_aes.function
+++ b/tests/suites/test_suite_aes.function
@@ -208,6 +208,8 @@ void aes_crypt_xts_size( int size, int retval )
     /* Valid pointers are passed for builds with MBEDTLS_CHECK_PARAMS, as
      * otherwise we wouldn't get to the size check we're interested in. */
     TEST_ASSERT( mbedtls_aes_crypt_xts( &ctx, MBEDTLS_AES_ENCRYPT, length, data_unit, src, output ) == retval );
+exit:
+    mbedtls_aes_xts_free( &ctx );
 }
 /* END_CASE */
 
diff --git a/tests/suites/test_suite_dhm.data b/tests/suites/test_suite_dhm.data
index c4795b6d34..6802f548cb 100644
--- a/tests/suites/test_suite_dhm.data
+++ b/tests/suites/test_suite_dhm.data
@@ -1,26 +1,92 @@
+Diffie-Hellman full exchange: tiny x_size
+dhm_do_dhm:10:"93450983094850938450983409623":1:10:"9345098304850938450983409622":0
+
 Diffie-Hellman parameter validation
 dhm_invalid_params:
 
-Diffie-Hellman full exchange #1
-dhm_do_dhm:10:"23":10:"5":0
+Diffie-Hellman full exchange: 5-bit, x_size=3
+dhm_do_dhm:10:"23":3:10:"5":0
 
-Diffie-Hellman full exchange #2
-dhm_do_dhm:10:"93450983094850938450983409623":10:"9345098304850938450983409622":0
+Diffie-Hellman full exchange: 5-bit, x_size=2
+dhm_do_dhm:10:"23":2:10:"5":0
 
-Diffie-Hellman full exchange #3
-dhm_do_dhm:10:"93450983094850938450983409623982317398171298719873918739182739712938719287391879381271":10:"9345098309485093845098340962223981329819812792137312973297123912791271":0
+## Repeat this test case and a few similar ones several times. The RNG state
+## changes, so we get to exercise the code with a few different values.
+Diffie-Hellman full exchange: 5-bit #1
+dhm_do_dhm:10:"23":1:10:"5":0
+
+Diffie-Hellman full exchange: 5-bit #2
+dhm_do_dhm:10:"23":1:10:"5":0
+
+Diffie-Hellman full exchange: 5-bit #3
+dhm_do_dhm:10:"23":1:10:"5":0
+
+Diffie-Hellman full exchange: 5-bit #4
+dhm_do_dhm:10:"23":1:10:"5":0
+
+Diffie-Hellman full exchange: 5-bit #5
+dhm_do_dhm:10:"23":1:10:"5":0
+
+## This is x_size = P_size + 1. Arguably x_size > P_size makes no sense,
+## but it's the current undocumented behavior to treat it the same as when
+## x_size = P_size. If this behavior changes in the future, change the expected
+## return status from 0 to MBEDTLS_ERR_DHM_BAD_INPUT_DATA.
+Diffie-Hellman full exchange: 97-bit, x_size=14
+dhm_do_dhm:10:"93450983094850938450983409623":14:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit #1
+dhm_do_dhm:10:"93450983094850938450983409623":13:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit #2
+dhm_do_dhm:10:"93450983094850938450983409623":13:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit #3
+dhm_do_dhm:10:"93450983094850938450983409623":13:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit #4
+dhm_do_dhm:10:"93450983094850938450983409623":13:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit #5
+dhm_do_dhm:10:"93450983094850938450983409623":13:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit, x_size=12
+dhm_do_dhm:10:"93450983094850938450983409623":12:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit, x_size=11
+dhm_do_dhm:10:"93450983094850938450983409623":11:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit, x_size=1 #1
+dhm_do_dhm:10:"93450983094850938450983409623":1:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit, x_size=1 #2
+dhm_do_dhm:10:"93450983094850938450983409623":1:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit, x_size=1 #3
+dhm_do_dhm:10:"93450983094850938450983409623":1:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit, x_size=1 #4
+dhm_do_dhm:10:"93450983094850938450983409623":1:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 97-bit, x_size=1 #5
+dhm_do_dhm:10:"93450983094850938450983409623":1:10:"9345098304850938450983409622":0
+
+Diffie-Hellman full exchange: 286-bit
+dhm_do_dhm:10:"93450983094850938450983409623982317398171298719873918739182739712938719287391879381271":36:10:"9345098309485093845098340962223981329819812792137312973297123912791271":0
 
 Diffie-Hellman trivial subgroup #1
-dhm_do_dhm:10:"23":10:"1":MBEDTLS_ERR_DHM_BAD_INPUT_DATA
+dhm_do_dhm:10:"23":1:10:"1":MBEDTLS_ERR_DHM_BAD_INPUT_DATA
 
 Diffie-Hellman trivial subgroup #2
-dhm_do_dhm:10:"23":10:"-1":MBEDTLS_ERR_DHM_BAD_INPUT_DATA
+dhm_do_dhm:10:"23":1:10:"-1":MBEDTLS_ERR_DHM_BAD_INPUT_DATA
 
 Diffie-Hellman small modulus
-dhm_do_dhm:10:"3":10:"5":MBEDTLS_ERR_DHM_MAKE_PARAMS_FAILED
+dhm_do_dhm:10:"3":1:10:"5":MBEDTLS_ERR_DHM_MAKE_PARAMS_FAILED
 
 Diffie-Hellman zero modulus
-dhm_do_dhm:10:"0":10:"5":MBEDTLS_ERR_DHM_BAD_INPUT_DATA
+dhm_do_dhm:10:"0":1:10:"5":MBEDTLS_ERR_DHM_BAD_INPUT_DATA
+
+Diffie-Hellman: x_size < 0
+dhm_do_dhm:10:"93450983094850938450983409623":-1:10:"9345098304850938450983409622":MBEDTLS_ERR_DHM_BAD_INPUT_DATA
 
 Diffie-Hellman MPI_MAX_SIZE modulus
 dhm_make_public:MBEDTLS_MPI_MAX_SIZE:10:"5":0
diff --git a/tests/suites/test_suite_dhm.function b/tests/suites/test_suite_dhm.function
index 6ec1e7e882..2e8644d6be 100644
--- a/tests/suites/test_suite_dhm.function
+++ b/tests/suites/test_suite_dhm.function
@@ -1,5 +1,66 @@
 /* BEGIN_HEADER */
 #include "mbedtls/dhm.h"
+
+/* Sanity checks on a Diffie-Hellman parameter: check the length-value
+ * syntax and check that the value is the expected one (taken from the
+ * DHM context by the caller). */
+static int check_dhm_param_output( const mbedtls_mpi *expected,
+                                   const unsigned char *buffer,
+                                   size_t size,
+                                   size_t *offset )
+{
+    size_t n;
+    mbedtls_mpi actual;
+    int ok = 0;
+    mbedtls_mpi_init( &actual );
+
+    TEST_ASSERT( size >= *offset + 2 );
+    n = ( buffer[*offset] << 8 ) | buffer[*offset + 1];
+    *offset += 2;
+    /* The DHM param output from Mbed TLS has leading zeros stripped, as
+     * permitted but not required by RFC 5246 \S4.4. */
+    TEST_EQUAL( n, mbedtls_mpi_size( expected ) );
+    TEST_ASSERT( size >= *offset + n );
+    TEST_EQUAL( 0, mbedtls_mpi_read_binary( &actual, buffer + *offset, n ) );
+    TEST_EQUAL( 0, mbedtls_mpi_cmp_mpi( expected, &actual ) );
+    *offset += n;
+
+    ok = 1;
+exit:
+    mbedtls_mpi_free( &actual );
+    return( ok );
+}
+
+/* Sanity checks on Diffie-Hellman parameters: syntax, range, and comparison
+ * against the context. */
+static int check_dhm_params( const mbedtls_dhm_context *ctx,
+                             size_t x_size,
+                             const unsigned char *ske, size_t ske_len )
+{
+    size_t offset = 0;
+
+    /* Check that ctx->X and ctx->GX are within range. */
+    TEST_ASSERT( mbedtls_mpi_cmp_int( &ctx->X, 1 ) > 0 );
+    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &ctx->X, &ctx->P ) < 0 );
+    TEST_ASSERT( mbedtls_mpi_size( &ctx->X ) <= x_size );
+    TEST_ASSERT( mbedtls_mpi_cmp_int( &ctx->GX, 1 ) > 0 );
+    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &ctx->GX, &ctx->P ) < 0 );
+
+    /* Check ske: it must contain P, G and G^X, each prefixed with a
+     * 2-byte size. */
+    if( !check_dhm_param_output( &ctx->P, ske, ske_len, &offset ) )
+        goto exit;
+    if( !check_dhm_param_output( &ctx->G, ske, ske_len, &offset ) )
+        goto exit;
+    if( !check_dhm_param_output( &ctx->GX, ske, ske_len, &offset ) )
+        goto exit;
+    TEST_EQUAL( offset, ske_len );
+
+    return( 1 );
+exit:
+    return( 0 );
+}
+
 /* END_HEADER */
 
 /* BEGIN_DEPENDENCIES
@@ -115,7 +176,7 @@ exit:
 /* END_CASE */
 
 /* BEGIN_CASE */
-void dhm_do_dhm( int radix_P, char *input_P,
+void dhm_do_dhm( int radix_P, char *input_P, int x_size,
                  int radix_G, char *input_G, int result )
 {
     mbedtls_dhm_context ctx_srv;
@@ -129,7 +190,7 @@ void dhm_do_dhm( int radix_P, char *input_P,
     size_t pub_cli_len = 0;
     size_t sec_srv_len;
     size_t sec_cli_len;
-    int x_size, i;
+    int i;
     rnd_pseudo_info rnd_info;
 
     mbedtls_dhm_init( &ctx_srv );
@@ -145,15 +206,18 @@ void dhm_do_dhm( int radix_P, char *input_P,
      */
     TEST_ASSERT( mbedtls_mpi_read_string( &ctx_srv.P, radix_P, input_P ) == 0 );
     TEST_ASSERT( mbedtls_mpi_read_string( &ctx_srv.G, radix_G, input_G ) == 0 );
-    x_size = mbedtls_mpi_size( &ctx_srv.P );
-    pub_cli_len = x_size;
+    pub_cli_len = mbedtls_mpi_size( &ctx_srv.P );
 
     /*
      * First key exchange
      */
-    TEST_ASSERT( mbedtls_dhm_make_params( &ctx_srv, x_size, ske, &ske_len, &rnd_pseudo_rand, &rnd_info ) == result );
+    TEST_ASSERT( mbedtls_dhm_make_params( &ctx_srv, x_size, ske, &ske_len,
+                                          &rnd_pseudo_rand,
+                                          &rnd_info ) == result );
     if ( result != 0 )
         goto exit;
+    if( !check_dhm_params( &ctx_srv, x_size, ske, ske_len ) )
+        goto exit;
 
     ske[ske_len++] = 0;
     ske[ske_len++] = 0;
@@ -185,7 +249,11 @@ void dhm_do_dhm( int radix_P, char *input_P,
      */
     p = ske;
 
-    TEST_ASSERT( mbedtls_dhm_make_params( &ctx_srv, x_size, ske, &ske_len, &rnd_pseudo_rand, &rnd_info ) == 0 );
+    TEST_ASSERT( mbedtls_dhm_make_params( &ctx_srv, x_size, ske, &ske_len,
+                                          &rnd_pseudo_rand,
+                                          &rnd_info ) == 0 );
+    if( !check_dhm_params( &ctx_srv, x_size, ske, ske_len ) )
+        goto exit;
     ske[ske_len++] = 0;
     ske[ske_len++] = 0;
     TEST_ASSERT( mbedtls_dhm_read_params( &ctx_cli, &p, ske + ske_len ) == 0 );