diff --git a/library/ecp.c b/library/ecp.c
index ecea591..c509c82 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -788,7 +788,7 @@
 }
 
 /*
- * Import a point from unsigned binary data (SEC1 2.3.4)
+ * Import a point from unsigned binary data (SEC1 2.3.4 and RFC7748)
  */
 int mbedtls_ecp_point_read_binary( const mbedtls_ecp_group *grp,
                                    mbedtls_ecp_point *pt,
@@ -803,24 +803,45 @@
     if( ilen < 1 )
         return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
-    if( buf[0] == 0x00 )
-    {
-        if( ilen == 1 )
-            return( mbedtls_ecp_set_zero( pt ) );
-        else
-            return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
-    }
-
     plen = mbedtls_mpi_size( &grp->P );
 
-    if( buf[0] != 0x04 )
-        return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+#if defined(ECP_MONTGOMERY)
+    if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
+    {
+        if( plen != ilen )
+            return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
 
-    if( ilen != 2 * plen + 1 )
-        return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary_le( &pt->X, buf, plen ) );
+        mbedtls_mpi_free( &pt->Y );
 
-    MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y, buf + 1 + plen, plen ) );
+        if( grp->id == MBEDTLS_ECP_DP_CURVE25519 )
+            /* Set most significant bit to 0 */
+            MBEDTLS_MPI_CHK( mbedtls_mpi_set_bit( &pt->X, plen * 8 - 1, 0 ) );
+    }
+#endif
+#if defined(ECP_SHORTWEIERSTRASS)
+    if( ecp_get_type( grp ) != ECP_TYPE_MONTGOMERY )
+    {
+        if( buf[0] == 0x00 )
+        {
+            if( ilen == 1 )
+                return( mbedtls_ecp_set_zero( pt ) );
+            else
+                return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+        }
+
+        if( buf[0] != 0x04 )
+            return( MBEDTLS_ERR_ECP_FEATURE_UNAVAILABLE );
+
+        if( ilen != 2 * plen + 1 )
+            return( MBEDTLS_ERR_ECP_BAD_INPUT_DATA );
+
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->X, buf + 1, plen ) );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_read_binary( &pt->Y,
+                                                  buf + 1 + plen, plen ) );
+    }
+#endif
+
     MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &pt->Z, 1 ) );
 
 cleanup:
diff --git a/tests/suites/test_suite_ecp.data b/tests/suites/test_suite_ecp.data
index 30d5ec6..77fa724 100644
--- a/tests/suites/test_suite_ecp.data
+++ b/tests/suites/test_suite_ecp.data
@@ -112,6 +112,18 @@
 depends_on:MBEDTLS_ECP_DP_SECP192R1_ENABLED
 ecp_read_binary:MBEDTLS_ECP_DP_SECP192R1:"0448d8082a3a1e3112bc03a8ef2f6d40d0a77a6f8e00cc99336ceed4d7cba482e288669ee1b6415626d6f34d28501e060c":"48d8082a3a1e3112bc03a8ef2f6d40d0a77a6f8e00cc9933":"6ceed4d7cba482e288669ee1b6415626d6f34d28501e060c":"01":0
 
+ECP read binary #7 (Montgomery, OK)
+depends_on:MBEDTLS_ECP_DP_CURVE25519_ENABLED
+ecp_read_binary:MBEDTLS_ECP_DP_CURVE25519:"8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a":"6a4e9baa8ea9a4ebf41a38260d3abf0d5af73eb4dc7d8b7454a7308909f02085":"0":"1":0
+
+ECP read binary #8 (Montgomery, masked first bit)
+depends_on:MBEDTLS_ECP_DP_CURVE25519_ENABLED
+ecp_read_binary:MBEDTLS_ECP_DP_CURVE25519:"8520f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4efa":"7a4e9baa8ea9a4ebf41a38260d3abf0d5af73eb4dc7d8b7454a7308909f02085":"0":"1":0
+
+ECP read binary #9 (Montgomery, invalid length)
+depends_on:MBEDTLS_ECP_DP_CURVE25519_ENABLED
+ecp_read_binary:MBEDTLS_ECP_DP_CURVE25519:"20f0098930a754748b7ddcb43ef75a0dbf3a0d26381af4eba4a98eaa9b4e6a":"6a4e9baa8ea9a4ebf41a38260d3abf0d5af73eb4dc7d8b7454a7308909f020":"0":"1":MBEDTLS_ERR_ECP_BAD_INPUT_DATA
+
 ECP tls read point #1 (zero, invalid length byte)
 depends_on:MBEDTLS_ECP_DP_SECP192R1_ENABLED
 mbedtls_ecp_tls_read_point:MBEDTLS_ECP_DP_SECP192R1:"0200":"01":"01":"00":MBEDTLS_ERR_ECP_BAD_INPUT_DATA
diff --git a/tests/suites/test_suite_ecp.function b/tests/suites/test_suite_ecp.function
index 606ddd2..58361db 100644
--- a/tests/suites/test_suite_ecp.function
+++ b/tests/suites/test_suite_ecp.function
@@ -760,8 +760,23 @@
     if( ret == 0 )
     {
         TEST_ASSERT( mbedtls_mpi_cmp_mpi( &P.X, &X ) == 0 );
-        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &P.Y, &Y ) == 0 );
-        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &P.Z, &Z ) == 0 );
+        /*
+         * At the time of writing, the following condition is equivalent with
+         * if( ecp_get_type( grp ) == ECP_TYPE_MONTGOMERY )
+         * but has the advantage of not using internal symbols.
+         */
+        if( grp.G.Y.p == NULL )
+        {
+            TEST_ASSERT( mbedtls_mpi_cmp_int( &Y, 0 ) == 0 );
+            TEST_ASSERT( P.Y.p == NULL );
+            TEST_ASSERT( mbedtls_mpi_cmp_int( &Z, 1 ) == 0 );
+            TEST_ASSERT( mbedtls_mpi_cmp_int( &P.Z, 1 ) == 0 );
+        }
+        else
+        {
+            TEST_ASSERT( mbedtls_mpi_cmp_mpi( &P.Y, &Y ) == 0 );
+            TEST_ASSERT( mbedtls_mpi_cmp_mpi( &P.Z, &Z ) == 0 );
+        }
     }
 
 exit: