diff --git a/ChangeLog b/ChangeLog
index c81c259e3..96f4b31f0 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -11,6 +11,8 @@ Bugfix
    * Fix resource leak on windows platform, in mbedtls_x509_crt_parse_path.
      In case of failure, when an error occures, goto cleanup.
      Found by redplait #590
+   * Add MBEDTLS_MPI_CHK to check for error value of mbedtls_mpi_fill_random.
+     Reported and fix suggested by guidovranken in #740
 
 Security
    * Fix authentication bypass in SSL/TLS: when auth_mode is set to optional,
diff --git a/library/dhm.c b/library/dhm.c
index a4715d170..bec52a11d 100644
--- a/library/dhm.c
+++ b/library/dhm.c
@@ -165,7 +165,7 @@ int mbedtls_dhm_make_params( mbedtls_dhm_context *ctx, int x_size,
      */
     do
     {
-        mbedtls_mpi_fill_random( &ctx->X, x_size, f_rng, p_rng );
+        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 ) );
@@ -251,7 +251,7 @@ int mbedtls_dhm_make_public( mbedtls_dhm_context *ctx, int x_size,
      */
     do
     {
-        mbedtls_mpi_fill_random( &ctx->X, x_size, f_rng, p_rng );
+        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 ) );
@@ -324,7 +324,7 @@ static int dhm_update_blinding( mbedtls_dhm_context *ctx,
     count = 0;
     do
     {
-        mbedtls_mpi_fill_random( &ctx->Vi, mbedtls_mpi_size( &ctx->P ), f_rng, p_rng );
+        MBEDTLS_MPI_CHK( mbedtls_mpi_fill_random( &ctx->Vi, mbedtls_mpi_size( &ctx->P ), f_rng, p_rng ) );
 
         while( mbedtls_mpi_cmp_mpi( &ctx->Vi, &ctx->P ) >= 0 )
             MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( &ctx->Vi, 1 ) );
diff --git a/library/ecp.c b/library/ecp.c
index 1cfd4b10f..5ad686398 100644
--- a/library/ecp.c
+++ b/library/ecp.c
@@ -1128,7 +1128,7 @@ static int ecp_randomize_jac( const mbedtls_ecp_group *grp, mbedtls_ecp_point *p
     /* Generate l such that 1 < l < p */
     do
     {
-        mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
+        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 ) );
@@ -1527,7 +1527,7 @@ static int ecp_randomize_mxz( const mbedtls_ecp_group *grp, mbedtls_ecp_point *P
     /* Generate l such that 1 < l < p */
     do
     {
-        mbedtls_mpi_fill_random( &l, p_size, f_rng, p_rng );
+        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 ) );