diff --git a/include/mbedtls/bignum.h b/include/mbedtls/bignum.h
index 7f718e647..5c9250397 100644
--- a/include/mbedtls/bignum.h
+++ b/include/mbedtls/bignum.h
@@ -894,6 +894,8 @@ int mbedtls_mpi_fill_random( mbedtls_mpi *X, size_t size,
  *
  * \return         \c 0 if successful.
  * \return         #MBEDTLS_ERR_MPI_ALLOC_FAILED if a memory allocation failed.
+ * \return         #MBEDTLS_ERR_MPI_BAD_INPUT_DATA if \p min or \p N is invalid
+ *                 or if they are incompatible.
  * \return         Another negative error code on failure.
  */
 int mbedtls_mpi_random( mbedtls_mpi *X,
diff --git a/library/bignum.c b/library/bignum.c
index 1cde6b0c2..9145a3d3c 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -2445,6 +2445,11 @@ int mbedtls_mpi_random( mbedtls_mpi *X,
     size_t n_bits = mbedtls_mpi_bitlen( N );
     size_t n_bytes = ( n_bits + 7 ) / 8;
 
+    if( min < 0 )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+    if( mbedtls_mpi_cmp_int( N, min ) <= 0 )
+        return( MBEDTLS_ERR_MPI_BAD_INPUT_DATA );
+
     /*
      * Match the procedure given in RFC 6979 §3.3 (deterministic ECDSA)
      * when f_rng is a suitably parametrized instance of HMAC_DRBG:
diff --git a/tests/suites/test_suite_mpi.data b/tests/suites/test_suite_mpi.data
index a057dcd88..fb2c553d0 100644
--- a/tests/suites/test_suite_mpi.data
+++ b/tests/suites/test_suite_mpi.data
@@ -1132,6 +1132,15 @@ mpi_random_many:1:"04":1000
 MPI random in range: 3..4
 mpi_random_many:1:"04":1000
 
+MPI random bad arguments: min < 0
+mpi_random_fail:-1:"04":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
+
+MPI random bad arguments: min = N = 0
+mpi_random_fail:0:"00":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
+
+MPI random bad arguments: min = N = 1
+mpi_random_fail:1:"01":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
+
 MPI Selftest
 depends_on:MBEDTLS_SELF_TEST
 mpi_selftest:
diff --git a/tests/suites/test_suite_mpi.function b/tests/suites/test_suite_mpi.function
index 8cf53b302..0ca6b6439 100644
--- a/tests/suites/test_suite_mpi.function
+++ b/tests/suites/test_suite_mpi.function
@@ -1537,6 +1537,28 @@ exit:
 }
 /* END_CASE */
 
+/* BEGIN_CASE */
+void mpi_random_fail( int min, data_t *bound_bytes, int expected_ret )
+{
+    mbedtls_mpi upper_bound;
+    mbedtls_mpi result;
+    int actual_ret;
+
+    mbedtls_mpi_init( &upper_bound );
+    mbedtls_mpi_init( &result );
+
+    TEST_EQUAL( 0, mbedtls_mpi_read_binary( &upper_bound,
+                                            bound_bytes->x, bound_bytes->len ) );
+    actual_ret = mbedtls_mpi_random( &result, min, &upper_bound,
+                                     mbedtls_test_rnd_std_rand, NULL );
+    TEST_EQUAL( expected_ret, actual_ret );
+
+exit:
+    mbedtls_mpi_free( &upper_bound );
+    mbedtls_mpi_free( &result );
+}
+/* END_CASE */
+
 /* BEGIN_CASE depends_on:MBEDTLS_SELF_TEST */
 void mpi_selftest(  )
 {