diff --git a/tests/suites/test_suite_bignum.function b/tests/suites/test_suite_bignum.function
index 6fd0b1b..9dc5e59 100644
--- a/tests/suites/test_suite_bignum.function
+++ b/tests/suites/test_suite_bignum.function
@@ -1296,8 +1296,45 @@
 /* END_CASE */
 
 /* BEGIN_CASE */
+void mpi_core_random_basic( int min, char *bound_bytes, int expected_ret )
+{
+    /* Same RNG as in mpi_random_values */
+    mbedtls_test_rnd_pseudo_info rnd = {
+        {'T', 'h', 'i', 's', ' ', 'i', ',', 'a',
+         's', 'e', 'e', 'd', '!', 0},
+        0, 0};
+    size_t limbs;
+    mbedtls_mpi_uint *lower_bound = NULL;
+    mbedtls_mpi_uint *upper_bound = NULL;
+    mbedtls_mpi_uint *result = NULL;
+
+    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &upper_bound, &limbs,
+                                               bound_bytes ) );
+    ASSERT_ALLOC( lower_bound, limbs * ciL );
+    lower_bound[0] = min;
+    ASSERT_ALLOC( result, limbs * ciL );
+
+    TEST_EQUAL( expected_ret,
+                mbedtls_mpi_core_random( result, min, upper_bound, limbs,
+                                         mbedtls_test_rnd_pseudo_rand, &rnd ) );
+
+    if( expected_ret == 0 )
+    {
+        TEST_EQUAL( 0, mbedtls_mpi_core_lt_ct( result, lower_bound, limbs ) );
+        TEST_EQUAL( 1, mbedtls_mpi_core_lt_ct( result, upper_bound, limbs ) );
+    }
+
+exit:
+    mbedtls_free( lower_bound );
+    mbedtls_free( upper_bound );
+    mbedtls_free( result );
+}
+/* END_CASE */
+
+/* BEGIN_CASE */
 void mpi_random_values( int min, char *max_hex )
 {
+    /* Same RNG as in mpi_core_random_basic */
     mbedtls_test_rnd_pseudo_info rnd_core = {
         {'T', 'h', 'i', 's', ' ', 'i', ',', 'a',
          's', 'e', 'e', 'd', '!', 0},
diff --git a/tests/suites/test_suite_bignum.misc.data b/tests/suites/test_suite_bignum.misc.data
index bc659c1..fa4c5bc 100644
--- a/tests/suites/test_suite_bignum.misc.data
+++ b/tests/suites/test_suite_bignum.misc.data
@@ -1788,6 +1788,51 @@
 Fill random: MAX_SIZE bytes, RNG failure after MAX_SIZE-1 bytes
 mpi_fill_random:MBEDTLS_MPI_MAX_SIZE:MBEDTLS_MPI_MAX_SIZE-1:0:MBEDTLS_ERR_ENTROPY_SOURCE_FAILED
 
+MPI core random basic: 0..1
+mpi_core_random_basic:0:"01":0
+
+MPI core random basic: 0..2
+mpi_core_random_basic:0:"02":0
+
+MPI core random basic: 1..2
+mpi_core_random_basic:1:"02":0
+
+MPI core random basic: 2^30..2^31
+mpi_core_random_basic:0x40000000:"80000000":0
+
+MPI core random basic: 0..2^128
+mpi_core_random_basic:0x40000000:"0100000000000000000000000000000000":0
+
+MPI core random basic: 2^30..2^129
+mpi_core_random_basic:0x40000000:"0200000000000000000000000000000000":0
+
+# Use the same data values for mpi_core_random_basic->NOT_ACCEPTABLE
+# and for mpi_random_values where we want to return NOT_ACCEPTABLE but
+# this isn't checked at runtime.
+MPI core random basic: 2^28-1..2^28 (NOT_ACCEPTABLE)
+mpi_core_random_basic:0x0fffffff:"10000000":MBEDTLS_ERR_MPI_NOT_ACCEPTABLE
+
+MPI random legacy=core: 2^28-1..2^28 (NOT_ACCEPTABLE)
+mpi_random_values:0x0fffffff:"10000000"
+
+MPI core random basic: 2^29-1..2^29 (NOT_ACCEPTABLE)
+mpi_core_random_basic:0x1fffffff:"20000000":MBEDTLS_ERR_MPI_NOT_ACCEPTABLE
+
+MPI random legacy=core: 2^29-1..2^29 (NOT_ACCEPTABLE)
+mpi_random_values:0x1fffffff:"20000000"
+
+MPI core random basic: 2^30-1..2^30 (NOT_ACCEPTABLE)
+mpi_core_random_basic:0x3fffffff:"40000000":MBEDTLS_ERR_MPI_NOT_ACCEPTABLE
+
+MPI random legacy=core: 2^30-1..2^30 (NOT_ACCEPTABLE)
+mpi_random_values:0x3fffffff:"40000000"
+
+MPI core random basic: 2^31-1..2^31 (NOT_ACCEPTABLE)
+mpi_core_random_basic:0x7fffffff:"80000000":MBEDTLS_ERR_MPI_NOT_ACCEPTABLE
+
+MPI random legacy=core: 2^31-1..2^31 (NOT_ACCEPTABLE)
+mpi_random_values:0x7fffffff:"80000000"
+
 MPI random in range: 1..2
 mpi_random_many:1:"02":1000