diff --git a/tests/suites/test_suite_ecp.data b/tests/suites/test_suite_ecp.data
index c007cad..5f92ca4 100644
--- a/tests/suites/test_suite_ecp.data
+++ b/tests/suites/test_suite_ecp.data
@@ -312,105 +312,6 @@
 ECP generate Montgomery key: Curve448, not enough entropy
 genkey_mx_known_answer:447:"4f0102030405060708090a0b0c0d0e0f101112131415161718191a1b1c1d1e1f202122232425262728292a2b2c2d2e2f30313233343536":""
 
-MPI random in range: 1..4
-mpi_random_many:1:"04":1000
-
-MPI random in range: 1..5
-mpi_random_many:1:"05":1000
-
-MPI random in range: 1..6
-mpi_random_many:1:"06":1000
-
-MPI random in range: 1..7
-mpi_random_many:1:"07":1000
-
-MPI random in range: 1..8
-mpi_random_many:1:"08":1000
-
-MPI random in range: 1..9
-mpi_random_many:1:"09":1000
-
-MPI random in range: 1..10
-mpi_random_many:1:"0a":1000
-
-MPI random in range: 1..11
-mpi_random_many:1:"0b":1000
-
-MPI random in range: 1..12
-mpi_random_many:1:"0c":1000
-
-MPI random in range: 1..255
-mpi_random_many:1:"ff":100
-
-MPI random in range: 1..256
-mpi_random_many:1:"0100":100
-
-MPI random in range: 1..257
-mpi_random_many:1:"0101":100
-
-MPI random in range: 1..272
-mpi_random_many:1:"0110":100
-
-MPI random in range: 1..2^64-1
-mpi_random_many:1:"ffffffffffffffff":100
-
-MPI random in range: 1..2^64
-mpi_random_many:1:"010000000000000000":100
-
-MPI random in range: 1..2^64+1
-mpi_random_many:1:"010000000000000001":100
-
-MPI random in range: 1..2^64+2^63
-mpi_random_many:1:"018000000000000000":100
-
-MPI random in range: 1..2^65-1
-mpi_random_many:1:"01ffffffffffffffff":100
-
-MPI random in range: 1..2^65
-mpi_random_many:1:"020000000000000000":100
-
-MPI random in range: 1..2^65+1
-mpi_random_many:1:"020000000000000001":100
-
-MPI random in range: 1..2^65+2^64
-mpi_random_many:1:"030000000000000000":100
-
-MPI random in range: 1..2^66+2^65
-mpi_random_many:1:"060000000000000000":100
-
-MPI random in range: 1..2^71-1
-mpi_random_many:1:"7fffffffffffffffff":100
-
-MPI random in range: 1..2^71
-mpi_random_many:1:"800000000000000000":100
-
-MPI random in range: 1..2^71+1
-mpi_random_many:1:"800000000000000001":100
-
-MPI random in range: 1..2^71+2^63
-mpi_random_many:1:"c00000000000000000":100
-
-MPI random in range: 1..2^72-1
-mpi_random_many:1:"ffffffffffffffffff":100
-
-MPI random in range: 1..2^72
-mpi_random_many:1:"01000000000000000000":100
-
-MPI random in range: 1..2^72+1
-mpi_random_many:1:"01000000000000000001":100
-
-MPI random in range: 1..2^72+2^63
-mpi_random_many:1:"01800000000000000000":100
-
-MPI random in range: 0..4
-mpi_random_many:0:"04":1000
-
-MPI random in range: 2..4
-mpi_random_many:1:"04":1000
-
-MPI random in range: 3..4
-mpi_random_many:1:"04":1000
-
 ECP read key #1 (short weierstrass, too small)
 depends_on:MBEDTLS_ECP_DP_SECP192R1_ENABLED
 mbedtls_ecp_read_key:MBEDTLS_ECP_DP_SECP192R1:"00":MBEDTLS_ERR_ECP_INVALID_KEY:0
diff --git a/tests/suites/test_suite_ecp.function b/tests/suites/test_suite_ecp.function
index fadc300..934598d 100644
--- a/tests/suites/test_suite_ecp.function
+++ b/tests/suites/test_suite_ecp.function
@@ -16,42 +16,6 @@
     mbedtls_ecp_point_free( x );    \
     mbedtls_ecp_point_init( x );
 
-#if defined(MBEDTLS_TEST_HOOKS) && defined(MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED)
-/* Test whether bytes represents (in big-endian base 256) a number B that
- * is "significantly" above a power of 2, which is defined as follows.
- * Let n be the integer such that 2^n <= B < 2^{n+1}. B is significantly
- * above a power of 2 if (B - 2^n) / 2^n is not negligible. "Negligible"
- * is defined as having a negligible chance that if you draw an integer
- * in the range [1, B-1] K times, the number will always be less than 2^n,
- * where K is the iteration count passed to genkey_sw_many.
- */
-static int is_significantly_above_a_power_of_2( data_t *bytes )
-{
-    const uint8_t *p = bytes->x;
-    size_t len = bytes->len;
-    unsigned x;
-    while( len > 0 && p[0] == 0 )
-    {
-        ++p;
-        --len;
-    }
-    if( len == 0 )
-        return( 0 );
-    else if( len == 1 )
-        x = p[0];
-    else
-        x = ( p[0] << 8 ) | p[1];
-
-    if( x <= 4 )
-        return( 0 );
-
-    while( ( x & 0x8000 ) == 0 )
-        x <<= 1;
-    x &= 0x7fff;
-    return( x >= 0x1000 );
-}
-#endif
-
 /* END_HEADER */
 
 /* BEGIN_DEPENDENCIES
@@ -1323,113 +1287,6 @@
 }
 /* END_CASE */
 
-/* BEGIN_CASE depends_on:MBEDTLS_TEST_HOOKS:MBEDTLS_ECP_SHORT_WEIERSTRASS_ENABLED */
-void mpi_random_many( int min, data_t *bound_bytes, int iterations )
-{
-    /* Generate numbers in the range 1..bound-1. Do it iterations times.
-     * This function assumes that the value of bound is at least 2 and
-     * that iterations is large enough that a one-in-2^iterations chance
-     * effectively never occurs.
-     */
-
-    mbedtls_mpi upper_bound;
-    size_t n_bits;
-    mbedtls_mpi result;
-    size_t b;
-    /* If upper_bound is small, stats[b] is the number of times the value b
-     * has been generated. Otherwise stats[b] is the number of times a
-     * value with bit b set has been generated. */
-    size_t *stats = NULL;
-    size_t stats_len;
-    int full_stats;
-    size_t i;
-
-    mbedtls_mpi_init( &upper_bound );
-    mbedtls_mpi_init( &result );
-
-    TEST_EQUAL( 0, mbedtls_mpi_read_binary( &upper_bound,
-                                            bound_bytes->x, bound_bytes->len ) );
-    n_bits = mbedtls_mpi_bitlen( &upper_bound );
-    /* Consider a bound "small" if it's less than 2^5. This value is chosen
-     * to be small enough that the probability of missing one value is
-     * negligible given the number of iterations. It must be less than
-     * 256 because some of the code below assumes that "small" values
-     * fit in a byte. */
-    if( n_bits <= 5 )
-    {
-        full_stats = 1;
-        stats_len = bound_bytes->x[bound_bytes->len - 1];
-    }
-    else
-    {
-        full_stats = 0;
-        stats_len = n_bits;
-    }
-    ASSERT_ALLOC( stats, stats_len );
-
-    for( i = 0; i < (size_t) iterations; i++ )
-    {
-        mbedtls_test_set_step( i );
-        TEST_EQUAL( 0, mbedtls_mpi_random( &result, min, &upper_bound,
-                                           mbedtls_test_rnd_std_rand, NULL ) );
-
-        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &result, &upper_bound ) < 0 );
-        TEST_ASSERT( mbedtls_mpi_cmp_int( &result, min ) >= 0 );
-        if( full_stats )
-        {
-            uint8_t value;
-            TEST_EQUAL( 0, mbedtls_mpi_write_binary( &result, &value, 1 ) );
-            TEST_ASSERT( value < stats_len );
-            ++stats[value];
-        }
-        else
-        {
-            for( b = 0; b < n_bits; b++ )
-                stats[b] += mbedtls_mpi_get_bit( &result, b );
-        }
-    }
-
-    if( full_stats )
-    {
-        for( b = 1; b < stats_len; b++ )
-        {
-            mbedtls_test_set_step( 1000000 + b );
-            /* Assert that each value has been reached at least once.
-             * This is almost guaranteed if the iteration count is large
-             * enough. This is a very crude way of checking the distribution.
-             */
-            TEST_ASSERT( stats[b] > 0 );
-        }
-    }
-    else
-    {
-        for( b = 0; b < n_bits; b++ )
-        {
-            mbedtls_test_set_step( 1000000 + b );
-            /* Assert that each bit has been set in at least one result and
-             * clear in at least one result. Provided that iterations is not
-             * too small, it would be extremely unlikely for this not to be
-             * the case if the results are uniformly distributed.
-             *
-             * As an exception, the top bit may legitimately never be set
-             * if bound is a power of 2 or only slightly above.
-             */
-            if( b != n_bits - 1 ||
-                is_significantly_above_a_power_of_2( bound_bytes ) )
-            {
-                TEST_ASSERT( stats[b] > 0 );
-            }
-            TEST_ASSERT( stats[b] < (size_t) iterations );
-        }
-    }
-
-exit:
-    mbedtls_mpi_free( &upper_bound );
-    mbedtls_mpi_free( &result );
-    mbedtls_free( stats );
-}
-/* END_CASE */
-
 /* BEGIN_CASE depends_on:MBEDTLS_SELF_TEST */
 void ecp_selftest(  )
 {
diff --git a/tests/suites/test_suite_mpi.data b/tests/suites/test_suite_mpi.data
index 59fd782..a057dcd 100644
--- a/tests/suites/test_suite_mpi.data
+++ b/tests/suites/test_suite_mpi.data
@@ -1033,6 +1033,105 @@
 Fill random: MAX_SIZE bytes, RNG failure after MAX_SIZE-1 bytes
 mpi_fill_random:MBEDTLS_MPI_MAX_SIZE:MBEDTLS_MPI_MAX_SIZE-1:MBEDTLS_ERR_ENTROPY_SOURCE_FAILED
 
+MPI random in range: 1..4
+mpi_random_many:1:"04":1000
+
+MPI random in range: 1..5
+mpi_random_many:1:"05":1000
+
+MPI random in range: 1..6
+mpi_random_many:1:"06":1000
+
+MPI random in range: 1..7
+mpi_random_many:1:"07":1000
+
+MPI random in range: 1..8
+mpi_random_many:1:"08":1000
+
+MPI random in range: 1..9
+mpi_random_many:1:"09":1000
+
+MPI random in range: 1..10
+mpi_random_many:1:"0a":1000
+
+MPI random in range: 1..11
+mpi_random_many:1:"0b":1000
+
+MPI random in range: 1..12
+mpi_random_many:1:"0c":1000
+
+MPI random in range: 1..255
+mpi_random_many:1:"ff":100
+
+MPI random in range: 1..256
+mpi_random_many:1:"0100":100
+
+MPI random in range: 1..257
+mpi_random_many:1:"0101":100
+
+MPI random in range: 1..272
+mpi_random_many:1:"0110":100
+
+MPI random in range: 1..2^64-1
+mpi_random_many:1:"ffffffffffffffff":100
+
+MPI random in range: 1..2^64
+mpi_random_many:1:"010000000000000000":100
+
+MPI random in range: 1..2^64+1
+mpi_random_many:1:"010000000000000001":100
+
+MPI random in range: 1..2^64+2^63
+mpi_random_many:1:"018000000000000000":100
+
+MPI random in range: 1..2^65-1
+mpi_random_many:1:"01ffffffffffffffff":100
+
+MPI random in range: 1..2^65
+mpi_random_many:1:"020000000000000000":100
+
+MPI random in range: 1..2^65+1
+mpi_random_many:1:"020000000000000001":100
+
+MPI random in range: 1..2^65+2^64
+mpi_random_many:1:"030000000000000000":100
+
+MPI random in range: 1..2^66+2^65
+mpi_random_many:1:"060000000000000000":100
+
+MPI random in range: 1..2^71-1
+mpi_random_many:1:"7fffffffffffffffff":100
+
+MPI random in range: 1..2^71
+mpi_random_many:1:"800000000000000000":100
+
+MPI random in range: 1..2^71+1
+mpi_random_many:1:"800000000000000001":100
+
+MPI random in range: 1..2^71+2^63
+mpi_random_many:1:"c00000000000000000":100
+
+MPI random in range: 1..2^72-1
+mpi_random_many:1:"ffffffffffffffffff":100
+
+MPI random in range: 1..2^72
+mpi_random_many:1:"01000000000000000000":100
+
+MPI random in range: 1..2^72+1
+mpi_random_many:1:"01000000000000000001":100
+
+MPI random in range: 1..2^72+2^63
+mpi_random_many:1:"01800000000000000000":100
+
+MPI random in range: 0..4
+mpi_random_many:0:"04":1000
+
+MPI random in range: 2..4
+mpi_random_many:1:"04":1000
+
+MPI random in range: 3..4
+mpi_random_many:1:"04":1000
+
 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 c5bb5a6..8cf53b3 100644
--- a/tests/suites/test_suite_mpi.function
+++ b/tests/suites/test_suite_mpi.function
@@ -64,6 +64,40 @@
     return( 0 );
 }
 
+/* Test whether bytes represents (in big-endian base 256) a number B that
+ * is "significantly" above a power of 2, which is defined as follows.
+ * Let n be the integer such that 2^n <= B < 2^{n+1}. B is significantly
+ * above a power of 2 if (B - 2^n) / 2^n is not negligible. "Negligible"
+ * is defined as having a negligible chance that if you draw an integer
+ * in the range [1, B-1] K times, the number will always be less than 2^n,
+ * where K is the iteration count passed to genkey_sw_many.
+ */
+static int is_significantly_above_a_power_of_2( data_t *bytes )
+{
+    const uint8_t *p = bytes->x;
+    size_t len = bytes->len;
+    unsigned x;
+    while( len > 0 && p[0] == 0 )
+    {
+        ++p;
+        --len;
+    }
+    if( len == 0 )
+        return( 0 );
+    else if( len == 1 )
+        x = p[0];
+    else
+        x = ( p[0] << 8 ) | p[1];
+
+    if( x <= 4 )
+        return( 0 );
+
+    while( ( x & 0x8000 ) == 0 )
+        x <<= 1;
+    x &= 0x7fff;
+    return( x >= 0x1000 );
+}
+
 /* END_HEADER */
 
 /* BEGIN_DEPENDENCIES
@@ -1396,6 +1430,113 @@
 }
 /* END_CASE */
 
+/* BEGIN_CASE */
+void mpi_random_many( int min, data_t *bound_bytes, int iterations )
+{
+    /* Generate numbers in the range 1..bound-1. Do it iterations times.
+     * This function assumes that the value of bound is at least 2 and
+     * that iterations is large enough that a one-in-2^iterations chance
+     * effectively never occurs.
+     */
+
+    mbedtls_mpi upper_bound;
+    size_t n_bits;
+    mbedtls_mpi result;
+    size_t b;
+    /* If upper_bound is small, stats[b] is the number of times the value b
+     * has been generated. Otherwise stats[b] is the number of times a
+     * value with bit b set has been generated. */
+    size_t *stats = NULL;
+    size_t stats_len;
+    int full_stats;
+    size_t i;
+
+    mbedtls_mpi_init( &upper_bound );
+    mbedtls_mpi_init( &result );
+
+    TEST_EQUAL( 0, mbedtls_mpi_read_binary( &upper_bound,
+                                            bound_bytes->x, bound_bytes->len ) );
+    n_bits = mbedtls_mpi_bitlen( &upper_bound );
+    /* Consider a bound "small" if it's less than 2^5. This value is chosen
+     * to be small enough that the probability of missing one value is
+     * negligible given the number of iterations. It must be less than
+     * 256 because some of the code below assumes that "small" values
+     * fit in a byte. */
+    if( n_bits <= 5 )
+    {
+        full_stats = 1;
+        stats_len = bound_bytes->x[bound_bytes->len - 1];
+    }
+    else
+    {
+        full_stats = 0;
+        stats_len = n_bits;
+    }
+    ASSERT_ALLOC( stats, stats_len );
+
+    for( i = 0; i < (size_t) iterations; i++ )
+    {
+        mbedtls_test_set_step( i );
+        TEST_EQUAL( 0, mbedtls_mpi_random( &result, min, &upper_bound,
+                                           mbedtls_test_rnd_std_rand, NULL ) );
+
+        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &result, &upper_bound ) < 0 );
+        TEST_ASSERT( mbedtls_mpi_cmp_int( &result, min ) >= 0 );
+        if( full_stats )
+        {
+            uint8_t value;
+            TEST_EQUAL( 0, mbedtls_mpi_write_binary( &result, &value, 1 ) );
+            TEST_ASSERT( value < stats_len );
+            ++stats[value];
+        }
+        else
+        {
+            for( b = 0; b < n_bits; b++ )
+                stats[b] += mbedtls_mpi_get_bit( &result, b );
+        }
+    }
+
+    if( full_stats )
+    {
+        for( b = 1; b < stats_len; b++ )
+        {
+            mbedtls_test_set_step( 1000000 + b );
+            /* Assert that each value has been reached at least once.
+             * This is almost guaranteed if the iteration count is large
+             * enough. This is a very crude way of checking the distribution.
+             */
+            TEST_ASSERT( stats[b] > 0 );
+        }
+    }
+    else
+    {
+        for( b = 0; b < n_bits; b++ )
+        {
+            mbedtls_test_set_step( 1000000 + b );
+            /* Assert that each bit has been set in at least one result and
+             * clear in at least one result. Provided that iterations is not
+             * too small, it would be extremely unlikely for this not to be
+             * the case if the results are uniformly distributed.
+             *
+             * As an exception, the top bit may legitimately never be set
+             * if bound is a power of 2 or only slightly above.
+             */
+            if( b != n_bits - 1 ||
+                is_significantly_above_a_power_of_2( bound_bytes ) )
+            {
+                TEST_ASSERT( stats[b] > 0 );
+            }
+            TEST_ASSERT( stats[b] < (size_t) iterations );
+        }
+    }
+
+exit:
+    mbedtls_mpi_free( &upper_bound );
+    mbedtls_mpi_free( &result );
+    mbedtls_free( stats );
+}
+/* END_CASE */
+
 /* BEGIN_CASE depends_on:MBEDTLS_SELF_TEST */
 void mpi_selftest(  )
 {