Merge pull request #6303 from gilles-peskine-arm/bignum-core-random

Bignum: Implement mbedtls_mpi_core_random
diff --git a/library/bignum.c b/library/bignum.c
index 65708c9..fc4ddf6 100644
--- a/library/bignum.c
+++ b/library/bignum.c
@@ -2032,75 +2032,19 @@
                         int (*f_rng)(void *, unsigned char *, size_t),
                         void *p_rng )
 {
-    int ret = MBEDTLS_ERR_MPI_BAD_INPUT_DATA;
-    int count;
-    unsigned lt_lower = 1, lt_upper = 0;
-    size_t n_bits = mbedtls_mpi_bitlen( N );
-    size_t n_bytes = ( n_bits + 7 ) / 8;
-    mbedtls_mpi lower_bound;
-
     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 );
 
-    /*
-     * When min == 0, each try has at worst a probability 1/2 of failing
-     * (the msb has a probability 1/2 of being 0, and then the result will
-     * be < N), so after 30 tries failure probability is a most 2**(-30).
-     *
-     * When N is just below a power of 2, as is the case when generating
-     * a random scalar on most elliptic curves, 1 try is enough with
-     * overwhelming probability. When N is just above a power of 2,
-     * as when generating a random scalar on secp224k1, each try has
-     * a probability of failing that is almost 1/2.
-     *
-     * The probabilities are almost the same if min is nonzero but negligible
-     * compared to N. This is always the case when N is crypto-sized, but
-     * it's convenient to support small N for testing purposes. When N
-     * is small, use a higher repeat count, otherwise the probability of
-     * failure is macroscopic.
-     */
-    count = ( n_bytes > 4 ? 30 : 250 );
-
-    mbedtls_mpi_init( &lower_bound );
-
     /* Ensure that target MPI has exactly the same number of limbs
      * as the upper bound, even if the upper bound has leading zeros.
-     * This is necessary for the mbedtls_mpi_lt_mpi_ct() check. */
-    MBEDTLS_MPI_CHK( mbedtls_mpi_resize_clear( X, N->n ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_grow( &lower_bound, N->n ) );
-    MBEDTLS_MPI_CHK( mbedtls_mpi_lset( &lower_bound, min ) );
+     * This is necessary for mbedtls_mpi_core_random. */
+    int ret = mbedtls_mpi_resize_clear( X, N->n );
+    if( ret != 0 )
+        return( ret );
 
-    /*
-     * Match the procedure given in RFC 6979 §3.3 (deterministic ECDSA)
-     * when f_rng is a suitably parametrized instance of HMAC_DRBG:
-     * - use the same byte ordering;
-     * - keep the leftmost n_bits bits of the generated octet string;
-     * - try until result is in the desired range.
-     * This also avoids any bias, which is especially important for ECDSA.
-     */
-    do
-    {
-        MBEDTLS_MPI_CHK( mbedtls_mpi_core_fill_random( X->p, X->n,
-                                                       n_bytes,
-                                                       f_rng, p_rng ) );
-        MBEDTLS_MPI_CHK( mbedtls_mpi_shift_r( X, 8 * n_bytes - n_bits ) );
-
-        if( --count == 0 )
-        {
-            ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
-            goto cleanup;
-        }
-
-        MBEDTLS_MPI_CHK( mbedtls_mpi_lt_mpi_ct( X, &lower_bound, &lt_lower ) );
-        MBEDTLS_MPI_CHK( mbedtls_mpi_lt_mpi_ct( X, N, &lt_upper ) );
-    }
-    while( lt_lower != 0 || lt_upper == 0 );
-
-cleanup:
-    mbedtls_mpi_free( &lower_bound );
-    return( ret );
+    return( mbedtls_mpi_core_random( X->p, min, N->p, X->n, f_rng, p_rng ) );
 }
 
 /*
diff --git a/library/bignum_core.c b/library/bignum_core.c
index 1ce8457..064b158 100644
--- a/library/bignum_core.c
+++ b/library/bignum_core.c
@@ -134,6 +134,27 @@
     }
 }
 
+/* Whether min <= A, in constant time.
+ * A_limbs must be at least 1. */
+unsigned mbedtls_mpi_core_uint_le_mpi( mbedtls_mpi_uint min,
+                                       const mbedtls_mpi_uint *A,
+                                       size_t A_limbs )
+{
+    /* min <= least significant limb? */
+    unsigned min_le_lsl = 1 ^ mbedtls_ct_mpi_uint_lt( A[0], min );
+
+    /* limbs other than the least significant one are all zero? */
+    mbedtls_mpi_uint msll_mask = 0;
+    for( size_t i = 1; i < A_limbs; i++ )
+        msll_mask |= A[i];
+    /* The most significant limbs of A are not all zero iff msll_mask != 0. */
+    unsigned msll_nonzero = mbedtls_ct_mpi_uint_mask( msll_mask ) & 1;
+
+    /* min <= A iff the lowest limb of A is >= min or the other limbs
+     * are not all zero. */
+    return( min_le_lsl | msll_nonzero );
+}
+
 void mbedtls_mpi_core_cond_assign( mbedtls_mpi_uint *X,
                                    const mbedtls_mpi_uint *A,
                                    size_t limbs,
@@ -561,6 +582,67 @@
     return( ret );
 }
 
+int mbedtls_mpi_core_random( mbedtls_mpi_uint *X,
+                             mbedtls_mpi_uint min,
+                             const mbedtls_mpi_uint *N,
+                             size_t limbs,
+                             int (*f_rng)(void *, unsigned char *, size_t),
+                             void *p_rng )
+{
+    unsigned ge_lower = 1, lt_upper = 0;
+    size_t n_bits = mbedtls_mpi_core_bitlen( N, limbs );
+    size_t n_bytes = ( n_bits + 7 ) / 8;
+    int ret = MBEDTLS_ERR_ERROR_CORRUPTION_DETECTED;
+
+    /*
+     * When min == 0, each try has at worst a probability 1/2 of failing
+     * (the msb has a probability 1/2 of being 0, and then the result will
+     * be < N), so after 30 tries failure probability is a most 2**(-30).
+     *
+     * When N is just below a power of 2, as is the case when generating
+     * a random scalar on most elliptic curves, 1 try is enough with
+     * overwhelming probability. When N is just above a power of 2,
+     * as when generating a random scalar on secp224k1, each try has
+     * a probability of failing that is almost 1/2.
+     *
+     * The probabilities are almost the same if min is nonzero but negligible
+     * compared to N. This is always the case when N is crypto-sized, but
+     * it's convenient to support small N for testing purposes. When N
+     * is small, use a higher repeat count, otherwise the probability of
+     * failure is macroscopic.
+     */
+    int count = ( n_bytes > 4 ? 30 : 250 );
+
+    /*
+     * Match the procedure given in RFC 6979 §3.3 (deterministic ECDSA)
+     * when f_rng is a suitably parametrized instance of HMAC_DRBG:
+     * - use the same byte ordering;
+     * - keep the leftmost n_bits bits of the generated octet string;
+     * - try until result is in the desired range.
+     * This also avoids any bias, which is especially important for ECDSA.
+     */
+    do
+    {
+        MBEDTLS_MPI_CHK( mbedtls_mpi_core_fill_random( X, limbs,
+                                                       n_bytes,
+                                                       f_rng, p_rng ) );
+        mbedtls_mpi_core_shift_r( X, limbs, 8 * n_bytes - n_bits );
+
+        if( --count == 0 )
+        {
+            ret = MBEDTLS_ERR_MPI_NOT_ACCEPTABLE;
+            goto cleanup;
+        }
+
+        ge_lower = mbedtls_mpi_core_uint_le_mpi( min, X, limbs );
+        lt_upper = mbedtls_mpi_core_lt_ct( X, N, limbs );
+    }
+    while( ge_lower == 0 || lt_upper == 0 );
+
+cleanup:
+    return( ret );
+}
+
 /* BEGIN MERGE SLOT 1 */
 
 static size_t exp_mod_get_window_size( size_t Ebits )
diff --git a/library/bignum_core.h b/library/bignum_core.h
index b7af4d0..bfc9725 100644
--- a/library/bignum_core.h
+++ b/library/bignum_core.h
@@ -129,6 +129,22 @@
 void mbedtls_mpi_core_bigendian_to_host( mbedtls_mpi_uint *A,
                                          size_t A_limbs );
 
+/** \brief         Compare a machine integer with an MPI.
+ *
+ *                 This function operates in constant time with respect
+ *                 to the values of \p min and \p A.
+ *
+ * \param min      A machine integer.
+ * \param[in] A    An MPI.
+ * \param A_limbs  The number of limbs of \p A.
+ *                 This must be at least 1.
+ *
+ * \return         1 if \p min is less than or equal to \p A, otherwise 0.
+ */
+unsigned mbedtls_mpi_core_uint_le_mpi( mbedtls_mpi_uint min,
+                                       const mbedtls_mpi_uint *A,
+                                       size_t A_limbs );
+
 /**
  * \brief   Perform a safe conditional copy of an MPI which doesn't reveal
  *          whether assignment was done or not.
@@ -496,6 +512,43 @@
                                   int (*f_rng)(void *, unsigned char *, size_t),
                                   void *p_rng );
 
+/** Generate a random number uniformly in a range.
+ *
+ * This function generates a random number between \p min inclusive and
+ * \p N exclusive.
+ *
+ * The procedure complies with RFC 6979 §3.3 (deterministic ECDSA)
+ * when the RNG is a suitably parametrized instance of HMAC_DRBG
+ * and \p min is \c 1.
+ *
+ * \note           There are `N - min` possible outputs. The lower bound
+ *                 \p min can be reached, but the upper bound \p N cannot.
+ *
+ * \param X        The destination MPI, with \p limbs limbs.
+ *                 It must not be aliased with \p N or otherwise overlap it.
+ * \param min      The minimum value to return.
+ * \param N        The upper bound of the range, exclusive, with \p limbs limbs.
+ *                 In other words, this is one plus the maximum value to return.
+ *                 \p N must be strictly larger than \p min.
+ * \param limbs    The number of limbs of \p N and \p X.
+ *                 This must not be 0.
+ * \param f_rng    The RNG function to use. This must not be \c NULL.
+ * \param p_rng    The RNG parameter to be passed to \p f_rng.
+ *
+ * \return         \c 0 if successful.
+ * \return         #MBEDTLS_ERR_MPI_NOT_ACCEPTABLE if the implementation was
+ *                 unable to find a suitable value within a limited number
+ *                 of attempts. This has a negligible probability if \p N
+ *                 is significantly larger than \p min, which is the case
+ *                 for all usual cryptographic applications.
+ */
+int mbedtls_mpi_core_random( mbedtls_mpi_uint *X,
+                             mbedtls_mpi_uint min,
+                             const mbedtls_mpi_uint *N,
+                             size_t limbs,
+                             int (*f_rng)(void *, unsigned char *, size_t),
+                             void *p_rng );
+
 /* BEGIN MERGE SLOT 1 */
 
 /**
diff --git a/tests/suites/test_suite_bignum.function b/tests/suites/test_suite_bignum.function
index 55bb2f5..01af2ff 100644
--- a/tests/suites/test_suite_bignum.function
+++ b/tests/suites/test_suite_bignum.function
@@ -2,6 +2,7 @@
 #include "mbedtls/bignum.h"
 #include "mbedtls/entropy.h"
 #include "constant_time_internal.h"
+#include "bignum_core.h"
 #include "test/constant_flow.h"
 
 #if MBEDTLS_MPI_MAX_BITS > 792
@@ -89,50 +90,6 @@
     return( 0 );
 }
 
-/* Test whether bytes represents (in big-endian base 256) a number b that
- * is significantly above a power of 2. That is, b must not have a long run
- * of unset bits after the most significant bit.
- *
- * Let n be the bit-size of b, i.e. the integer such that 2^n <= b < 2^{n+1}.
- * This function returns 1 if, when drawing a number between 0 and b,
- * the probability that this number is at least 2^n is not negligible.
- * This probability is (b - 2^n) / b and this function checks that this
- * number is above some threshold A. The threshold value is heuristic and
- * based on the needs of mpi_random_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;
-
-    /* Skip leading null bytes */
-    while( len > 0 && p[0] == 0 )
-    {
-        ++p;
-        --len;
-    }
-    /* 0 is not significantly above a power of 2 */
-    if( len == 0 )
-        return( 0 );
-    /* Extract the (up to) 2 most significant bytes */
-    if( len == 1 )
-        x = p[0];
-    else
-        x = ( p[0] << 8 ) | p[1];
-
-    /* Shift the most significant bit of x to position 8 and mask it out */
-    while( ( x & 0xfe00 ) != 0 )
-        x >>= 1;
-    x &= 0x00ff;
-
-    /* At this point, x = floor((b - 2^n) / 2^(n-8)). b is significantly above
-     * a power of 2 iff x is significantly above 0 compared to 2^8.
-     * Testing x >= 2^4 amounts to picking A = 1/16 in the function
-     * description above. */
-    return( x >= 0x10 );
-}
-
 /* END_HEADER */
 
 /* BEGIN_DEPENDENCIES
@@ -1295,170 +1252,6 @@
 /* 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( sign_is_valid( &result ) );
-        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 = min; 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
-    {
-        int statistically_safe_all_the_way =
-            is_significantly_above_a_power_of_2( bound_bytes );
-        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( statistically_safe_all_the_way || b != n_bits - 1 )
-            {
-                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 */
-void mpi_random_sizes( int min, data_t *bound_bytes, int nlimbs, int before )
-{
-    mbedtls_mpi upper_bound;
-    mbedtls_mpi result;
-
-    mbedtls_mpi_init( &upper_bound );
-    mbedtls_mpi_init( &result );
-
-    if( before != 0 )
-    {
-        /* Set result to sign(before) * 2^(|before|-1) */
-        TEST_ASSERT( mbedtls_mpi_lset( &result, before > 0 ? 1 : -1 ) == 0 );
-        if( before < 0 )
-            before = - before;
-        TEST_ASSERT( mbedtls_mpi_shift_l( &result, before - 1 ) == 0 );
-    }
-
-    TEST_EQUAL( 0, mbedtls_mpi_grow( &result, nlimbs ) );
-    TEST_EQUAL( 0, mbedtls_mpi_read_binary( &upper_bound,
-                                            bound_bytes->x, bound_bytes->len ) );
-    TEST_EQUAL( 0, mbedtls_mpi_random( &result, min, &upper_bound,
-                                       mbedtls_test_rnd_std_rand, NULL ) );
-    TEST_ASSERT( sign_is_valid( &result ) );
-    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &result, &upper_bound ) < 0 );
-    TEST_ASSERT( mbedtls_mpi_cmp_int( &result, min ) >= 0 );
-
-exit:
-    mbedtls_mpi_free( &upper_bound );
-    mbedtls_mpi_free( &result );
-}
-/* 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 */
 void most_negative_mpi_sint( )
 {
     /* Ad hoc tests for n = -p = -2^(biL-1) as a mbedtls_mpi_sint. We
@@ -1481,7 +1274,6 @@
     mbedtls_mpi_init( &R );
     mbedtls_mpi_init( &X );
 
-    const size_t biL = 8 * sizeof( mbedtls_mpi_sint );
     mbedtls_mpi_uint most_positive_plus_1 = (mbedtls_mpi_uint) 1 << ( biL - 1 );
     const mbedtls_mpi_sint most_positive = most_positive_plus_1 - 1;
     const mbedtls_mpi_sint most_negative = - most_positive - 1;
diff --git a/tests/suites/test_suite_bignum.misc.data b/tests/suites/test_suite_bignum.misc.data
index dc6830e..5eda4c1 100644
--- a/tests/suites/test_suite_bignum.misc.data
+++ b/tests/suites/test_suite_bignum.misc.data
@@ -1788,176 +1788,6 @@
 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 random in range: 1..2
-mpi_random_many:1:"02":1000
-
-MPI random in range: 1..3
-mpi_random_many:1:"03":1000
-
-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":200
-
-MPI random in range: 1..256
-mpi_random_many:1:"0100":200
-
-MPI random in range: 1..257
-mpi_random_many:1:"0101":200
-
-MPI random in range: 1..272
-mpi_random_many:1:"0110":200
-
-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+2^70
-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+2^71
-mpi_random_many:1:"01800000000000000000":100
-
-MPI random in range: 0..1
-mpi_random_many:0:"04":10000
-
-MPI random in range: 0..4
-mpi_random_many:0:"04":10000
-
-MPI random in range: 2..4
-mpi_random_many:2:"04":10000
-
-MPI random in range: 3..4
-mpi_random_many:3:"04":10000
-
-MPI random in range: smaller result
-mpi_random_sizes:1:"aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb":1:0
-
-MPI random in range: same size result (32-bit limbs)
-mpi_random_sizes:1:"aaaaaaaaaaaaaaaa":2:0
-
-MPI random in range: same size result (64-bit limbs)
-mpi_random_sizes:1:"aaaaaaaaaaaaaaaa":1:0
-
-MPI random in range: larger result
-mpi_random_sizes:1:"aaaaaaaaaaaaaaaa":3:0
-
-## The "0 limb in upper bound" tests rely on the fact that
-## mbedtls_mpi_read_binary() bases the size of the MPI on the size of
-## the input, without first checking for leading zeros. If this was
-## not the case, the tests would still pass, but would not exercise
-## the advertised behavior.
-MPI random in range: leading 0 limb in upper bound #0
-mpi_random_sizes:1:"00aaaaaaaaaaaaaaaa":0:0
-
-MPI random in range: leading 0 limb in upper bound #1
-mpi_random_sizes:1:"00aaaaaaaaaaaaaaaa":1:0
-
-MPI random in range: leading 0 limb in upper bound #2
-mpi_random_sizes:1:"00aaaaaaaaaaaaaaaa":2:0
-
-MPI random in range: leading 0 limb in upper bound #3
-mpi_random_sizes:1:"00aaaaaaaaaaaaaaaa":3:0
-
-MPI random in range: leading 0 limb in upper bound #4
-mpi_random_sizes:1:"00aaaaaaaaaaaaaaaa":4:0
-
-MPI random in range: previously small >0
-mpi_random_sizes:1:"1234567890":4:1
-
-MPI random in range: previously small <0
-mpi_random_sizes:1:"1234567890":4:-1
-
-MPI random in range: previously large >0
-mpi_random_sizes:1:"1234":4:65
-
-MPI random in range: previously large <0
-mpi_random_sizes:1:"1234":4:-65
-
-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 random bad arguments: min > N = 0
-mpi_random_fail:1:"00":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
-
-MPI random bad arguments: min > N = 1
-mpi_random_fail:2:"01":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
-
-MPI random bad arguments: min > N = 1, 0 limb in upper bound
-mpi_random_fail:2:"000000000000000001":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
-
 Most negative mbedtls_mpi_sint
 most_negative_mpi_sint:
 
diff --git a/tests/suites/test_suite_bignum_core.function b/tests/suites/test_suite_bignum_core.function
index 7872115..9cb314b 100644
--- a/tests/suites/test_suite_bignum_core.function
+++ b/tests/suites/test_suite_bignum_core.function
@@ -345,6 +345,56 @@
 /* END_CASE */
 
 /* BEGIN_CASE */
+void mpi_core_uint_le_mpi( char *input_A )
+{
+    mbedtls_mpi_uint *A = NULL;
+    size_t A_limbs = 0;
+
+    TEST_EQUAL( mbedtls_test_read_mpi_core( &A, &A_limbs, input_A ), 0 );
+
+    int is_large = 0; /* nonzero limbs beyond the lowest-order one? */
+    for( size_t i = 1; i < A_limbs; i++ )
+    {
+        if( A[i] != 0 )
+        {
+            is_large = 1;
+            break;
+        }
+    }
+
+    TEST_CF_SECRET( A, A_limbs * sizeof( *A ) );
+
+    TEST_EQUAL( mbedtls_mpi_core_uint_le_mpi( 0, A, A_limbs ), 1 );
+    TEST_EQUAL( mbedtls_mpi_core_uint_le_mpi( A[0], A, A_limbs ), 1 );
+
+    if( is_large )
+    {
+        TEST_EQUAL( mbedtls_mpi_core_uint_le_mpi( A[0] + 1,
+                                                  A, A_limbs ), 1 );
+        TEST_EQUAL( mbedtls_mpi_core_uint_le_mpi( (mbedtls_mpi_uint)( -1 ) >> 1,
+                                                  A, A_limbs ), 1 );
+        TEST_EQUAL( mbedtls_mpi_core_uint_le_mpi( (mbedtls_mpi_uint)( -1 ),
+                                                  A, A_limbs ), 1 );
+    }
+    else
+    {
+        TEST_EQUAL( mbedtls_mpi_core_uint_le_mpi( A[0] + 1,
+                                                  A, A_limbs ),
+                    A[0] + 1 <= A[0] );
+        TEST_EQUAL( mbedtls_mpi_core_uint_le_mpi( (mbedtls_mpi_uint)( -1 ) >> 1,
+                                                  A, A_limbs ),
+                    (mbedtls_mpi_uint)( -1 ) >> 1 <= A[0] );
+        TEST_EQUAL( mbedtls_mpi_core_uint_le_mpi( (mbedtls_mpi_uint)( -1 ),
+                                                  A, A_limbs ),
+                    (mbedtls_mpi_uint)( -1 ) <= A[0] );
+    }
+
+exit:
+    mbedtls_free( A );
+}
+/* END_CASE */
+
+/* BEGIN_CASE */
 void mpi_core_cond_assign( char * input_X,
                            char * input_Y,
                            int input_bytes )
diff --git a/tests/suites/test_suite_bignum_core.misc.data b/tests/suites/test_suite_bignum_core.misc.data
index 62480e4..81a767a 100644
--- a/tests/suites/test_suite_bignum_core.misc.data
+++ b/tests/suites/test_suite_bignum_core.misc.data
@@ -242,6 +242,69 @@
 mbedtls_mpi_core_lt_ct: x>y (alternating limbs)
 mpi_core_lt_ct:"FF1111111111111111":"11FFFFFFFFFFFFFFFF":0
 
+Test mbedtls_mpi_core_uint_le_mpi: 0 (1 limb)
+mpi_core_uint_le_mpi:"00"
+
+Test mbedtls_mpi_core_uint_le_mpi: 0 (>=2 limbs)
+mpi_core_uint_le_mpi:"000000000000000000"
+
+Test mbedtls_mpi_core_uint_le_mpi: 1 (1 limb)
+mpi_core_uint_le_mpi:"01"
+
+Test mbedtls_mpi_core_uint_le_mpi: 1 (>=2 limbs)
+mpi_core_uint_le_mpi:"000000000000000001"
+
+Test mbedtls_mpi_core_uint_le_mpi: 42 (1 limb)
+mpi_core_uint_le_mpi:"2a"
+
+Test mbedtls_mpi_core_uint_le_mpi: 42 (>=2 limbs)
+mpi_core_uint_le_mpi:"000000000000000042"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^31-1
+mpi_core_uint_le_mpi:"7fffffff"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^31-1 with leading zero limb
+mpi_core_uint_le_mpi:"00000000007fffffff"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^32-1
+mpi_core_uint_le_mpi:"ffffffff"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^32-1 with leading zero limb
+mpi_core_uint_le_mpi:"0000000000ffffffff"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^32
+mpi_core_uint_le_mpi:"10000000"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^32 with leading zero limb
+mpi_core_uint_le_mpi:"000000000010000000"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^32+1
+mpi_core_uint_le_mpi:"10000001"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^32+1 with leading zero limb
+mpi_core_uint_le_mpi:"000000000010000001"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^63-1
+mpi_core_uint_le_mpi:"7fffffffffffffff"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^63-1 with leading zero limb
+mpi_core_uint_le_mpi:"007fffffffffffffff"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^64-1
+mpi_core_uint_le_mpi:"ffffffffffffffff"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^64-1 with leading zero limb
+mpi_core_uint_le_mpi:"00ffffffffffffffff"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^64
+mpi_core_uint_le_mpi:"010000000000000000"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^64+1
+mpi_core_uint_le_mpi:"010000000000000001"
+
+Test mbedtls_mpi_core_uint_le_mpi: 2^64+2
+mpi_core_uint_le_mpi:"010000000000000002"
+
 mbedtls_mpi_core_cond_assign: 1 limb
 mpi_core_cond_assign:"FFFFFFFF":"11111111":4
 
diff --git a/tests/suites/test_suite_bignum_random.data b/tests/suites/test_suite_bignum_random.data
new file mode 100644
index 0000000..fe29053
--- /dev/null
+++ b/tests/suites/test_suite_bignum_random.data
@@ -0,0 +1,235 @@
+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
+
+MPI random in range: 1..3
+mpi_random_many:1:"03":1000
+
+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":200
+
+MPI random in range: 1..256
+mpi_random_many:1:"0100":200
+
+MPI random in range: 1..257
+mpi_random_many:1:"0101":200
+
+MPI random in range: 1..272
+mpi_random_many:1:"0110":200
+
+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+2^70
+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+2^71
+mpi_random_many:1:"01800000000000000000":100
+
+MPI random in range: 0..1
+mpi_random_many:0:"04":10000
+
+MPI random in range: 0..4
+mpi_random_many:0:"04":10000
+
+MPI random in range: 2..4
+mpi_random_many:2:"04":10000
+
+MPI random in range: 3..4
+mpi_random_many:3:"04":10000
+
+MPI random in range: smaller result
+mpi_random_sizes:1:"aaaaaaaaaaaaaaaabbbbbbbbbbbbbbbb":1:0
+
+MPI random in range: same size result (32-bit limbs)
+mpi_random_sizes:1:"aaaaaaaaaaaaaaaa":2:0
+
+MPI random in range: same size result (64-bit limbs)
+mpi_random_sizes:1:"aaaaaaaaaaaaaaaa":1:0
+
+MPI random in range: larger result
+mpi_random_sizes:1:"aaaaaaaaaaaaaaaa":3:0
+
+## The "0 limb in upper bound" tests rely on the fact that
+## mbedtls_mpi_read_binary() bases the size of the MPI on the size of
+## the input, without first checking for leading zeros. If this was
+## not the case, the tests would still pass, but would not exercise
+## the advertised behavior.
+MPI random in range: leading 0 limb in upper bound #0
+mpi_random_sizes:1:"00aaaaaaaaaaaaaaaa":0:0
+
+MPI random in range: leading 0 limb in upper bound #1
+mpi_random_sizes:1:"00aaaaaaaaaaaaaaaa":1:0
+
+MPI random in range: leading 0 limb in upper bound #2
+mpi_random_sizes:1:"00aaaaaaaaaaaaaaaa":2:0
+
+MPI random in range: leading 0 limb in upper bound #3
+mpi_random_sizes:1:"00aaaaaaaaaaaaaaaa":3:0
+
+MPI random in range: leading 0 limb in upper bound #4
+mpi_random_sizes:1:"00aaaaaaaaaaaaaaaa":4:0
+
+MPI random in range: previously small >0
+mpi_random_sizes:1:"1234567890":4:1
+
+MPI random in range: previously small <0
+mpi_random_sizes:1:"1234567890":4:-1
+
+MPI random in range: previously large >0
+mpi_random_sizes:1:"1234":4:65
+
+MPI random in range: previously large <0
+mpi_random_sizes:1:"1234":4:-65
+
+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 random bad arguments: min > N = 0
+mpi_random_fail:1:"00":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
+
+MPI random bad arguments: min > N = 1
+mpi_random_fail:2:"01":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
+
+MPI random bad arguments: min > N = 1, 0 limb in upper bound
+mpi_random_fail:2:"000000000000000001":MBEDTLS_ERR_MPI_BAD_INPUT_DATA
+
+MPI random legacy=core: 0..1
+mpi_random_values:0:"01"
+
+MPI random legacy=core: 0..2
+mpi_random_values:0:"02"
+
+MPI random legacy=core: 1..2
+mpi_random_values:1:"02"
+
+MPI random legacy=core: 2^30..2^31
+mpi_random_values:0x40000000:"80000000"
+
+MPI random legacy=core: 2^31-1..2^32-1
+mpi_random_values:0x7fffffff:"ffffffff"
+
+MPI random legacy=core: 0..2^256
+mpi_random_values:0:"010000000000000000000000000000000000000000000000000000000000000000"
+
+MPI random legacy=core: 0..2^256+1
+mpi_random_values:0:"010000000000000000000000000000000000000000000000000000000000000001"
diff --git a/tests/suites/test_suite_bignum_random.function b/tests/suites/test_suite_bignum_random.function
new file mode 100644
index 0000000..184de5a
--- /dev/null
+++ b/tests/suites/test_suite_bignum_random.function
@@ -0,0 +1,334 @@
+/* BEGIN_HEADER */
+/* Dedicated test suite for mbedtls_mpi_core_random() and the upper-layer
+ * functions. Due to the complexity of how these functions are tested,
+ * we test all the layers in a single test suite, unlike the way other
+ * functions are tested with each layer in its own test suite.
+ */
+
+#include "mbedtls/bignum.h"
+#include "mbedtls/entropy.h"
+#include "bignum_core.h"
+#include "constant_time_internal.h"
+
+/* This test suite only manipulates non-negative bignums. */
+static int sign_is_valid( const mbedtls_mpi *X )
+{
+    return( X->s == 1 );
+}
+
+/* A common initializer for test functions that should generate the same
+ * sequences for reproducibility and good coverage. */
+const mbedtls_test_rnd_pseudo_info rnd_pseudo_seed = {
+    /* 16-word key */
+    {'T', 'h', 'i', 's', ' ', 'i', 's', ' ',
+     'a', ' ', 's', 'e', 'e', 'd', '!', 0},
+    /* 2-word initial state, should be zero */
+    0, 0};
+
+/* Test whether bytes represents (in big-endian base 256) a number b that
+ * is significantly above a power of 2. That is, b must not have a long run
+ * of unset bits after the most significant bit.
+ *
+ * Let n be the bit-size of b, i.e. the integer such that 2^n <= b < 2^{n+1}.
+ * This function returns 1 if, when drawing a number between 0 and b,
+ * the probability that this number is at least 2^n is not negligible.
+ * This probability is (b - 2^n) / b and this function checks that this
+ * number is above some threshold A. The threshold value is heuristic and
+ * based on the needs of mpi_random_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;
+
+    /* Skip leading null bytes */
+    while( len > 0 && p[0] == 0 )
+    {
+        ++p;
+        --len;
+    }
+    /* 0 is not significantly above a power of 2 */
+    if( len == 0 )
+        return( 0 );
+    /* Extract the (up to) 2 most significant bytes */
+    if( len == 1 )
+        x = p[0];
+    else
+        x = ( p[0] << 8 ) | p[1];
+
+    /* Shift the most significant bit of x to position 8 and mask it out */
+    while( ( x & 0xfe00 ) != 0 )
+        x >>= 1;
+    x &= 0x00ff;
+
+    /* At this point, x = floor((b - 2^n) / 2^(n-8)). b is significantly above
+     * a power of 2 iff x is significantly above 0 compared to 2^8.
+     * Testing x >= 2^4 amounts to picking A = 1/16 in the function
+     * description above. */
+    return( x >= 0x10 );
+}
+
+/* END_HEADER */
+
+/* BEGIN_DEPENDENCIES
+ * depends_on:MBEDTLS_BIGNUM_C
+ * END_DEPENDENCIES
+ */
+
+/* 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 = rnd_pseudo_seed;
+    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 );
+    lower_bound[0] = min;
+    ASSERT_ALLOC( result, limbs );
+
+    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 = rnd_pseudo_seed;
+    mbedtls_test_rnd_pseudo_info rnd_legacy;
+    memcpy( &rnd_legacy, &rnd_core, sizeof( rnd_core ) );
+    mbedtls_mpi max_legacy;
+    mbedtls_mpi_init( &max_legacy );
+    mbedtls_mpi_uint *R_core = NULL;
+    mbedtls_mpi R_legacy;
+    mbedtls_mpi_init( &R_legacy );
+
+    TEST_EQUAL( 0, mbedtls_test_read_mpi( &max_legacy, max_hex ) );
+    size_t limbs = max_legacy.n;
+    ASSERT_ALLOC( R_core, limbs );
+
+    /* Call the legacy function and the core function with the same random
+     * stream. */
+    int core_ret = mbedtls_mpi_core_random( R_core, min, max_legacy.p, limbs,
+                                            mbedtls_test_rnd_pseudo_rand,
+                                            &rnd_core );
+    int legacy_ret = mbedtls_mpi_random( &R_legacy, min, &max_legacy,
+                                         mbedtls_test_rnd_pseudo_rand,
+                                         &rnd_legacy );
+
+    /* They must return the same status, and, on success, output the
+     * same number, with the same limb count. */
+    TEST_EQUAL( core_ret, legacy_ret );
+    if( core_ret == 0 )
+    {
+        ASSERT_COMPARE( R_core, limbs * ciL,
+                        R_legacy.p, R_legacy.n * ciL );
+    }
+
+    /* Also check that they have consumed the RNG in the same way. */
+    /* This may theoretically fail on rare platforms with padding in
+     * the structure! If this is a problem in practice, change to a
+     * field-by-field comparison. */
+    ASSERT_COMPARE( &rnd_core, sizeof( rnd_core ),
+                    &rnd_legacy, sizeof( rnd_legacy ) );
+
+exit:
+    mbedtls_mpi_free( &max_legacy );
+    mbedtls_free( R_core );
+    mbedtls_mpi_free( &R_legacy );
+}
+/* END_CASE */
+
+/* BEGIN_CASE */
+void mpi_random_many( int min, char *bound_hex, 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.
+     */
+
+    data_t bound_bytes = {NULL, 0};
+    mbedtls_mpi_uint *upper_bound = NULL;
+    size_t limbs;
+    size_t n_bits;
+    mbedtls_mpi_uint *result = NULL;
+    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;
+
+    TEST_EQUAL( 0, mbedtls_test_read_mpi_core( &upper_bound, &limbs,
+                                               bound_hex ) );
+    ASSERT_ALLOC( result, limbs );
+
+    n_bits = mbedtls_mpi_core_bitlen( upper_bound, limbs );
+    /* 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 = (uint8_t) upper_bound[0];
+    }
+    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_core_random( result,
+                                                min, upper_bound, limbs,
+                                                mbedtls_test_rnd_std_rand, NULL ) );
+
+        /* Temporarily use a legacy MPI for analysis, because the
+         * necessary auxiliary functions don't exist yet in core. */
+        mbedtls_mpi B = {1, limbs, upper_bound};
+        mbedtls_mpi R = {1, limbs, result};
+
+        TEST_ASSERT( mbedtls_mpi_cmp_mpi( &R, &B ) < 0 );
+        TEST_ASSERT( mbedtls_mpi_cmp_int( &R, min ) >= 0 );
+        if( full_stats )
+        {
+            uint8_t value;
+            TEST_EQUAL( 0, mbedtls_mpi_write_binary( &R, &value, 1 ) );
+            TEST_ASSERT( value < stats_len );
+            ++stats[value];
+        }
+        else
+        {
+            for( b = 0; b < n_bits; b++ )
+                stats[b] += mbedtls_mpi_get_bit( &R, b );
+        }
+    }
+
+    if( full_stats )
+    {
+        for( b = min; 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
+    {
+        bound_bytes.len = limbs * sizeof( mbedtls_mpi_uint );
+        ASSERT_ALLOC( bound_bytes.x, bound_bytes.len );
+        mbedtls_mpi_core_write_be( upper_bound, limbs,
+                                   bound_bytes.x, bound_bytes.len );
+        int statistically_safe_all_the_way =
+            is_significantly_above_a_power_of_2( &bound_bytes );
+        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( statistically_safe_all_the_way || b != n_bits - 1 )
+            {
+                TEST_ASSERT( stats[b] > 0 );
+            }
+            TEST_ASSERT( stats[b] < (size_t) iterations );
+        }
+    }
+
+exit:
+    mbedtls_free( bound_bytes.x );
+    mbedtls_free( upper_bound );
+    mbedtls_free( result );
+    mbedtls_free( stats );
+}
+/* END_CASE */
+
+/* BEGIN_CASE */
+void mpi_random_sizes( int min, data_t *bound_bytes, int nlimbs, int before )
+{
+    mbedtls_mpi upper_bound;
+    mbedtls_mpi result;
+
+    mbedtls_mpi_init( &upper_bound );
+    mbedtls_mpi_init( &result );
+
+    if( before != 0 )
+    {
+        /* Set result to sign(before) * 2^(|before|-1) */
+        TEST_ASSERT( mbedtls_mpi_lset( &result, before > 0 ? 1 : -1 ) == 0 );
+        if( before < 0 )
+            before = - before;
+        TEST_ASSERT( mbedtls_mpi_shift_l( &result, before - 1 ) == 0 );
+    }
+
+    TEST_EQUAL( 0, mbedtls_mpi_grow( &result, nlimbs ) );
+    TEST_EQUAL( 0, mbedtls_mpi_read_binary( &upper_bound,
+                                            bound_bytes->x, bound_bytes->len ) );
+    TEST_EQUAL( 0, mbedtls_mpi_random( &result, min, &upper_bound,
+                                       mbedtls_test_rnd_std_rand, NULL ) );
+    TEST_ASSERT( sign_is_valid( &result ) );
+    TEST_ASSERT( mbedtls_mpi_cmp_mpi( &result, &upper_bound ) < 0 );
+    TEST_ASSERT( mbedtls_mpi_cmp_int( &result, min ) >= 0 );
+
+exit:
+    mbedtls_mpi_free( &upper_bound );
+    mbedtls_mpi_free( &result );
+}
+/* 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 */