Statistically test BN_rand_range().
Add a Chi^2 goodness of fit test to empirically provide a degree of confidence
in the uniformity of the output of the random range generation function.
@@ -1954,6 +1954,73 @@ static int test_rand(void)
return st;
}
+/*
+ * Run some statistical tests to provide a degree confidence that the
+ * BN_rand_range() function works as expected. The critical value
+ * is computed using the R statistical suite:
+ *
+ * qchisq(alpha, df=iterations - 1)
+ *
+ * where alpha is the significance level (0.95 is used here) and iterations
+ * is the number of samples being drawn.
+ */
+static const struct {
+ unsigned int range;
+ unsigned int iterations;
+ double critical;
+} rand_range_cases[] = {
+ { 2, 100, 123.2252 /* = qchisq(.95, df=99) */ },
+ { 12, 1000, 1073.643 /* = qchisq(.95, df=999) */ },
+ { 1023, 100000, 100735.7 /* = qchisq(.95, df=99999) */ },
+};
+
+static int test_rand_range(int n)
+{
+ const unsigned int range = rand_range_cases[n].range;
+ const unsigned int iterations = rand_range_cases[n].iterations;
+ const double critical = rand_range_cases[n].critical;
+ const double expected = iterations / (double)range;
+ double sum = 0;
+ BIGNUM *rng = NULL, *val = NULL;
+ size_t *counts;
+ unsigned int i, v;
+ int res = 0;
+
+ if (!TEST_ptr(counts = OPENSSL_zalloc(sizeof(*counts) * range))
+ || !TEST_ptr(rng = BN_new())
+ || !TEST_ptr(val = BN_new())
+ || !TEST_true(BN_set_word(rng, range)))
+ goto err;
+ for (i = 0; i < iterations; i++) {
+ if (!TEST_true(BN_rand_range(val, rng))
+ || !TEST_uint_lt(v = (unsigned int)BN_get_word(val), range))
+ goto err;
+ counts[v]++;
+ }
+
+ TEST_note("range %u iterations %u critical %.4f", range, iterations,
+ critical);
+ if (range < 20) {
+ TEST_note("frequencies (expected %.2f)", expected);
+ for (i = 0; i < range; i++)
+ TEST_note(" %2u %6zu", i, counts[i]);
+ }
+ for (i = 0; i < range; i++) {
+ const double delta = counts[i] - expected;
+ sum += delta * delta;
+ }
+ sum /= expected;
+ TEST_note("test statistic %.4f", sum);
+
+ if (TEST_double_lt(sum, critical))
+ res = 1;
+err:
+ BN_free(rng);
+ BN_free(val);
+ OPENSSL_free(counts);
+ return res;
+}
+
static int test_negzero(void)
{
BIGNUM *a = NULL, *b = NULL, *c = NULL, *d = NULL;
@@ -2432,6 +2499,7 @@ int setup_tests(void)
#endif
ADD_ALL_TESTS(test_is_prime, (int)OSSL_NELEM(primes));
ADD_ALL_TESTS(test_not_prime, (int)OSSL_NELEM(not_primes));
+ ADD_ALL_TESTS(test_rand_range, OSSL_NELEM(rand_range_cases));
} else {
ADD_ALL_TESTS(run_file_tests, n);
}
