In FIPS mode only use "Generation by Testing Candidates" equivalent.

crypto/bn/bn_rand.c

@@ -247,7 +247,15 @@ static int bn_rand_range(int pseudo, BIGNUM *r, const BIGNUM *range)
 
 	if (n == 1)
 		BN_zero(r);
+#ifdef OPENSSL_FIPS
+	/* FIPS 186-3 is picky about how random numbers for keys etc are
+	 * generated. So we just use the second case which is equivalent to
+	 * "Generation by Testing Candidates" mentioned in B.1.2 et al.
+	 */
+	else if (!FIPS_mode() && !BN_is_bit_set(range, n - 2) && !BN_is_bit_set(range, n - 3))
+#else
 	else if (!BN_is_bit_set(range, n - 2) && !BN_is_bit_set(range, n - 3))
+#endif
 		{
 		/* range = 100..._2,
 		 * so  3*range (= 11..._2)  is exactly one bit longer than  range */