diff --git a/src/common/sae.c b/src/common/sae.c
index a1445bb15..e49225341 100644
--- a/src/common/sae.c
+++ b/src/common/sae.c
@@ -123,28 +123,34 @@ static void buf_shift_right(u8 *buf, size_t len, size_t bits)
 }
 
 
-static struct crypto_bignum * sae_get_rand(const u8 *order,
-					   size_t order_len_bits)
+static struct crypto_bignum * sae_get_rand(struct sae_data *sae)
 {
 	u8 val[SAE_MAX_PRIME_LEN];
 	int iter = 0;
+	struct crypto_bignum *bn = NULL;
+	int order_len_bits = crypto_bignum_bits(sae->order);
 	size_t order_len = (order_len_bits + 7) / 8;
-	struct crypto_bignum *bn;
 
 	if (order_len > sizeof(val))
 		return NULL;
 
-	do {
+	for (;;) {
 		if (iter++ > 100)
 			return NULL;
 		if (random_get_bytes(val, order_len) < 0)
 			return NULL;
 		if (order_len_bits % 8)
 			buf_shift_right(val, order_len, 8 - order_len_bits % 8);
-	} while (os_memcmp(val, order, order_len) >= 0 ||
-		 val_zero_or_one(val, order_len));
+		if (val_zero_or_one(val, order_len))
+			continue;
+		bn = crypto_bignum_init_set(val, order_len);
+		if (bn == NULL)
+			return NULL;
+		if (crypto_bignum_cmp(bn, sae->order) >= 0)
+			continue;
+		break;
+	}
 
-	bn = crypto_bignum_init_set(val, order_len);
 	os_memset(val, 0, order_len);
 	return bn;
 }
@@ -152,28 +158,11 @@ static struct crypto_bignum * sae_get_rand(const u8 *order,
 
 static struct crypto_bignum * sae_get_rand_and_mask(struct sae_data *sae)
 {
-	u8 order[SAE_MAX_PRIME_LEN];
-	size_t prime_len_bits = crypto_ec_prime_len_bits(sae->ec);
-
-	if (crypto_bignum_to_bin(sae->order, order, sizeof(order),
-				 sae->prime_len) < 0)
-		return NULL;
-
 	crypto_bignum_deinit(sae->sae_rand, 1);
-	sae->sae_rand = sae_get_rand(order, prime_len_bits);
+	sae->sae_rand = sae_get_rand(sae);
 	if (sae->sae_rand == NULL)
 		return NULL;
-	return sae_get_rand(order, prime_len_bits);
-}
-
-
-static struct crypto_bignum * sae_get_rand_and_mask_dh(struct sae_data *sae)
-{
-	crypto_bignum_deinit(sae->sae_rand, 1);
-	sae->sae_rand = sae_get_rand(sae->dh->order, sae->dh->order_len * 8);
-	if (sae->sae_rand == NULL)
-		return NULL;
-	return sae_get_rand(sae->dh->order, sae->dh->order_len * 8);
+	return sae_get_rand(sae);
 }
 
 
@@ -521,7 +510,7 @@ static int sae_derive_commit_dh(struct sae_data *sae, struct crypto_bignum *pwe)
 	struct crypto_bignum *x, *mask, *elem;
 	int ret = -1;
 
-	mask = sae_get_rand_and_mask_dh(sae);
+	mask = sae_get_rand_and_mask(sae);
 	if (mask == NULL) {
 		wpa_printf(MSG_DEBUG, "SAE: Could not get rand/mask");
 		return -1;
diff --git a/src/crypto/crypto.h b/src/crypto/crypto.h
index 7c19d2b81..9170a0f3b 100644
--- a/src/crypto/crypto.h
+++ b/src/crypto/crypto.h
@@ -589,6 +589,22 @@ int crypto_bignum_mulmod(const struct crypto_bignum *a,
 			 const struct crypto_bignum *c,
 			 struct crypto_bignum *d);
 
+/**
+ * crypto_bignum_cmp - Compare two bignums
+ * @a: Bignum
+ * @b: Bignum
+ * Returns: -1 if a < b, 0 if a == b, or 1 if a > b
+ */
+int crypto_bignum_cmp(const struct crypto_bignum *a,
+		      const struct crypto_bignum *b);
+
+/**
+ * crypto_bignum_bits - Get size of a bignum in bits
+ * @a: Bignum
+ * Returns: Number of bits in the bignum
+ */
+int crypto_bignum_bits(const struct crypto_bignum *a);
+
 /**
  * struct crypto_ec - Elliptic curve context
  *
diff --git a/src/crypto/crypto_openssl.c b/src/crypto/crypto_openssl.c
index 80bc50fab..eeda57dea 100644
--- a/src/crypto/crypto_openssl.c
+++ b/src/crypto/crypto_openssl.c
@@ -987,6 +987,19 @@ int crypto_bignum_mulmod(const struct crypto_bignum *a,
 }
 
 
+int crypto_bignum_cmp(const struct crypto_bignum *a,
+		      const struct crypto_bignum *b)
+{
+	return BN_cmp((const BIGNUM *) a, (const BIGNUM *) b);
+}
+
+
+int crypto_bignum_bits(const struct crypto_bignum *a)
+{
+	return BN_num_bits((const BIGNUM *) a);
+}
+
+
 #ifdef CONFIG_ECC
 
 struct crypto_ec {