diff --git a/src/crypto/crypto_openssl.c b/src/crypto/crypto_openssl.c
index 9c2ba58d5..ac53cc81a 100644
--- a/src/crypto/crypto_openssl.c
+++ b/src/crypto/crypto_openssl.c
@@ -607,7 +607,8 @@ int crypto_mod_exp(const u8 *base, size_t base_len,
 	    bn_result == NULL)
 		goto error;
 
-	if (BN_mod_exp(bn_result, bn_base, bn_exp, bn_modulus, ctx) != 1)
+	if (BN_mod_exp_mont_consttime(bn_result, bn_base, bn_exp, bn_modulus,
+				      ctx, NULL) != 1)
 		goto error;
 
 	*result_len = BN_bn2bin(bn_result, result);
@@ -1360,8 +1361,9 @@ int crypto_bignum_exptmod(const struct crypto_bignum *a,
 	bnctx = BN_CTX_new();
 	if (bnctx == NULL)
 		return -1;
-	res = BN_mod_exp((BIGNUM *) d, (const BIGNUM *) a, (const BIGNUM *) b,
-			 (const BIGNUM *) c, bnctx);
+	res = BN_mod_exp_mont_consttime((BIGNUM *) d, (const BIGNUM *) a,
+					(const BIGNUM *) b, (const BIGNUM *) c,
+					bnctx, NULL);
 	BN_CTX_free(bnctx);
 
 	return res ? 0 : -1;
@@ -1380,6 +1382,11 @@ int crypto_bignum_inverse(const struct crypto_bignum *a,
 	bnctx = BN_CTX_new();
 	if (bnctx == NULL)
 		return -1;
+#ifdef OPENSSL_IS_BORINGSSL
+	/* TODO: use BN_mod_inverse_blinded() ? */
+#else /* OPENSSL_IS_BORINGSSL */
+	BN_set_flags((BIGNUM *) a, BN_FLG_CONSTTIME);
+#endif /* OPENSSL_IS_BORINGSSL */
 	res = BN_mod_inverse((BIGNUM *) c, (const BIGNUM *) a,
 			     (const BIGNUM *) b, bnctx);
 	BN_CTX_free(bnctx);
@@ -1413,6 +1420,9 @@ int crypto_bignum_div(const struct crypto_bignum *a,
 	bnctx = BN_CTX_new();
 	if (bnctx == NULL)
 		return -1;
+#ifndef OPENSSL_IS_BORINGSSL
+	BN_set_flags((BIGNUM *) a, BN_FLG_CONSTTIME);
+#endif /* OPENSSL_IS_BORINGSSL */
 	res = BN_div((BIGNUM *) c, NULL, (const BIGNUM *) a,
 		     (const BIGNUM *) b, bnctx);
 	BN_CTX_free(bnctx);
@@ -1504,8 +1514,8 @@ int crypto_bignum_legendre(const struct crypto_bignum *a,
 	    /* exp = (p-1) / 2 */
 	    !BN_sub(exp, (const BIGNUM *) p, BN_value_one()) ||
 	    !BN_rshift1(exp, exp) ||
-	    !BN_mod_exp(tmp, (const BIGNUM *) a, exp, (const BIGNUM *) p,
-			bnctx))
+	    !BN_mod_exp_mont_consttime(tmp, (const BIGNUM *) a, exp,
+				       (const BIGNUM *) p, bnctx, NULL))
 		goto fail;
 
 	if (BN_is_word(tmp, 1))