diff --git a/crypto/fipsmodule/ec/ec.c b/crypto/fipsmodule/ec/ec.c
index 977cd26..266baa2 100644
--- a/crypto/fipsmodule/ec/ec.c
+++ b/crypto/fipsmodule/ec/ec.c
@@ -817,6 +817,24 @@
   return ec_GFp_simple_invert(group, a, ctx);
 }
 
+static int arbitrary_bignum_to_scalar(const EC_GROUP *group, EC_SCALAR *out,
+                                      const BIGNUM *in, BN_CTX *ctx) {
+  const BIGNUM *order = EC_GROUP_get0_order(group);
+  if (BN_is_negative(in) || BN_num_bits(in) > BN_num_bits(order)) {
+    // This is an unusual input, so we do not guarantee constant-time
+    // processing, even ignoring |bn_correct_top|.
+    BN_CTX_start(ctx);
+    BIGNUM *tmp = BN_CTX_get(ctx);
+    int ok = tmp != NULL &&
+             BN_nnmod(tmp, in, order, ctx) &&
+             ec_bignum_to_scalar(group, out, tmp);
+    BN_CTX_end(ctx);
+    return ok;
+  }
+
+  return ec_bignum_to_scalar(group, out, in);
+}
+
 int EC_POINT_mul(const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar,
                  const EC_POINT *p, const BIGNUM *p_scalar, BN_CTX *ctx) {
   // Previously, this function set |r| to the point at infinity if there was
@@ -828,30 +846,27 @@
     return 0;
   }
 
-  // We cannot easily process arbitrary scalars in constant-time, and there is
-  // no need to do so. Require that scalars be the same size as the order.
-  //
-  // One could require they be fully reduced, but some consumers try to check
-  // that |order| * |pubkey| is the identity. This comes from following NIST SP
-  // 800-56A section 5.6.2.3.2. (Though all our curves have cofactor one, so
-  // this check isn't useful.)
   int ret = 0;
   EC_SCALAR g_scalar_storage, p_scalar_storage;
   EC_SCALAR *g_scalar_arg = NULL, *p_scalar_arg = NULL;
-  unsigned order_bits = BN_num_bits(&group->order);
+  BN_CTX *new_ctx = NULL;
+  if (ctx == NULL) {
+    new_ctx = BN_CTX_new();
+    if (new_ctx == NULL) {
+      goto err;
+    }
+    ctx = new_ctx;
+  }
+
   if (g_scalar != NULL) {
-    if (BN_is_negative(g_scalar) || BN_num_bits(g_scalar) > order_bits ||
-        !ec_bignum_to_scalar(group, &g_scalar_storage, g_scalar)) {
-      OPENSSL_PUT_ERROR(EC, EC_R_INVALID_SCALAR);
+    if (!arbitrary_bignum_to_scalar(group, &g_scalar_storage, g_scalar, ctx)) {
       goto err;
     }
     g_scalar_arg = &g_scalar_storage;
   }
 
   if (p_scalar != NULL) {
-    if (BN_is_negative(p_scalar) || BN_num_bits(p_scalar) > order_bits ||
-        !ec_bignum_to_scalar(group, &p_scalar_storage, p_scalar)) {
-      OPENSSL_PUT_ERROR(EC, EC_R_INVALID_SCALAR);
+    if (!arbitrary_bignum_to_scalar(group, &p_scalar_storage, p_scalar, ctx)) {
       goto err;
     }
     p_scalar_arg = &p_scalar_storage;
@@ -860,6 +875,7 @@
   ret = ec_point_mul_scalar(group, r, g_scalar_arg, p, p_scalar_arg, ctx);
 
 err:
+  BN_CTX_free(new_ctx);
   OPENSSL_cleanse(&g_scalar_storage, sizeof(g_scalar_storage));
   OPENSSL_cleanse(&p_scalar_storage, sizeof(p_scalar_storage));
   return ret;
diff --git a/crypto/fipsmodule/ec/ec_test.cc b/crypto/fipsmodule/ec/ec_test.cc
index 5e5ce94..139840e 100644
--- a/crypto/fipsmodule/ec/ec_test.cc
+++ b/crypto/fipsmodule/ec/ec_test.cc
@@ -439,6 +439,52 @@
       << "p * order did not return point at infinity.";
 }
 
+// Test that |EC_POINT_mul| works with out-of-range scalars. Even beyond the
+// usual |bn_correct_top| disclaimer, we completely disclaim all hope here as a
+// reduction is needed, but we'll compute the right answer.
+TEST_P(ECCurveTest, MulOutOfRange) {
+  bssl::UniquePtr<EC_GROUP> group(EC_GROUP_new_by_curve_name(GetParam().nid));
+  ASSERT_TRUE(group);
+
+  bssl::UniquePtr<BIGNUM> n_minus_one(BN_dup(EC_GROUP_get0_order(group.get())));
+  ASSERT_TRUE(n_minus_one);
+  ASSERT_TRUE(BN_sub_word(n_minus_one.get(), 1));
+
+  bssl::UniquePtr<BIGNUM> minus_one(BN_new());
+  ASSERT_TRUE(minus_one);
+  ASSERT_TRUE(BN_one(minus_one.get()));
+  BN_set_negative(minus_one.get(), 1);
+
+  bssl::UniquePtr<BIGNUM> seven(BN_new());
+  ASSERT_TRUE(seven);
+  ASSERT_TRUE(BN_set_word(seven.get(), 7));
+
+  bssl::UniquePtr<BIGNUM> ten_n_plus_seven(
+      BN_dup(EC_GROUP_get0_order(group.get())));
+  ASSERT_TRUE(ten_n_plus_seven);
+  ASSERT_TRUE(BN_mul_word(ten_n_plus_seven.get(), 10));
+  ASSERT_TRUE(BN_add_word(ten_n_plus_seven.get(), 7));
+
+  bssl::UniquePtr<EC_POINT> point1(EC_POINT_new(group.get())),
+      point2(EC_POINT_new(group.get()));
+  ASSERT_TRUE(point1);
+  ASSERT_TRUE(point2);
+
+  ASSERT_TRUE(EC_POINT_mul(group.get(), point1.get(), n_minus_one.get(),
+                           nullptr, nullptr, nullptr));
+  ASSERT_TRUE(EC_POINT_mul(group.get(), point2.get(), minus_one.get(), nullptr,
+                           nullptr, nullptr));
+  EXPECT_EQ(0, EC_POINT_cmp(group.get(), point1.get(), point2.get(), nullptr))
+      << "-1 * G and (n-1) * G did not give the same result";
+
+  ASSERT_TRUE(EC_POINT_mul(group.get(), point1.get(), seven.get(), nullptr,
+                           nullptr, nullptr));
+  ASSERT_TRUE(EC_POINT_mul(group.get(), point2.get(), ten_n_plus_seven.get(),
+                           nullptr, nullptr, nullptr));
+  EXPECT_EQ(0, EC_POINT_cmp(group.get(), point1.get(), point2.get(), nullptr))
+      << "7 * G and (10n + 7) * G did not give the same result";
+}
+
 // Test that 10×∞ + G = G.
 TEST_P(ECCurveTest, Mul) {
   bssl::UniquePtr<EC_GROUP> group(EC_GROUP_new_by_curve_name(GetParam().nid));