gh-95778: Correctly pre-check for int-to-str conversion (#96537)

Converting a large enough `int` to a decimal string raises `ValueError` as expected. However, the raise comes _after_ the quadratic-time base-conversion algorithm has run to completion. For effective DOS prevention, we need some kind of check before entering the quadratic-time loop. Oops! =)

The quick fix: essentially we catch _most_ values that exceed the threshold up front. Those that slip through will still be on the small side (read: sufficiently fast), and will get caught by the existing check so that the limit remains exact.

The justification for the current check. The C code check is:
```c
max_str_digits / (3 * PyLong_SHIFT) <= (size_a - 11) / 10
```

In GitHub markdown math-speak, writing $M$ for `max_str_digits`, $L$ for `PyLong_SHIFT` and $s$ for `size_a`, that check is:
$$\left\lfloor\frac{M}{3L}\right\rfloor \le \left\lfloor\frac{s - 11}{10}\right\rfloor$$

From this it follows that
$$\frac{M}{3L} < \frac{s-1}{10}$$
hence that
$$\frac{L(s-1)}{M} > \frac{10}{3} > \log_2(10).$$
So
$$2^{L(s-1)} > 10^M.$$
But our input integer $a$ satisfies $|a| \ge 2^{L(s-1)}$, so $|a|$ is larger than $10^M$. This shows that we don't accidentally capture anything _below_ the intended limit in the check.

<!-- gh-issue-number: gh-95778 -->
* Issue: gh-95778
<!-- /gh-issue-number -->

Co-authored-by: Gregory P. Smith [Google LLC] <[email protected]>

Author: mdickinson

Lib/test/test_int.py

@@ -1,4 +1,5 @@
 import sys
+import time
 
 import unittest
 from test import support
@@ -571,6 +572,87 @@ def test_max_str_digits(self):
         with self.assertRaises(ValueError):
             str(i)
 
+    def test_denial_of_service_prevented_int_to_str(self):
+        """Regression test: ensure we fail before performing O(N**2) work."""
+        maxdigits = sys.get_int_max_str_digits()
+        assert maxdigits < 50_000, maxdigits  # A test prerequisite.
+        get_time = time.process_time
+        if get_time() <= 0:  # some platforms like WASM lack process_time()
+            get_time = time.monotonic
+
+        huge_int = int(f'0x{"c"*65_000}', base=16)  # 78268 decimal digits.
+        digits = 78_268
+        with support.adjust_int_max_str_digits(digits):
+            start = get_time()
+            huge_decimal = str(huge_int)
+        seconds_to_convert = get_time() - start
+        self.assertEqual(len(huge_decimal), digits)
+        # Ensuring that we chose a slow enough conversion to measure.
+        # It takes 0.1 seconds on a Zen based cloud VM in an opt build.
+        if seconds_to_convert < 0.005:
+            raise unittest.SkipTest('"slow" conversion took only '
+                                    f'{seconds_to_convert} seconds.')
+
+        # We test with the limit almost at the size needed to check performance.
+        # The performant limit check is slightly fuzzy, give it a some room.
+        with support.adjust_int_max_str_digits(int(.995 * digits)):
+            with self.assertRaises(ValueError) as err:
+                start = get_time()
+                str(huge_int)
+            seconds_to_fail_huge = get_time() - start
+        self.assertIn('conversion', str(err.exception))
+        self.assertLess(seconds_to_fail_huge, seconds_to_convert/8)
+
+        # Now we test that a conversion that would take 30x as long also fails
+        # in a similarly fast fashion.
+        extra_huge_int = int(f'0x{"c"*500_000}', base=16)  # 602060 digits.
+        with self.assertRaises(ValueError) as err:
+            start = get_time()
+            # If not limited, 8 seconds said Zen based cloud VM.
+            str(extra_huge_int)
+        seconds_to_fail_extra_huge = get_time() - start
+        self.assertIn('conversion', str(err.exception))
+        self.assertLess(seconds_to_fail_extra_huge, seconds_to_convert/8)
+
+    def test_denial_of_service_prevented_str_to_int(self):
+        """Regression test: ensure we fail before performing O(N**2) work."""
+        maxdigits = sys.get_int_max_str_digits()
+        assert maxdigits < 100_000, maxdigits  # A test prerequisite.
+        get_time = time.process_time
+        if get_time() <= 0:  # some platforms like WASM lack process_time()
+            get_time = time.monotonic
+
+        digits = 133700
+        huge = '8'*digits
+        with support.adjust_int_max_str_digits(digits):
+            start = get_time()
+            int(huge)
+        seconds_to_convert = get_time() - start
+        # Ensuring that we chose a slow enough conversion to measure.
+        # It takes 0.1 seconds on a Zen based cloud VM in an opt build.
+        if seconds_to_convert < 0.005:
+            raise unittest.SkipTest('"slow" conversion took only '
+                                    f'{seconds_to_convert} seconds.')
+
+        with support.adjust_int_max_str_digits(digits - 1):
+            with self.assertRaises(ValueError) as err:
+                start = get_time()
+                int(huge)
+            seconds_to_fail_huge = get_time() - start
+        self.assertIn('conversion', str(err.exception))
+        self.assertLess(seconds_to_fail_huge, seconds_to_convert/8)
+
+        # Now we test that a conversion that would take 30x as long also fails
+        # in a similarly fast fashion.
+        extra_huge = '7'*1_200_000
+        with self.assertRaises(ValueError) as err:
+            start = get_time()
+            # If not limited, 8 seconds in the Zen based cloud VM.
+            int(extra_huge)
+        seconds_to_fail_extra_huge = get_time() - start
+        self.assertIn('conversion', str(err.exception))
+        self.assertLess(seconds_to_fail_extra_huge, seconds_to_convert/8)
+
     def test_power_of_two_bases_unlimited(self):
         """The limit does not apply to power of 2 bases."""
         maxdigits = sys.get_int_max_str_digits()

Misc/NEWS.d/next/Security/2022-08-07-16-53-38.gh-issue-95778.ch010gps.rst

@@ -11,4 +11,4 @@ limitation <int_max_str_digits>` documentation.  The default limit is 4300
 digits in string form.
 
 Patch by Gregory P. Smith [Google] and Christian Heimes [Red Hat] with feedback
-from Victor Stinner, Thomas Wouters, Steve Dower, and Ned Deily.
+from Victor Stinner, Thomas Wouters, Steve Dower, Ned Deily, and Mark Dickinson.

Objects/longobject.c

@@ -47,7 +47,8 @@ static PyLongObject small_ints[NSMALLNEGINTS + NSMALLPOSINTS];
 Py_ssize_t quick_int_allocs, quick_neg_int_allocs;
 #endif
 
-#define _MAX_STR_DIGITS_ERROR_FMT "Exceeds the limit (%d) for integer string conversion: value has %zd digits"
+#define _MAX_STR_DIGITS_ERROR_FMT_TO_INT "Exceeds the limit (%d) for integer string conversion: value has %zd digits"
+#define _MAX_STR_DIGITS_ERROR_FMT_TO_STR "Exceeds the limit (%d) for integer string conversion"
 
 static PyObject *
 get_small_int(sdigit ival)
@@ -1606,6 +1607,23 @@ long_to_decimal_string_internal(PyObject *aa,
     size_a = Py_ABS(Py_SIZE(a));
     negative = Py_SIZE(a) < 0;
 
+    /* quick and dirty pre-check for overflowing the decimal digit limit,
+       based on the inequality 10/3 >= log2(10)
+
+       explanation in https://github.com/python/cpython/pull/96537
+    */
+    if (size_a >= 10 * _PY_LONG_MAX_STR_DIGITS_THRESHOLD
+                  / (3 * PyLong_SHIFT) + 2) {
+        PyInterpreterState *interp = _PyInterpreterState_GET();
+        int max_str_digits = interp->int_max_str_digits;
+        if ((max_str_digits > 0) &&
+            (max_str_digits / (3 * PyLong_SHIFT) <= (size_a - 11) / 10)) {
+            PyErr_Format(PyExc_ValueError, _MAX_STR_DIGITS_ERROR_FMT_TO_STR,
+                         max_str_digits);
+            return -1;
+        }
+    }
+
     /* quick and dirty upper bound for the number of digits
        required to express a in base _PyLong_DECIMAL_BASE:
 
@@ -1670,8 +1688,8 @@ long_to_decimal_string_internal(PyObject *aa,
         Py_ssize_t strlen_nosign = strlen - negative;
         if ((max_str_digits > 0) && (strlen_nosign > max_str_digits)) {
             Py_DECREF(scratch);
-            PyErr_Format(PyExc_ValueError, _MAX_STR_DIGITS_ERROR_FMT,
-                         max_str_digits, strlen_nosign);
+            PyErr_Format(PyExc_ValueError, _MAX_STR_DIGITS_ERROR_FMT_TO_STR,
+                         max_str_digits);
             return -1;
         }
     }
@@ -2344,7 +2362,7 @@ digit beyond the first.
         if (digits > _PY_LONG_MAX_STR_DIGITS_THRESHOLD) {
             int max_str_digits = _PyRuntime.int_max_str_digits;
             if ((max_str_digits > 0) && (digits > max_str_digits)) {
-                PyErr_Format(PyExc_ValueError, _MAX_STR_DIGITS_ERROR_FMT,
+                PyErr_Format(PyExc_ValueError, _MAX_STR_DIGITS_ERROR_FMT_TO_INT,
                              max_str_digits, digits);
                 return NULL;
             }