…GH-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:```cmax_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:pythongh-95778 -->* Issue:pythongh-95778<!-- /gh-issue-number -->Co-authored-by: Gregory P. Smith [Google LLC] <greg@krypto.org>(cherry picked from commitb126196)Co-authored-by: Mark Dickinson <dickinsm@gmail.com>

…ythonGH-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:```cmax_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:pythongh-95778 -->* Issue:pythongh-95778<!-- /gh-issue-number -->Co-authored-by: Gregory P. Smith [Google LLC] <greg@krypto.org>(cherry picked from commitb126196)Co-authored-by: Mark Dickinson <dickinsm@gmail.com>

…#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:```cmax_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:pythongh-95778 -->* Issue:pythongh-95778<!-- /gh-issue-number -->Co-authored-by: Gregory P. Smith [Google LLC] <greg@krypto.org>

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:```cmax_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] <greg@krypto.org>(cherry picked from commitb126196)Co-authored-by: Mark Dickinson <dickinsm@gmail.com>

…#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:```cmax_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:pythongh-95778 -->* Issue:pythongh-95778<!-- /gh-issue-number -->Co-authored-by: Gregory P. Smith [Google LLC] <greg@krypto.org>

…#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:```cmax_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:pythongh-95778 -->* Issue:pythongh-95778<!-- /gh-issue-number -->Co-authored-by: Gregory P. Smith [Google LLC] <greg@krypto.org>

) (#96563)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:```cmax_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] <greg@krypto.org>(cherry picked from commitb126196)Co-authored-by: Mark Dickinson <dickinsm@gmail.com>

* 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:```cmax_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] <greg@krypto.org>Co-authored-by: Christian Heimes <christian@python.org>Co-authored-by: Mark Dickinson <dickinsm@gmail.com>

Summary:cherry-picked the upstream 3.10 backport```git cherry-pick8f0fa4beace09e```this one ispython/cpython#96537original commit message below--------Integer to and from text conversions via CPython's bignum `int` type is not safe against denial of service attacks due to malicious input. Very large input strings with hundred thousands of digits can consume several CPU seconds.This PR comes fresh from a pile of work done in our private PSRT security response team repo.This backportspython/cpython#96499 aka511ca94Signed-off-by: Christian Heimes [Red Hat] <christian@python.org>Tons-of-polishing-up-by: Gregory P. Smith [Google] <greg@krypto.org>Reviews via the private PSRT repo via many others (see the NEWS entry in the PR).<!-- gh-issue-number: gh-95778 -->* Issue: gh-95778<!-- /gh-issue-number -->I wrote up [a one pager for the release managers](https://docs.google.com/document/d/1KjuF_aXlzPUxTK4BMgezGJ2Pn7uevfX7g0_mvgHlL7Y/edit#).Reviewed By: alexmalyshevDifferential Revision: D39369518fbshipit-source-id:6ed2def