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<img src="./regexide.png" style="height: 4rem; display: inline-block" alt="Regexide Logo"/>

<h1>Denials of Service in Regular Expression</h1>

This whole situation began with a simple question, "How do I remove XML comments in JavaScript?". The Internet hivemind converged on one general approach: <b>regular expressions</b>.

This has one big problem. If you're not careful, parsing relatively small amounts of data could lead to browsers or servers freezing for extended periods of time. The official category for this weakness is "CWE-1333"[^5] "Inefficient Regular Expression Complexity". Some resources also use the phrase "Catastrophic backtracking" to describe the issue.

This discussion focuses on what we've come to call "Regexide", which we've defined as the act of identifying and replacing flawed regular expressions with other techniques that better reflect the intended effect. Let's look at a few examples.

[TOC]

## How the Regular Expression Works

For the purposes of this discussion, it's important to understand exactly what XML comments are. XML comments are special notes that parsers should not treat as data. XML comments start with `<!--` and end with `-->`. Technically XML comments must not contain the string `--` within the comment body. Many programs and people write invalid XML comments, so parsers will typically allow for nested `--`.

For example, the following XML comment is technically invalid but accepted by many parsers:

```xml
<!-- I used to be a programmer like you,
     then I took an <!-- in the Kleene -->
```

(Kleene wrote a seminal paper[^2] on regular expressions.)

The regular expression body `/<!--[\s\S]*?-->/` has three parts:

A) `<!--` matches the four literal characters
B) `[\s\S]*?` matches any number of characters
C) `-->` matches the three literal characters

In (B), `[\s\S]` matches any character. The `*?` is a "non-greedy quantifier" that instructs the regular expression engine to take the shortest match.

<details><summary><b>Example of greedy and non-greedy matches</b> (click to show)</summary>

Consider the following string:

<pre class="language-text">
&lt;!-- &lt;!-- &lt;!-- --&gt; --&gt; --&gt;
</pre>

The "greedy" `/<!--[\s\S]*-->/` will match from the first `<!--` to the last `-->`:

<pre class="language-text">
<span style="background-color: #FFFF00">&lt;!-- &lt;!-- &lt;!-- --&gt; --&gt; --&gt;</span>  /&lt;!--[\s\S]*--&gt;/
</pre>

The non-greedy `/<!--[\s\S]*?-->/` will match from the first `<!--` to the first `-->`:

<pre class="language-text">
<span style="background-color: #FFFF00">&lt;!-- &lt;!-- &lt;!-- --&gt;</span> --&gt; --&gt;  /&lt;!--[\s\S]*?--&gt;/
</pre>

</details>

The modern variant of the regular expression uses the `/s` flag:

```js
str = str.replace(/<!--.*?-->/gs, ""); // even worse
                  ^^^^^^^^^^^^^^
```

The `/s` flag modifies the `.` character class to include line terminators.

## Usage in Open Source Projects

Many popular open source projects use problematic regular expressions. The most frequently recommended answer is:

```js
str = str.replace(/<!--[\s\S]*?-->/g, ""); // bad, do not use
                  ^^^^^^^^^^^^^^^^^^
```

[Nunjucks](https://github.com/mozilla/nunjucks/blob/ea0d6d5396d39d9eed1b864febb36fbeca908f23/nunjucks/src/filters.js#L491) used this regular expression within in the `striptags` filter expression:

```js
let tags = /<\/?([a-z][a-z0-9]*)\b[^>]*>|<!--[\s\S]*?-->/gi
```

[PrettierJS](https://github.com/prettier/prettier/blob/45ad4668ebc133621c7f94e678ce399cab318068/scripts/lint-changelog.js#L51) used this regular expression in the build sequence:

```js
const templateComments = template.match(/<!--.*?-->/gs)
```

[RollupJS](https://github.com/rollup/rollup/blob/18372035f167ec104280e1e91ef795e4f7033f1e/scripts/release-helpers.js#L76) used this regular expression in the build sequence:

```js
const bodyWithoutComments = data.body.replace(/<!--[\S\s]*?-->/g, "")
```

[SheetJS](https://github.com/SheetJS/sheetjs/blob/master/xlsx.mjs#L18117) used this regular expression in parsing:

```js
str = str.replace(/<!--([\s\S]*?)-->/gm, "")
```

[ViteJS](https://github.com/vitejs/vite/blob/9fc5d9cb3a1b9df067e00959faa9da43ae03f776/packages/vite/src/node/optimizer/scan.ts#L259) used the nascent `s` flag to ensure `.` matches newline characters:

```js
export const commentRE = /<!--.*?-->/gs

// Avoid matching the content of the comment
raw = raw.replace(commentRE, "<!---->")
```

[VueJS 2](https://github.com/vuejs/vue/blob/v2.2.3/dist/vue.esm.js#L7404) used regular expressions in processing:

```js
text = text
  .replace(/<!--([\s\S]*?)-->/g, "$1")
  .replace(/<!\[CDATA\[([\s\S]*?)]]>/g, "$1")
```

[WordPress](https://github.com/WordPress/WordPress/blob/master/wp-admin/js/word-count.js#L73) used regular expressions in the word count calculator:

```js
		HTMLcommentRegExp: /<!--[\s\S]*?-->/g,
```

[Element Plus](https://github.com/element-plus/element-plus/blob/4ac4750158fa634aa9da186111bce86c2898fda2/internal/build/src/tasks/helper.ts#L60) used a similar regular expression to match blocks starting with `<del>` and ending with `</del>`:

```js
const str = removeTag(value).replaceAll(/<del>.*<\/del>/g, "")
// ---------^^^^^^^^^^^^^^^^^^ -- start <del> end </del>
```

## A Troubling Consensus

It's surprising to see that most resources recommend this approach. A prominent O'Reilly textbook, "Regular Expressions Cookbook"[^3], explicitly recommends `/<!--[\s\S]*?-->/` in section 9.9 for matching XML comments. **StackOverflow Answers** recommend this regular expression and variants such as `/<!--[\s\S\n]*?-->/` (which are, for all practical purposes, equivalent). **ChatGPT4** has also recommended the previous regular expression. It also generated code for a complete unrelated tag. 🙄

_ChatGPT4 Incorrect interpretation_

![ChatGPT incorrect interpretation](gpt4.png)

_ChatGPT4 Correct interpretation, solution uses vulnerable regular expression_

![ChatGPT correct interpretation](chatgpt.png)

**Bing AI** proposed unrelated command line tools for JavaScript.

<details><summary><b>ChatGPT4 and Bing AI Screenshots</b> (click to show)</summary>

_Bing AI Correct Interpretation, solution uses vulnerable regular expression_

![Bing AI correct interpretation](bing.png)

</details>

## But Why is it So Slow?

Consider a string that repeats the header part `<!--` many times. In general, this type of string can be generated in JavaScript using `String.prototype.repeat`:

```js
var string_repeated_65536_times = "<!--".repeat(65536)
```

The `replace` operation is surprisingly slow. Try the following snippet in a new browser window or NodeJS terminal:

```js
// this loop doubles each time
for (var n = 64; n < 1000000; n *= 2) {
  var s = "<!--".repeat(n) // generate repeated string
  console.time(n)
  s.replace(/<!--([\s\S]*?)-->/gm, "") // replace
  console.timeEnd(n)
}
```

Results are from local tests on a 2019 Intel i9 MacBook Pro. The following chart displays runtime in seconds (vertical axis) as a function of repetitions (horizontal axis). The quadratic trend line closely fits the data.

<img src="./data/js.png" style="max-height:200px" alt="javascript performance test - quadratic complexity"/>

[Download the raw data as a CSV](./data/js.csv)

When the number of repetitions doubled, the runtime roughly quadrupled. This is a "quadratic" relationship.

The regular expression matches a string that starts with `<!--` and ends with `-->`. Consider a function that repeatedly looks for the `<!--` string and tries to find the first `-->` that appears afterwards. Computer scientists classify this algorithm as "Backtracking"[^4]:

```js {.line-numbers}
function match_all_regex_comments(str) {
  const results = []

  /* look for the first instance of <!-- */
  let start_index = str.indexOf("<!--")

  /* this loop runs while start_index is valid */
  while (start_index > -1) {
    /* look for the first instance of --> after <!-- */
    let end_index = str.indexOf("-->", start_index + 4)

    /* if --> is found, then we have a match! */
    if (end_index > -1) {
      /* add to array */
      results.push(str.slice(start_index, end_index + 3))

      /* start scanning from the end of the `-->` */
      start_index = str.indexOf("<!--", end_index + 3)
    } else {
      /* jump to the next potential starting point */
      start_index = str.indexOf("<!--", start_index + 1)
    }
  }

  /* return the final list */
  return results
}
```

!!! info Optimization

    The keen-eyed reader will notice that the loop can be terminated once the search for `-->` fails (line 25 should be `break;`).

    **Engines designed for JavaScript regular expressions do not currently perform this optimization.**

    It can be shown that the runtime complexity of the modified algorithm is $\Theta(L+M)$ where $L$ is the string length and $M$ is the number of matches

### A Side Note About Rust

Everyone writes high-performance code in Rust, right? Rust does not have built-in support for regular expressions. The Rust `regress`[^6] crate is designed for JavaScript regular expressions. It represents a true apples-to-apples comparison with JavaScript. `regress` shows the same quadratic behavior as other JavaScript regular expression engines.

```rust
    let re = regress::Regex::new(r"<!--([\s\S]*?)-->").unwrap();
    let mut str = "<!--<!--<!--";
    let _match = re.find(str);
```

<details><summary><b>Complete Example</b> (click to show)</summary>

```rust {.line-numbers}
fn main() {
    let re = regress::Regex::new(r"<!--([\s\S]*?)-->").unwrap();

    /* construct string by repeating with itself */
    let mut str = "<!--";
    let mut _str = format!("{}{}", str, str);
    let mut rept: u64 = 1;
    for _i in 1..8 {
        _str = format!("{}{}", str, str);
        str = _str.as_str();
        rept *= 2;
    }

    for _j in 1..11 {
        /* test regular expression against string */
        let start_time = std::time::Instant::now();
        let _caps = re.find(str);
        let elapsed_time = start_time.elapsed();
        println!("{}: {:?}", rept, elapsed_time);

        /* double string length by repeating with itself */
        _str = format!("{}{}", str, str);
        str = _str.as_str();
        rept *= 2;
    }
}
```

<img src="./data/regress.png" style="max-height:200px" alt="rust regress performance test - quadratic complexity"/>
<p>Results are from local tests on a 2019 Intel i9 MacBook Pro. </p>
[Download the raw data as a CSV](./data/regress.csv)

</details>

### A Closer Look at the Math

If `-->` is not in the string, the scan `str.indexOf("-->", start_index + 4)` will look at every character in the string starting from `start_index + 4`. In the worst case, with repeated `<!--`, the scan will start from index `4`, then index `8`, then index `12`, etc.

The following diagram shows the first three scans when running the function against the string formed by repeating `<!--` 5 times. The `<!--` matches are highlighted in yellow and the scans for the `-->` are highlighted in blue.

<pre>
<span style="background-color: #FFFF00">&lt;!--</span><span style="background-color: rgb(0,0,255,0.125)">&lt;!--&lt;!--&lt;!--&lt;!--</span>
^^^^             (first  match of &lt;!--     0 - 3)
    ............ (scan for --> from index  4 to end)   L -  4 characters

&lt;!--<span style="background-color: #FFFF00">&lt;!--</span><span style="background-color: rgb(0,0,255,0.125)">&lt;!--&lt;!--&lt;!--</span>
    ^^^^         (second match of &lt;!--     4 - 7)
        ........ (scan for --> from index  8 to end)   L -  8 characters


&lt;!--&lt;!--<span style="background-color: #FFFF00">&lt;!--</span><span style="background-color: rgb(0,0,255,0.125)">&lt;!--&lt;!--</span>
        ^^^^     (third  match of &lt;!--     8 - 11)
            .... (scan for --> from index 12 to end)   L - 12 characters
</pre>

For $N$ repetitions of `<!--`, the total string length is $L = 4 * N$. There will be $N$ matches.

<details><summary><b>Mathematical Analysis</b> (click to show)</summary>

The first scan will start on character 4 (end of the first match) and inspect $L-4$ characters (to the end of the string).

The second scan will start on character $2 * 4 = 8$ and inspect $L-8$ characters.

In general, the $K$-th scan will start on character $4 * K$ and inspect $L - 4*K$ characters.

The total number of characters scanned when looking for the end tag (line 11 in the code) is:

$$
\begin{array}{rl}
Scanned &= (L-4) + (L-4\cdot 2) + \ldots + (L-(N-1)\cdot 4) + (L - N\cdot 4) \\
&= N\cdot L - 4 \cdot 1 - 4 \cdot 2 - \ldots - 4 \cdot (N-1) - 4 \cdot N \\
&= N\cdot L - 4 \cdot \displaystyle\sum_{i=1}^{N} i \\
&= 4\cdot N^2 - 4 \cdot \dfrac{N \cdot (N+1)}{2} \\
&= 4 \cdot N^2 - 2 \cdot N^2 - 2 \cdot N = \dfrac{L^2}{8} - \dfrac{L}{2}
\end{array}
$$

</details>

In the worst case, the number of characters scanned is roughly proportional to the square of the length of the string. In "Big-O Notation", the complexity is $O(L^2)$. This is colloquially described as a "quadratic blowup".

## Workarounds

There are a few general approaches to address the issue.

### Use a Different Engine

By limiting the supported featureset, other regular expression engines have stricter performance guarantees.

#### NodeJS

The `re2`[^7] C++ engine sacrifices backreference and lookaround support for performance. There are bindings for many server-side programming languages.

The `re2`[^8] NodeJS package is a native binding to the C++ engine and can be used in server-side environments. With modern versions of NodeJS, normal regular expressions can be wrapped with `RE2`:

```js
var out = str.replace(new RE2(/<!--([\s\S]*?)-->/gm), "") // replace
```

<details><summary><b>Complete Example</b> (click to show)</summary>

```js
var RE2 = require("re2")
// this loop doubles each time
for (var n = 64; n < 100000000; n *= 2) {
  var s = "<!--".repeat(n) // generate repeated string
  console.time(n)
  s.replace(new RE2(/<!--([\s\S]*?)-->/gm), "") // replace
  console.timeEnd(n)
}
```

</details>

The `re2` implementation uses algorithms whose performance scales linearly with the size of the input.

<img src="./data/re2.png" style="max-height:200px" alt="nodejs re2 performance test - linear complexity"/>

[Download the raw data as a CSV](./data/re2.csv)

#### Rust

The Rust `regex`[^9] crate sacrifices support for performance. It is the same tradeoff made by the `re2` engine.

Since it does not use lookaround or backreferences, the original regular expression is compatible with the `regex` crate:

```rust
    let re = regex::Regex::new(r"<!--([\s\S]*?)-->").unwrap();
    let mut str = "<!--<!--<!--";
    let _match = re.find(str);
```

<details><summary><b>Complete Example</b> (click to show)</summary>

```rust
fn main() {
    let re = regex::Regex::new(r"<!--([\s\S]*?)-->").unwrap();

    /* construct string by repeating with itself */
    let mut str = "<!--";
    let mut _str = format!("{}{}", str, str);
    let mut rept: u64 = 1;
    for _i in 1..25 {
        _str = format!("{}{}", str, str);
        str = _str.as_str();
        rept *= 2;
    }

    for _j in 1..11 {
        /* find all matches */
        let start_time = std::time::Instant::now();
        let _caps = re.captures(str);
        let elapsed_time = start_time.elapsed();
        println!("{}: {:?}", rept, elapsed_time);

        /* double string length by repeating with itself */
        _str = format!("{}{}", str, str);
        str = _str.as_str();
        rept *= 2;
    }
}
```

The Rust `regex` implementation uses algorithms whose performance scales linearly with the size of the input.

<img src="./data/regex.png" style="max-height:200px" alt="rust regex performance test - linear complexity"/>

[Download the raw data as a CSV](./data/regex.csv)

### Exogenous Constraints

Most problems have additional constraints. Addressing the constraints allow for more precise regular expressions with better performance.

For the problem of matching comments, various specifications impose limitations.

#### XML Comments

The XML 1.0 specification[^10] disallows `--` within comments.

```
(this comment is not valid in XML 1.0)
<!-- - .... .. ... / -.-. --- -- -- . -. - / .. ... / .. -. ...- .- .-.. .. -.. -->
```

[PrettierJS](https://github.com/prettier/prettier/blob/ff83d55d05e92ceef10ec0cb1c0272ab894a00a0/src/language-markdown/mdx.js#L28) uses a regular expression in the MDX parser that enforces the XML constraint:

```js
const COMMENT_REGEX = /<!---->|<!---?[^>-](?:-?[^-])*-->/
```

Commonly-used regular expression engines can optimize for this pattern and avoid backtracking.

!!! info Spreadsheet Engines

    The XML parser in Excel powering the [Excel Workbook (XLSX) format](https://docs.sheetjs.com/docs/miscellany/formats/#excel-2007-xml-xlsxxlsm) expects proper XML comments with no `--` in the comment body.

    The XML parser in Excel powering the [Excel 2003-2004 (SpreadsheetML) format](https://docs.sheetjs.com/docs/miscellany/formats#excel-2003-2004-spreadsheetml) allows `--` in the comment body.

#### HTML Comments

The HTML5 standard[^11] permits `--` but forbids `<!--` within comment text. For example, the following comment is not valid according to the standard:

<pre class="language-text">
&lt;!-- I used to be a programmer like you, then I took an <span style="text-decoration-line:underline;text-decoration-color:red;text-decoration-style:wavy;">&lt;!--</span> in the Kleene --&gt;
</pre>

[yt-dlp](https://github.com/yt-dlp/yt-dlp/blob/95e82347b398d8bb160767cdd975edecd62cbabd/yt_dlp/extractor/common.py#L1709) uses a regular expression with a negative lookahead to ensure `<!--` does not appear in the body:

```python
    html = re.sub(r'<!--(?:(?!<!--).)*-->', '', html)
```

This expression allows `--` but disallows `<!--` in the comment body. In practice, it will match comments starting from the innermost `<!--`. Using the previous example:

<pre class="language-text">
&lt;!-- I used to be a programmer like you, then I took an <span style="background-color: #FFFF00">&lt;!-- in the Kleene --&gt;</span>
</pre>

!!! info Web Browsers

    Web browsers generally allow `<!--` in comments. Text between the first `<!--` and the first `-->` are treated as a comment. For example, consider the following HTML:

    ```html
    <pre><!-- this is a nested comment <!-- --> --> more text</pre>
         |                                    |^^^^^^^^^^^^^^ --- content
         |  this is interpreted as a comment  |
    ```

    This exact HTML code is added below:

    <pre><!-- this is a nested comment <!-- --> --> more text</pre>

    Chromium and other browsers will display `--> more text`

### Remove the Regular Expression

Regular expression operations can be reimplemented using standard string operations.

For example, the replacement

```js
str = str.replace(/<!--([\s\S]*?)-->/, "")
```

can be rewritten with a loop. The core idea is to collect non-commented fragments:

```js {.line-numbers}
function remove_xml_comments(str) {
  const START = "<!--",
    END = "-->"
  const results = []
  /* this index tracks the last analyzed character */
  let last_index = 0

  /* look for the first instance of <!-- */
  let start_index = str.indexOf(START)

  /* this loop runs while start_index is valid */
  while (start_index > -1) {
    /* add the fragment that precedes the comment */
    results.push(str.slice(last_index, start_index))
    last_index = start_index

    /* look for the first instance of --> after <!-- */
    let end_index = str.indexOf(END, start_index + START.length)

    /* if --> is found, then we have a match! */
    if (end_index > -1) {
      /* skip the comment */
      last_index = end_index + END.length

      /* search for next comment open tag */
      start_index = str.indexOf(START, last_index)
    } else break

    /* if there is no end comment tag, stop processing */
  }

  /* add remaining part of string */
  results.push(str.slice(last_index))

  /* concatenate the fragments */
  return results.join("")
}
```

### Validate Data

In the places where ViteJS used the vulnerable regular expression, the text was validated using a separate HTML parser.

It is still strongly recommended to replace the regular expression.

### Limit to Trusted Data

PrettierJS and RollupJS use the vulnerable regular expression in internal scripts. The expressions are not used or added in websites. The data sources are trusted and malformed data can be corrected manually.

## Special Thanks

Special thanks to [Asadbek](https://asadbek.dev/), [Jardel](http://francoatmega.com/), and members of the [SheetJS team](https://sheetjs.com) for early feedback.

[^1]: See ["Origin and Goals"](https://www.w3.org/TR/REC-xml/#sec-origin-goals) in the Extensible Markup Language (XML) 1.0 specification.
[^2]: The theoretical underpinnings of modern regular expressions were established in the working paper ["Representation of Events in Nerve Nets and Finite Automata"](https://www.rand.org/content/dam/rand/pubs/research_memoranda/2008/RM704.pdf)
[^3]: See ["9.9 Remove XML-Style Comments"](https://www.oreilly.com/library/view/regular-expressions-cookbook/9781449327453/ch09s10.html) on the official site for the book.
[^4]: See [the Wikipedia article for "Backtracking"](https://en.wikipedia.org/wiki/Backtracking) for more details and resources.
[^5]: See [the definition in the "CWE List"](https://cwe.mitre.org/data/definitions/1333.html) for more details and resources.
[^6]: See [the listing for `regress` crate](https://crates.io/crates/regress) for more details.
[^7]: See [the `google/re2` project on GitHub](https://github.com/google/re2) for more details.
[^8]: See [the listing for the `re2` NodeJS package](https://www.npmjs.com/package/re2) for more details.
[^9]: See [the listing for `regex` crate](https://crates.io/crates/regex) for more details.
[^10]: See ["Comments"](https://www.w3.org/TR/REC-xml/#sec-comments) in the XML 1.0 specification.
[^11]: See ["Comments"](https://html.spec.whatwg.org/multipage/syntax.html#comments) in the WHATWG HTML Living Standard.