---
type: Whitepaper
title: "Riding out DOMsday: Towards Detecting and Preventing DOM Cross-Site Scripting"
description: A browser with taint tracking in its JavaScript engine crawled the Alexa top 10,000 to measure DOM XSS, with a better test for whether a source-to-sink flow is truly exploitable, finding 83 percent more bugs than the prior method. It traces the causes, shows custom HTML templating can itself be buggy, and finds three static analysers miss 90 percent of the confirmed bugs.
resource: "https://www.ndss-symposium.org/wp-content/uploads/2018/02/ndss2018_07A-4_Melicher_paper.pdf"
tags: [whitepaper, webseclist-reference, xss, dom, javascript, dynamic-analysis, static-analysis, measurement-study, large-scale-scan, detection, owasp-a03-2021, owasp-a09-2021]
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    title: "Riding out DOMsday: Towards Detecting and Preventing DOM Cross-Site Scripting"
    author: William Melicher, Anupam Das, Mahmood Sharif, Lujo Bauer, Limin Jia
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authors:
  - William Melicher
  - Anupam Das
  - Mahmood Sharif
  - Lujo Bauer
  - Limin Jia
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# Riding out DOMsday: Towards Detecting and Preventing DOM Cross-Site Scripting

**Riding out DOMsday: Towards Detecting and Preventing DOM Cross-Site Scripting** - William Melicher, Anupam Das, Mahmood Sharif, Lujo Bauer, Limin Jia, Publisher not stated.

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# Riding out DOMsday: Towards Detecting and Preventing DOM Cross-Site Scripting

Riding out DOMsday: Toward Detecting and
             Preventing DOM Cross-Site Scripting

                            William Melicher, Anupam Das, Mahmood Sharif, Lujo Bauer, Limin Jia
                                        {billy, anupamd, mahmoods, lbauer, liminjia}@cmu.edu

    Abstract—Cross-site scripting (XSS) vulnerabilities are the        of a threat as JavaScript on the web becomes increasingly
most frequently reported web application vulnerability. As com-        complicated. Traditional methods for defending against XSS
plex JavaScript applications become more widespread, DOM               vulnerabilities in server-side code—for example, server-side
(Document Object Model) XSS vulnerabilities—a type of XSS              taint tracking or web application firewalls—typically do not
vulnerability where the vulnerability is located in client-side        apply because the vulnerability lies entirely in client code and
JavaScript, rather than server-side code—are becoming more
                                                                       servers may not even have logs to detect when an attack occurs.
common. As the first contribution of this work, we empirically
assess the impact of DOM XSS on the web using a browser with               In this paper, we aim to answer the following questions
taint tracking embedded in the JavaScript engine. Building on          about DOM XSS. Are DOM XSS vulnerabilities becoming
the methodology used in a previous study that crawled popular          more or less common? How do state-of-the-art methods for
websites, we collect a current dataset of potential DOM XSS            detecting DOM XSS vulnerabilities compare? Are web de-
vulnerabilities. We improve on the methodology for confirming
XSS vulnerabilities, and using this improved methodology, we
                                                                       velopers learning to avoid such vulnerabilities through good
find 83% more vulnerabilities than previous methodology applied        coding practices, for example, using encoding schemes or
to the same dataset. As a second contribution, we identify the         design patterns such as HTML templating? What are the causes
causes of and discuss how to prevent DOM XSS vulnerabilities.          of DOM XSS? Do shared libraries or web-content-generation
One example of our findings is that custom HTML templating             frameworks propagate DOM XSS vulnerabilities across a large
designs—a design pattern that could prevent DOM XSS vul-               number of sites?
nerabilities analogous to parameterized SQL—can be buggy in
practice, allowing DOM XSS attacks. As our third contribution,             To answer these questions, we use a dynamic approach
we evaluate the error rates of three static-analysis tools to detect   to detect DOM XSS vulnerabilities on the Internet. Prior
DOM XSS vulnerabilities found with dynamic analysis techniques         work showed how to detect DOM XSS vulnerabilities using
using in-the-wild examples. We find static-analysis tools to miss      taint tracking to track flows of attacker-controllable infor-
90% of bugs found by our dynamic analysis, though some tools           mation sources to sensitive sink functions (e.g., eval and
can have very few false positives and at the same time find            document.write) [8], [22]. The existence of such flows
vulnerabilities not found using the dynamic analysis.                  only indicates that data from a source can reach a sink, but
                                                                       does not account for whether the data has been sanitized by
                       I.    I NTRODUCTION                             the programmer. Thus, once a flow with a potential DOM XSS
                                                                       vulnerability is observed, the flow must be confirmed to be
    Cross-site scripting (XSS) is the most frequently reported         exploitable. In this paper, we show how to more accurately
class of web-application vulnerabilities, constituting 25% of          detect whether a flow that is potentially vulnerable is capable
web vulnerabilities reported in 2014 [9]. By compromising              of being exploited. Although an attacker can use several
client-side browser security using XSS, attackers can gain con-        types of sources (e.g., cross-origin messages and cookies), we
trol over login cookies, passwords, and authentication tokens,         focus, similarly to prior work [22], on confirming flows from
and perform application-level actions as users, for example,           URL-based sources. These are of particular interest because,
send emails or make financial transactions [25]. Preventing            compared to other flows, they are easy for attackers to exploit.
XSS typically requires website owners to not only sanitize all
                                                                           We used this methodology to detect DOM XSS vulnerabil-
untrusted inputs to their web application, but also to sanitize
                                                                       ities on Internet. We crawled the homepages and five random
all input that could be received by the client’s JavaScript
                                                                       subpages of websites on the Alexa Top 10,000 most popular
interpreter—a task that can be error-prone due to the complex-
                                                                       websites list [11]. Compared to previous work [22], we ob-
ity of web applications and the widespread use of sensitive
                                                                       served both more flows per web page and determined a higher
functions in JavaScript. Document Object Model cross-site
                                                                       proportion of those flows to be vulnerable, even when using the
scripting (DOM XSS)—a particular type of XSS vulnerability
                                                                       same methodology as previous work to determine which flows
that occurs entirely in client-side JavaScript—is more and more
                                                                       are vulnerable. Using our improved method for determining
                                                                       which flows are vulnerable, we found 83% more vulnerabilities
                                                                       than by using prior methodology [22]. We believe this indicates
                                                                       that DOM XSS vulnerabilities are becoming more common in
                                                                       the four years since the previous study was undertaken.
Network and Distributed Systems Security (NDSS) Symposium 2018             In addition, we qualitatively examined the code paths that
18-21 February 2018, San Diego, CA, USA
ISBN 1-891562-49-5                                                     led to the vulnerabilities. We observed, for example, that most
http://dx.doi.org/10.14722/ndss.2018.23309                             of the vulnerabilities did not share code, implying that the
www.ndss-symposium.org                                                 vulnerabilities we found are due to custom code, rather than
                                                                        document.write(
the inclusion of buggy shared libraries. We also observed                 ’<a href="’ + document.location +
errors in the implementation of HTML templating that allowed              ’">Link</a>’);
XSS vulnerabilities. Templating can be an effective way to
prevent DOM XSS vulnerabilities, and is similar to using
parameterized SQL queries. We found cases where bespoke                 Fig. 1: Example of a DOM XSS vulnerability.
templated HTML designs failed to properly encode template               An attacker could inject arbitrary markup using
values, which attackers could then inject code into.                    document.location as an attack vector by crafting
                                                                        a link that injects an attacker-controlled script into the
    Finally, using our collected dataset of DOM XSS vulner-
                                                                        page. An attacker may execute code by crafting a link like:
abilities, we evaluated static-analysis tools that are designed
                                                                        http://[website]/[page]#"><script>CODE</script><!--.
to detect DOM XSS. In the past, researchers have com-
pared the effectiveness of vulnerability scanners on synthetic
datasets [16], [36], whereas we used real-world vulnerabili-
ties. We found that static-analysis tools performed poorly at           work that discusses the impact of previously discovered vul-
detecting the vulnerabilities found by the dynamic analysis.            nerabilities. Next, we describe prior work on detecting DOM
However, some static tools were shown to have low false-                XSS vulnerabilities using taint tracking in Section II-D. We
negative rates and at the same time identify DOM XSS issues             describe prior work on comparing web-application scanners
not found by the dynamic analysis, suggesting that dynamic              in Section II-E. Finally, we describe how static-analysis tools
analyses and static analyses are finding qualitatively different        help prevent DOM XSS in Section II-F.
types of vulnerabilities. Our findings on static-analysis tools
suggest that testing using both dynamic and static approaches
may be necessary to secure web applications from DOM XSS.               A. DOM XSS vulnerabilities
   In summary, our contributions are as follows.                            Cross-site-scripting (XSS) vulnerabilities are a type of
                                                                        injection vulnerability in which an attacker can inject arbitrary
• We improve the methodology to confirm DOM XSS vul-                    code into a running web application to, for example, take
  nerabilities, and find that 83% more detected flows are               control of the data and credentials used in the application. For
  vulnerable than suggested by prior work [22].                         example, attackers may get access to the websites’s cookies
• We empirically analyze the prevalence of and causes behind            (which potentially contain login tokens), or may execute
  DOM XSS vulnerabilities. This yields a number of insights             user actions with respect to the compromised website [25].
  for example, that HTML templating is error prone to im-               In XSS, the injected code is JavaScript that runs in a web
  plement and that DOM XSS vulnerabilities are becoming                 application with the permissions of the compromised website.
  more prevalent. We also provide guidance for preventing               Unlike traditional XSS attacks in which an attacker’s injection
  DOM XSS vulnerabilities.                                              might be the result of a server-side failure to sanitize input,
• We compare static-analysis tools that detect DOM XSS vul-             DOM XSS is a relatively new type of XSS vulnerability
  nerabilities, finding them to detect different vulnerabilities        that occurs purely as a result of JavaScript executing on
  than our dynamic analysis.                                            the client. Figure 1 shows a example. In the example, an
• We develop a modified version of Chromium for tracking                attacker could craft a link that breaks out of the href’s single
  the taint information of strings, which we are releasing as           quoted attribute and inject an arbitrary script; for example,
  open source.1                                                         http://[website]/[page]#"><script>CODE</script><!--.
                                                                        This link, when clicked, would execute the attacker-controlled
    Next, in Section II, we provide background on DOM                   code (CODE). An attacker may convince their victims to
XSS vulnerabilities and compare our work to prior work for              click on the link using social engineering, or may embed
detecting DOM XSS vulnerabilities. Then, in Section III, we             the link in an iframe on a website that the attacker controls.
detail our methodology for crawling the Internet for DOM XSS            Like traditional XSS bugs, the details depend heavily on the
vulnerabilities, and our improved technique for confirming po-          website and the victim’s browser. Chromium, for example,
tentially vulnerable flows. In Section IV we describe the results       does not encode any characters after the ‘#’ symbol, whereas
of our experiments for detecting DOM XSS vulnerabilities and            Firefox encodes such characters using URL encoding. Hence,
evaluating static-analysis tools for detecting DOM XSS. We              it is not uncommon for a specific exploit to work only in
describe the limitations of our work in Section V. We discuss           specific browsers [29].
the implications of our findings in Section VI, and conclude
in Section VII.                                                            For a DOM XSS vulnerability to be present, there
                                                                        must be a flow of information from a potentially attacker-
                                                                        controlled source to a sensitive sink function. Examples
           II.   BACKGROUND AND RELATED WORK                            of potentially attacker-controlled sources include: the URL
    Here, we cover background and prior work relevant to                of the document, accessed via the document.location
DOM XSS vulnerabilities. First, we give examples of and                 JavaScript object; data passed in cross origin messages us-
general background on DOM XSS vulnerabilities in Sec-                   ing the postMessage API; cookies, accessed via the
tion II-A. Then, in Section II-B, we give examples of general           document.cookie object; and the HTTP referrer ac-
XSS defense mechanisms and why those mechanisms fail to                 cessed by the document.referrer JavaScript object
adequately apply to DOM XSS. In Section II-C, we cover                  and other methods. Sinks can include any mechanism to
                                                                        execute arbitrary code, for example: the eval function,
  1 https://github.com/wrmelicher/ChromiumTaintTracking                 document.write, JavaScript event handlers (e.g., the

                                                                    2
“onclick” attribute), and URLs that have a JavaScript scheme            of strings in JavaScript [8]. It is the oldest tool to apply
(e.g., <a href='javascript:...'>).                                      taint tracking to JavaScript. In 2013, Lekies et al. showed
                                                                        that DOM XSS is prevalent, and introduced a method for
B. Generic XSS defenses                                                 detecting DOM XSS using more precise, byte-level taint
                                                                        tracking of JavaScript code, also accounting for the built-
     Many methods have been used to mitigate or defend against          in encoding functions used in JavaScript [22]. To generate
XSS vulnerabilities in general but do not apply to DOM                  automated exploits, the researchers used a context-specific
XSS. Server-side taint-tracking and static-analysis techniques          exploit generation methodology designed to create a workable
fundamentally cannot be applied for detecting client-side vul-          exploit by analyzing the context in which the tainted string
nerabilities [14], [37]. Content Security Policies (CSPs) also          occurs in the sink. Their technique was tested by performing a
aim to solve the problem. However, the adoption of CSPs                 crawl of the Alexa Top 5,000 websites searching for DOM
has been limited and developers frequently misconfigure the             XSS vulnerabilities. Their work showed that automatically
policies, allowing unsafe code to execute [15], [38]. Web-              generated exploits can be created and that DOM XSS vul-
application firewalls attempt to solve the problem by blocking          nerabilities affect 9.6% of domains on the Alexa Top 5,000
all requests that match certain patterns (often lists of regular        websites. Our work uses a similar methodology as Lekies et
expressions) that indicate an XSS attack is occurring. However,         al.’s work for identifying tainted flows, but we use a new and
web-application firewalls are known to allow many attacks               novel method for confirming whether flows are indicative of
due to their reliance on simple pattern matching [13], [18].            DOM XSS vulnerabilities. We describe in detail the similarities
Furthermore, since DOM XSS exploits might not be sent to                and differences between our methodologies and results in
the server, the injection may never be visible to a firewall on         Sections III and VI.
the network. Dynamic taint tracking, a technique to observe the
flows of information throughout a program, has been proposed                Other work, building upon a system for detecting DOM
as a run-time defense against DOM XSS attacks [34]; however,            XSS vulnerabilities using browser-agnostic taint tracking [29],
it requires large infrastructure changes to web browsers. Addi-         provided a method to track taint information and inject an
tionally, taint tracking at run time can decrease performance.          extension that sanitizes injected strings at run time just before
The effect of such dynamic instrumentation on performance               those strings are inserted into the sensitive sink functions [28].
can potentially be small; however, it often has high variability,       The browser-agnostic framework allows detecting vulnerabili-
where a handful of websites have a serious performance                  ties that are specific to certain browsers; however, such vulner-
decrease [23]. In contrast, our work uses taint tracking to             abilities account for a small fraction of all vulnerabilities [29].
detect vulnerabilities, rather than defending against attacks at        Their work focused on their proposed defense mechanism and
run time.                                                               the capability of using a browser agnostic taint tracking, in
                                                                        contrast to our work which provides a measurement of the
C. Studying the impact of known vulnerabilities                         prevalence of DOM XSS vulnerabilities and the ability of
                                                                        static-analysis tools to detect DOM XSS vulnerabilities.
    Prior research has studied the impact of known vulner-
abilities on websites. Researchers found that in 2017, 37%                  Researchers have also shown how to use taint tracking to
of websites included at least one version of a library with a           defend against DOM XSS vulnerabilities at run time [34]. That
known vulnerability [21]. Researchers in that work measured             work began from a list of known DOM XSS vulnerabilities,
the prevalence of websites including old, outdated versions of          and showed that in 73% of cases, current client-side filtering
72 popular libraries. Other work has found that many websites           technology—the XSS Auditor in webkit-based browsers—fails
include third-party JavaScript that does not take all necessary         to filter an attack. The work proposes the use of browser-based
security precautions [24]. Our focus differs from these works in        taint tracking to more precisely prevent XSS vulnerabilities.
that, rather than studying the prevalence of already known vul-         However, this requires modification of the browser engine and,
nerabilities, we detect vulnerabilities without prior knowledge         as mentioned earlier, can cause performance degradation. The
of them. In addition, our approach goes beyond vulnerabilities          researchers conclude that many domains make use of partly-
in outdated versions of code in popular libraries and allows us         tainted HTML markup injection, and that blocking all such
to discover potentially unknown vulnerabilities.                        cases would not be feasible, instead recommending a specific
                                                                        heuristic policy to separate safe cases from dangerous cases.
D. Finding DOM XSS vulnerabilities using taint tracking                     Additionally, prior work quantitatively examined DOM
     The state of the art for detecting DOM XSS vulnerabilities         XSS vulnerabilities [35], finding that while many vulnera-
is using dynamic taint tracking. This technique marks poten-            bilities are of low complexity, some are the result of highly
tially attacker-controlled sources as “tainted” and propagates          complex JavaScript interactions. The researchers found that
information about tainted values throughout the program. For            many DOM XSS bugs are the result of vulnerable third-
example, the taint-tracking engine might mark the concatena-            party scripts, missing knowledge about browser-provided APIs,
tion of one tainted piece of information and one untainted as           unaware developers, or incompatible first- and third- party
also tainted. When a tainted string is used in a sensitive sink,        code. Our findings about vulnerability complexity and the role
the taint-tracking engine may flag this as a potential DOM              of third-party code are similar; we compare them in detail in
XSS vulnerability.                                                      Sections IV-A and IV-C. Differently from previous work, we
                                                                        also explore the role of advertising domains, the effectiveness
    A variety of tools and research have used dynamic taint             of static-analysis tools, the distribution of vulnerabilities across
tracking to detect DOM XSS vulnerabilities. The DOMinator               and within domains, and design-level prevention mechanisms
tool is a Firefox-based technology that tracks the taint status         such as HTML templating.

                                                                    3
                                                                          document.write(
E. Web-application scanners                                                 ’<a href="’ + encodeURI(document.location) +
    Web-application scanners are commonly used tools to                     ’">Link</a>’);
actively test for a variety of security issues in web applications.
Scanners use different methods to detect security issues, of
which DOM XSS is one. Prior work has surveyed web-                        Fig. 2: Modified example of Figure 1, in which the code
application scanners, finding them to overlook many classes               would have a DOM XSS vulnerability if the encoding function
of vulnerabilities, and to be limited by their ability to crawl           was not applied. In this example, the encodeURI function
websites; however, that work did not focus on DOM XSS, and                encodes the location so that the double-quote character cannot
also did not examine web vulnerabilities in the wild, instead             be injected.
creating a test environment [16]. Other work reports on the
false-positive and false-negative rates of web scanners [36].
That work also tests against a set of manufactured vulnerabil-                To crawl websites, we started by visiting the Alexa Top
ities and not on in-the-wild vulnerabilities and does not focus           10,000 websites, a list of the globally most popular web-
specifically on DOM XSS vulnerabilities.                                  sites [11]. Then, we collected all the links to other web pages
                                                                          on the home page of each website, and randomly selected five
F. Static-analysis tools                                                  web pages that were hosted on the same domain as the original
                                                                          domain to limit our crawl to a manageable size given our
    Static-analysis tools that support JavaScript, such as                resource constraints. This crawl is broader, but more shallow,
ScanJS [12] and JSLint [10], have gained popularity. Those                than Lekies et al.’s [22], and the difference between the two
tools statically, without executing code, attempt to detect com-          offers the opportunity for new insights about the incidence
mon programming errors in JavaScript, for example, pointing               of DOM XSS vulnerabilities (see Section VI-A). We also
out the use of dangerous functions or undefined variables. In             obeyed the robots.txt directives, which direct automated
general, static-analysis tools suffer from more false positives           programs—robots—as to which pages may be traversed [7].
than dynamic approaches [27], [31]. However, static-analysis              We automated the process of visiting web pages and extracting
tools are becoming a generally accepted part of the way that              the links on a page by developing and using a browser plugin.
software is developed—passing a static analysis without errors            Whenever any web page did not load correctly—for example,
is a requirement often listed in style guides (e.g., [1], [5]).           because of a timeout—we attempted to load the same page
In part, this is due to their ability to be run practically and           three times. If the failed page was not the top-level page
repeatably with little setup, for example, in nightly builds [27].        of a domain, we attempted to load a different web page
Some vulnerability detection tools, like Burp Suite [32], also            in the same domain. Crawling occurred during the summer
have a static-analysis component. However, the degree to                  of 2017, roughly four years after Lekies et al.’s work was
which static-analysis tools can detect and prevent real DOM               published [22].
XSS vulnerabilities is unknown. In addition, JavaScript as
a programming language has traditionally been difficult to
statically analyze because of its dynamic features (for example,          B. Dynamic taint analysis
widespread use of the eval function and reliance on dynamic                   Like prior work [22], we instrumented Chromium to per-
typing). In this work, we study the ability of static-analysis            form byte-precise tracking of the provenance of each byte of
tools to detect DOM XSS vulnerabilities in JavaScript.                    strings in JavaScript. We will not focus on the design of our
                                                                          taint-aware browser because it is not a core contribution of
                     III.   M ETHODOLOGY                                  our work and the design is similar to prior work. We have
                                                                          released the source code for our modified, taint-aware version
    Next, we describe the methodology for our experiments                 of Chromium and V8, the JavaScript engine used in Chromium
to detect DOM XSS vulnerabilities on the Internet. In Sec-                (see https://github.com/wrmelicher/ChromiumTaintTracking).
tion III-A, we describe how we crawled websites and which
web pages we visited. In Section III-B, we discuss the specifics              To summarize the design of the taint-aware browser:
of the taint-tracking engine we developed. In Section III-C,              We first allocated space in each JavaScript string primi-
we describe how we confirmed vulnerabilities. Finally, we                 tive for a one-byte taint value that stores the provenance
detail the methodology for testing static-analysis tools in               of each byte of the string. This allows taint information
Section III-D.                                                            to be precisely propagated during string concatenation or
                                                                          slicing. In addition to the provenance of each string byte,
A. Crawling for DOM XSS vulnerabilities                                   each bookkeeping byte also records which built-in encod-
                                                                          ing methods have been applied. For example, using the
    We first crawled the Internet using a browser instrumented            encodeURIComponent JavaScript function will modify
to perform taint tracking. The browser collected information              the taint information to reflect that the string has been
about what data flows occurred in the page, and output a                  encoded using the encodeURIComponent function. Dur-
log file detailing the flows and the encoding methods applied.            ing taint propagation, matching encoding-decoding pairs will
Then, for a subset of flows, we tested whether the flow was               cancel each other. For example, if a string is encoded
exploitable by generating example inputs crafted to deliver               using encodeURIComponent and later decoded using
a payload to the sensitive sink. This methodology builds on               decodeURIComponent, then the string will be identified
the methodology used in prior work for detecting DOM XSS                  as having no encoding applied. The taint information is only
vulnerabilities at scale [22]. We describe the differences from           stored for string types and not for arbitrary JavaScript objects.
this prior work in this Section and in Section III-C.                     This prevents tracking across different data types: for example,

                                                                      4
parsing a string into an integer and then writing the integer to          Method A: injection at end of URL
a string would remove all taint information.                              Observed URL:
                                                                            example.url.com/path?param=test&a=b
    Our browser checks the arguments of sensitive functions               Generated injection URL:
(e.g., the eval function or document.write; see Ap-                         example.url.com/path?param=test&a=b#INJECT
pendix VIII for an exhaustive list) for tainted bytes. If an
argument contains tainted bytes, then a record is written to              Method B: injection into parameter
a log file describing the flow, including: the type of taint, the         Observed URL:
locations of the tainted bytes, the sensitive sink function, and            example.url.com/path?param=test&a=b
a stack trace. Afterwards, we analyze the logs to determine               Observed eval-ed string:
which flows are potentially vulnerable to DOM XSS attacks                   var a = 'test';
and which flows are not.                                                  Observed taint location:
                                                                            The 9th through 13th bytes of the string—starting with the
    Whether a flow is vulnerable depends on the context of the              first ‘t’ in test and ending with the last ‘t’ in test.
injection in the HTML or JavaScript, the encoding functions               Generated injection URL:
that have been applied, and the source and sink types. For                  example.url.com/path?a=b#&param=INJECT
example, if we detect that a tainted value is not encoded and
begins in the context of an HTML double-quoted attribute,
then that flow is potentially vulnerable. However, if the string is
                                                                          Fig. 3: Explanation of injection methods using an artificial
encoded using the encodeURIComponent built-in function,
                                                                          example. In Method A, the injection is inserted at the end of
then a double quoted attribute is not vulnerable because the
                                                                          the string. In Method B, we attempt to insert the injection into
encodeURIComponent function encodes the double quote
                                                                          the parameter value that matches the tainted string in the text
as “%22”. Figure 2 shows code that would have a DOM XSS
                                                                          of the observed argument to the sensitive sink. INJECT marks
vulnerability if an encoding function was not applied. This
                                                                          the point of injection.
list of potentially vulnerable flows is then tested to decide
whether the flow is actually vulnerable to XSS attacks using
a process we describe in Section III-C. One example of a
potentially vulnerable flow that is not actually vulnerable to            the tainted bytes in the sink. An example is shown in Figure 3.
DOM XSS attacks is when the application performs custom                   The log files contain the information about which bytes of the
sanitization of inputs that is not detected by the taint-tracking         string are tainted and the semantic source label for those bytes
engine—for example, by halting execution if the input does                (e.g., from the URL). Therefore, we can infer which bytes of
not match a certain form that is known to be safe. The log                the source will make their way into the sink by examining
files also contain the stack trace for the sink call of each flow.        the string that is injected into the sink and comparing it to
In addition to making the flow more repeatable for post-hoc               the source string. The insight behind this method comes from
manual analysis, this allows us to examine the code path that             the observation that many of the values injected into sinks
led to the vulnerability (see Section IV-A).                              are values of parameters provided in the URL. Our method
                                                                          is designed to capture URL parsing in client-side code. It is
C. Attack confirmation                                                    relatively commonplace for JavaScript code to manually parse
                                                                          query parameters on the client, for example, by parsing the
     By crawling web pages using the taint-aware browser                  URL looking for the special characters that signal parameters:
described in Section III-B, we generate a list of poten-                  ?, &, and =. In this way, the URL is often used to pass
tially vulnerable flows. We then simulate an exploit to test              parameters to other links or to control the display of the web
those potentially vulnerable flows to decide whether they                 page. While this method of confirming that a flow is vulnerable
are actually vulnerable. We experimented with two meth-                   is extremely simple, in practice we find the combination of
ods of automatically crafting injections to test: one used                both methods to generate 83% more exploits than just the first
by prior work, which appends the injection to the end                     method (method A).
of the string [22]; and a novel method that attempts to
more accurately pinpoint the specific bytes of the string                     To test candidate exploits purely in the browser, i.e., with-
in which to inject a payload. For the purposes of auto-                   out affecting the website, we limit our candidate exploits to the
matically crafting injections we limited ourselves to URL-                part of the URL string after the hash (the ‘#’ character), as this
based sources (e.g., the document.location.href ob-                       segment of the URL string is not sent to the website hosting the
ject and derivatives like document.location.search,                       page, but only processed internally by the JavaScript running
document.location.hash, etc.). Those types of poten-                      in the browser.
tial vulnerabilities are straightforward to generate potential                We also did not craft actual valid HTML and JavaScript
exploits for, and therefore can be easily verified to be actual           exploits for attack confirmation, but rather crafted a unique
vulnerabilities. For the same reasons, they are the flows com-            string that included characters necessary for an exploit (e.g.,
monly targeted by attackers [26].                                         the single quote character if injecting a value into a single
                                                                          quoted HTML attribute). In our payload, we injected the string
    The first method (termed method A), used in prior
                                                                          marker<>’" and then examined our sink injection log files
work [22], appended the exploit to the end of the URL.
                                                                          for this string.
The new method (termed method B), which more accurately
pinpoints where in the string to inject the payload, attempts to             We believe that avoiding the use of valid HTML and
insert the exploit into the bytes of the source string that match         JavaScript in simulated exploits and targeting only the portion

                                                                      5
of the URL string after the hash—beyond limiting risk to web                compared a wide variety of these proprietary tools for general
servers—leads to simulated exploits that are both easier to                 purpose vulnerability detection (i.e., not restricted to DOM
generate and less likely to be caught by client or server-side              XSS vulnerabilities), and found them to have comparable error
filters. Such filters are notorious for being easily bypassable             rates to each other [36].
by humans [13], [18]. However, for an automated injection,
                                                                                The static-analysis tools that we chose appear to have
we wanted our approach to scale to many websites and
                                                                            different tradeoffs. ScanJS is a tool meant to help people
detect when an exploit could likely be crafted, instead of
                                                                            avoid coding practices that lead to, among other things, DOM
being filtered by an easily bypassable defense mechanism. To
                                                                            XSS vulnerabilities. As such, it flags code that could be
confirm that a flow was vulnerable to DOM XSS attacks, we
                                                                            unsafe without aiming to identify whether the code leads to
searched the logs for the unique injection string in the output.
                                                                            an exploitable bug. For example, it may point out all locations
To confirm that our methodology did not yield false positives,
                                                                            where the document.write function was used with a non-
we randomly sampled 40 flows that our process flagged as
                                                                            static string as an argument. While this is a good practice
vulnerable and manually developed a working exploit. We
                                                                            to avoid, it is not always indicative of a vulnerability. In
found that all 40 instances were vulnerable; therefore, we
                                                                            fact, the majority of cases are benign. Burp Suite attaches a
believe that the vast majority of cases found by our automated
                                                                            confidence rating to each potential vulnerability that it flags,
method were actual vulnerabilities.
                                                                            giving guidance about which findings are most reliable. Burp
    After confirming vulnerabilities, we qualitatively examined             Suite also receives code from the website by acting as a
a subset of these vulnerabilities for insights into the root                proxy between the browser and the website, meaning that
cases of DOM XSS vulnerabilities. For each vulnerability                    it has access to code that is dynamically loaded (e.g., by
that we manually analyzed, a researcher manually reproduced                 a <script> tag added during execution) unlike the other
the vulnerability based on the saved stack trace in our log                 tools; however, it still is not able to analyze code that is
files. Then, we distilled the vulnerability to a small amount of            dynamically generated (e.g., by using the eval function).
code that could describe the flow of data in the vulnerability.             Esflow is unique in that it often attaches source and sink
These code snippets were then analyzed to extract the themes                information to its issue reports for easier debugging.
common to vulnerabilities. We classified vulnerabilities by
complexity and also noted other interesting aspects of the                                          IV.    R ESULTS
code that had the vulnerability. Our results for this analysis                  We used the taint-tracking and crawling methodology de-
are presented in Section IV-C.                                              scribed in Section III to collect a dataset of tainted flows. We
                                                                            visited 44,722 web pages, which had in total 319,481 frames.
D. Static analysis                                                          One would expect that trying to visit five subpages on each
    After we collected a list of confirmed DOM XSS vulner-                  domain, we would have visited 60,000 web pages: 10,000 top
abilities, one of the analyses we performed was to evaluate                 level pages and 50,000 subpages. However, we skipped loading
the effectiveness of static-analysis tools to detect these vulner-          1,761 web pages due to robots.txt directives; and we were
abilities. We sampled our dataset in two ways to create test                unable to load 4,094 web pages after three attempts due to
sets to evaluate the false-positive rate and the rate with which            timeouts, 462 because Chromium would not load the page
the tested static-analysis tools detect these vulnerabilities. First,       (most often due to SSL warnings), and 26 because Chromium
we sampled websites that have known vulnerabilities from our                crashed when rendering them. Some of the pages unable to be
dataset of confirmed DOM XSS vulnerabilities, found using                   loaded were top-level pages; in that case we also did not visit
methodology described in Section III-C. Then, we sampled                    other pages on that domain.
from all websites that we visited to measure the false-positive                 We describe how we detected DOM XSS vulnerabilities
rate. Note that for measuring the false-positive rate, we sam-              using our dynamic analyses in Section IV-A. Then, in Sec-
pled from all websites, not only from websites where we did                 tion IV-B, we use the results from our dynamic analysis
not detect a vulnerability. We sampled in this way so that our              to evaluate different static-analysis tools for detecting DOM
sampling would not be biased towards sites that might be less               XSS vulnerabilities. Finally, in Section IV-C, we describe the
buggy. Sampling from our dataset of known vulnerabilities,                  qualitative trends that we observed from manually analyzing a
rather than using manufactured vulnerabilities, has the benefit             sample of our dataset.
that we are using real-world bugs.
                                                                            A. DOM XSS vulnerabilities detected using dynamic analysis
       a) Description of static-analysis tools: We evalu-
ated three tools for detecting DOM XSS vulnerabilities:                         After crawling our set of web pages, we post-processed the
ScanJS [12], esflow [4], and the static-analysis tools in Burp              generated taint-tracking logs to generate a list of observed data
Suite Pro [32]. We also attempted to test jsprime [30], but were            flows. Each flow has a source, through which an attacker could
unable to get it to work without crashing. We focused on open-              inject code, and a sink, a sensitive function that consumes
source or inexpensive proprietary tools that statically detect              data derived from the source of the flow. We tracked flows
DOM XSS vulnerabilities. There are variety of other, more                   that have sources that could be potentially manipulated by an
expensive proprietary vulnerability scanning tools, including:              attacker, and sinks that could potentially execute JavaScript, in-
IBM Security AppScan, Acunetix, Trustwave App Scanner,                      cluding functions that directly execute JavaScript (e.g., eval),
Retina web application scanner, Qualys web inspect, HP                      functions that inject HTML (e.g., assigning to innerHTML or
Fortify static code analyzer, and Coverity’s JavaScript scanner.            calling document.write), and JavaScript event handlers.
However, for our application of scanning a large number of                  A summary of the sources and sinks that we tracked can be
domains, these were prohibitively expensive. Prior work has                 found in Table I.

                                                                        6
                                                                                              Sinks




                                  Anchor src




                                                                                                                                                                                setTimeout
                                                                                  Embed src




                                                                                                                 Iframe src




                                                                                                                                                    JavaScript




                                                                                                                                                                                                                  Script src
                                                                      Css style




                                                                                                                                                                                                   Location
                                                                                                                                  IMG src
                                                                      attribute




                                                                                                                                                                  handler
                                                     Cookie




                                                                                                  HTML




                                                                                                                                                                  Event




                                                                                                                                                                                                                                       Total
                                                                Css
            Cookie            11,269             256,784        297     297        0           61,164          2,098          115,363          20,469               114          28               582          50,176            518,641
            Message           16,704              18,373        311     311        0           20,974          3,475           70,517       1,182,456                98          73               535          24,393          1,338,220
            Multiple               4                   0          0       0        0                9              3               35               0                 0           0                 0              15                 66
            Referrer          62,476               3,670         31      31        0           55,796          3,657           42,193             645                11          11               537          16,659            185,717
            Storage           11,023               4,590        112     112        0            3,712            396            7,146           3,541                 9           1                23           9,494             40,159
            URL              226,214              31,150        418     418       15          237,714        137,364          193,200           2,446               914         140             2,711         238,354          1,071,058
            URL hash           1,601                 171          2       2        0            1,938            148            2,322             173                 0         101                33           2,400              8,891
  Sources




            URL host           3,383             116,967         19      19        0           17,147         10,035           25,394             389                 6           3               308           5,716            179,386
            URL hostname      21,494             612,759        127     127        0           44,903         24,761          104,664           1,001               269          74               400          16,218            826,797
            URL origin        21,225                  46          1       1        0            1,801         47,887            3,273             336                 0           2                64           1,762             76,398
            URL pathname      20,235               9,807         15      15        0            3,913          1,301          102,945           1,457               628          12               193          13,326            153,847
            URL search         4,549               2,922          0       0        0            5,665            474           13,425              63                 0           0                48           2,759             29,905
            URL port               0                   0          0       0        0                0              0                2               0                 0           0                 0               0                  2
            URL protocol      82,953                 661         92      92        1           94,538         20,746          152,501             123                11          33               356          72,075            424,182
            window.name        2,109               4,504          8       8        0           24,845            160            3,826          12,621                 0           3                67           2,374             50,525
            Total            485,239           1,062,404      1,433   1,433       16          574,119        252,505          836,806       1,225,720             2,060         481             5,857         455,721

TABLE I: Source-to-sink flow counts for different source-sink pairs. Rows in the table are sources and columns are sinks. We
focus on the shaded columns and rows in this work. “Cookie” as a sink means assignment to the document.cookie object;
as a source means data originating from document.cookie. “Location” refers to assignment to document.location.


                                                                                                                                               #                                                   as % of total flows
     Step #                                                                                                                   this work            25m flows [22]                            this work       25m flows [22]
                  Seed domains                                                                                                   10,000                     5,000
                  Web pages                                                                                                      44,722                   504,275
                  Frames                                                                                                        319,481                 4,358,031
     1            Total flows                                                                                                 4,140,873               24,474,306
     2            URL∗ , referrer, window.name sources to JS, HTML sinks                                                        363,034                 1,825,598                              8.77%                           7.46%
                  URL∗ sources to JS, HTML sinks                                                                                285,147                                     ‡
                                                                                                                                                                                               6.89%
     3            Flows from step 2 excluding those blocked by encoding methods                                                  97,924                          313,794                       2.36%                           1.28%
                                                                                                                                                                            ‡
     4            Flows from step 3 excluding those blocked by natural encoding in Chromium                                      93,481                                                        2.26%
                                                                                                                                                                            ‡
     5            Flows from step 4 including only URL-based sources                                                             54,954                                                        1.33%
     6            Unique† flows from step 5                                                                                       5,217                                     ‡
                                                                                                                                                                                               0.13%
     7a           Unique† vulnerabilities from step 6 after exploit step using method A§                                          1,754                          6,167‡‡                       0.04%                           0.03%
     7b           Unique† vulnerabilities from step 6 after exploit step using method A and B††                                   3,219                                                        0.08%
                                                                                                                                                                            ‡
                  Vulnerable iframe URLs                                                                                          4,668
                  Vulnerable domains                                                                                                364                             480
                  Unique vulnerabilities as percent of pages visited using method A                                                  4%                            1.2%
                  Unique vulnerabilities as percent of pages visited using method A + B                                            7.3%

TABLE II: Break down of flows comparing replication of prior work with the same methodology [22]. *) Excludes the JavaScript
location.protocol property as it is not readily exploitable. †) Applying the uniqueness filter of hosting domain, code
location, breakout sequence. ‡) not reported in that work. §) Method A appends the injection to the end of the source string.
††) Method B inserts the injection into the bytes of the source string which match the tainted bytes in the sink after encodings
and decodings have been applied. ‡‡) Includes flows from window.name sources because that work includes those exploits.



    Overall, visiting 44,722 pages resulted in 4,140,873 de-                                                 is expecting it. With the exception of message flows, URL-
tected flows. We focus on flows with URL sources and HTML                                                    based sources account for the largest number of flows to sinks
or JavaScript sinks, as these are the most straightforward to                                                that can execute arbitrary JavaScript (HTML and JavaScript
exploit. Consistently with that, research has generally focused                                              sinks). Hence, these are the flows we analyze, and we show
on examining this subset of flows or found it to account for                                                 that they lead to many instances of DOM XSS vulnerabilities.
the majority of exploitable flows (e.g., [22], [29]).                                                        Of the 4,140,873 flows we detected, 285,147 (7%) had a URL-
                                                                                                             based source.
    Other flows have preconditions that make automatically
exploiting them more difficult at scale. For example, to exploit                                                    a) Confirmed vulnerable flows: We determine whether
a cookie flow, an attacker must find a way to manipulate the                                                 a tainted flow is vulnerable as follows. We first discard
victim’s cookies; for message flows, an attacker must find a                                                 flows in which the tainted value is encoded using a built-in
potential flow whose code does not check the message origin                                                  encoding method, for example, the encodeURIComponent
and also send the message at the proper time, when the receiver                                              function; we are certain that such flows would ordinarily not

                                                                                                         7
         Method                             # of unique vulnerabilities




                                                                              # of bugs found on domain
         Only injection at end                                     715                                    1000
         Only injection in key-value pair                       1,465
                                                                                                           300
         Both methods                                           1,039
         Total                                                  3,219                                      100

                                                                                                            30
TABLE III: Summary of the injection methods used to confirm
different vulnerabilities. “Only at end” refers to the injection                                            10
method that inserts the injection at the end of the source
                                                                                                            3
(Method A). “Only key-value pair” refers to the injection that
inserts the injection in the value of a tainted query key-value                                             1
pair (Method B). “Both methods” refers to cases where either
method would have identified the flow.                                                                           1   10            100
                                                                                                                     Domain rank
                                                                              Fig. 4: Distribution of unique vulnerabilities across domains.
                                                                              The y-axis shows the number of unique vulnerabilities found
be exploitable. This eliminates 66% of the flows we focus                     on a particular domain in log scale. The x-axis shows domains
on (URL sources to JavaScript or HTML sinks). We next                         sorted by frequency; for example, ten on the axis shows the
remove from consideration flows that could not be exploited                   domain with the 10th most vulnerabilities. For example, the
in Chromium due to Chromium’s natural encoding of some                        domain with the most vulnerabilities had nearly 1,987 unique
URL variables (for example, Chromium automatically encodes                    vulnerabilities.
the content of document.location.search to prevent
the occurrence of any character that would not be allowed in
a URL). After removing those types of flows, we determine
which of the remaining 1.33% (54,954 flows) of flows are                      are identified by their domain, their location in the script, and
actually vulnerable by attempting injections. A summary of the                the context (e.g., inside a double-quoted attribute or the name
number of flows removed at each stage compared to previous                    of an element attribute) of the tainted section of the string
work with similar methodology [22] can be seen in Table II.                   argument to the sensitive sink.
     In our taint-tracking system, we specially mark flows                        We also computed the number of unique vulnerabilities
that have multiple, incompatible encodings with a flag that                   across different domains, as shown in Figure 4. We found
represents the use of multiple encodings, but not which specific              that the majority of vulnerabilities come from a handful of
encodings or in what order. Such flows accounted for 2% of                    domains, and that many domains had only a few unique
flows overall. While we did not attempt to determine whether                  vulnerabilities or one vulnerability: the ten domains with the
these flows were actually vulnerable, there were 716 unique                   most vulnerabilities had in total 2703 unique vulnerabilities;
flows of this type that may have been potentially vulnerable                  the remaining 354 domains accounted for the remaining 516
(i.e., that could have been included in row 6 of Table II). If they           vulnerabilities.
had been included, they would account for 12% of potentially
vulnerable flows.                                                                 Interestingly, when performing the vulnerability confirma-
                                                                              tion crawl we observed vulnerabilities in six iframe URLs that
    We used two methods to confirm vulnerabilities—each                       were not previously seen in our first crawl. These iframe URLs
described in Section III-C—based on where to insert the                       were part of the confirmation crawl because either they or
injected payload: inserting the payload at the end of the URL                 the top-level pages that included them had previously been
or inserting the payload into the key-value pair from which                   marked as potentially containing a vulnerability. The difference
we observed a flow to a sink. We found that 45% of the                        in time between collecting data and confirming vulnerabilities
confirmed vulnerabilities we detected were due to flows from                  was nine days.
key-value pairs, 22% of the vulnerabilities were only the result
of inserting the payload at the end of the source, and 32% of                         b) Vulnerability attribution by domain and domain cat-
the vulnerabilities were observed to work with both methods.2                 egory: We next attempted to shed light on the cause of the
Table III shows the breakdown of how many of the 3,219                        vulnerabilities that we observed by examining where they
unique vulnerabilities came from which injection method. Both                 occurred. Were they due to third-party scripts, old versions
methods of injection work in cases where the entire URL                       of popular libraries, custom code for each website, or other
is concatenated with markup (i.e., document.location,                         causes? For this measurement, we used the URL of the frame
rather than a specific substring, is included in markup). Our                 where the vulnerability was found, since this is the context
key-value pair injection method identifies vulnerabilities that               in which an attacker would be able to execute JavaScript,
involve parsing URL parameters, while inserting the injection                 rather than using the URL of the top-level frame. We used the
at the end identifies vulnerabilities in which part of the path               location of the sink as a starting point for determining to which
or URL besides the URL parameters is used as part of the                      entity to attribute the vulnerability. In particular, we examined
parameter to the sink.                                                        the distribution of vulnerabilities in three ways: (1) the domain
                                                                              on the iframe in which the script executed; (2) the domain on
    To count unique vulnerabilities, we removed duplicates                    which the script was hosted (web pages often import scripts
using the same method used as Lekies et al. [22]: unique bugs                 from other domains); and (3) the domain of the top-level page
                                                                              that the user was visiting. Rather than reporting results about
  2 Numbers do not add up to 100% due to rounding.                            individual domains, we report them by the topic category of the

                                                                          8
    10000




               2681
               2645
     1000

                    126
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        100       76
                       52
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                            45
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Fig. 5: The count of URL domains and script domains in different website categories. The bar height shows the number of script
domains or frame domains with the corresponding category in our dataset of unique vulnerabilities. The y-axis is in logarithic
scale. Script domains are the domains that the vulnerable scripts were hosted on. Frame domains are the domain of the frame
where the vulnerability was located. Note: the numbers for script domains do not add to 3,219 because some sinks did not have
a script URL. This may happen when the sink location is in dynamically generated code.



domains. We use the Blue Coat K9 classification of domains                                                    0.4
                                                                              % of vulns script was present




into topics [2] for this purpose.
    We found that the vast majority, 2,645 of 3,219 of our                                                    0.3
unique vulnerabilities (82%), were found to execute inside
iframes with domains that were known to serve web advertise-
                                                                                                              0.2
ments or perform analytics. Other domain types that accounted
for many vulnerabilities included shopping and news.
    We also analyzed what type of domains hosted the scripts                                                  0.1
in which we found vulnerabilities. Similarly to the above
result, we found that 2,681 of 3,219 vulnerabilities (83%) were
                                                                                                              0.0
in scripts hosted on advertising and analytics domains. Figure 5                                                    1                   10                       100               1000
shows the analysis of the types of script domains and website                                                                                        Script rank
domains with confirmed vulnerabilities. For this measurement,
                                                                          Fig. 6: The percent of stack traces from the dataset of unique
we used the domain of the script where the sink function call
                                                                          vulnerabilities that scripts were found in. The x-axis shows the
was found. While advertising domains were the most popular
                                                                          rank in log scale of the scripts in a sorted list; for example, 10
source of vulnerable scripts, our data-collection infrastructure
                                                                          shows the script that was 10th most frequently present in stack
did not capture enough information to similarly categorize
                                                                          traces. The y-axis is the percent of script URLs that were less
scripts that did not have potentially vulnerable flows. Hence,
                                                                          than that rank. For example, the first script was present in the
while we can report that, in web pages that had at least one
                                                                          stack traces of 0.34% (11 of 3,219) unique vulnerabilities.
flow, 38% of the time the flow originated in a script that
was categorized as an advertising script, we cannot determine
whether the fraction of advertising-domain scripts that was
vulnerable was greater than the fraction of scripts from other
domain categories.                                                        vulnerabilities were present in web pages that were subframes
                                                                          of multiple web pages. In contrast to Figure 5, where the most
    We matched the unique vulnerabilities that we found with              popular category was web ads and analytics, here the popular
the top-level web pages that contained those vulnerabilities in           topics are news/media (27.7%) and entertainment (12.9%).
our dataset. Many of the vulnerabilities that we found were on
subframes of other web pages, and we wanted to understand                     In total, for 282 (8.8%) of the vulnerabilities we found the
how much exposure users would have if they visited the top-               domain the script was hosted on was different from the domain
level pages in our dataset. Table IV shows the categories of              of the iframe in which the script executed. This suggests
these top-level web pages. Note that there are significantly              that while a non-trivial fraction (8.8%) of vulnerabilities may
more data points than unique vulnerabilities because some                 be caused by developers relying on third-party scripts, the

                                                                      9
                %    Count   Category of top level website                prevent many vulnerabilities. At the same time, if some scripts
            27.7%     2856   News/Media
            12.9%     1337   Entertainment
                                                                          occur in many stack traces of vulnerabilities, this could indicate
             9.9%     1026   Technology/Internet                          that developers misunderstand how to correctly use that script.
             5.1%      523   Games
             4.4%      453   Education                                        For our 3,219 confirmed vulnerabilities, we identified the
             4.1%      424   Sports/Recreation
             3.6%      376   Reference
                                                                          scripts in the stack trace of each vulnerability, and then
             3.5%      362   Shopping                                     counted how many stack traces each script was present in.
             2.8%      289   Hacking                                      For this analysis we removed jQuery from our results because
             2.7%      280   Business/Economy
             2.4%      246   Society/Daily Living                         many websites use various HTML rendering functions (e.g.,
             2.0%      202   Mixed Content/Potentially Adult              the html or append jQuery methods) that are working as
             1.7%      178   Newsgroups/Forums                            intended, but misused by the caller. Hence, we removed any
             1.6%      164   Health
             1.4%      143   Search Engines/Portals                       script name that contained the string “jquery” without respect
             1.2%      119   Brokerage/Trading                            to character case.
             1.1%      114   Political/Social Advocacy
             1.1%      113   Financial Services                               We found that the majority of vulnerable scripts was
             1.0%      107   Travel
             0.9%       98   Vehicles                                     present in only one unique vulnerability stack trace—implying
             0.8%       80   Restaurants/Dining/Food                      that the causes of vulnerabilities are unique. Figure 6 shows
             0.7%       76   Uncategorized                                the percentage of stack traces that each script is seen in.
             0.7%       71   Real Estate
             0.6%       62   Job Search/Careers
             0.5%       55   File Storage/Sharing                                 d) Vulnerabilities in commonly blocked content: Inter-
             0.5%       51   Audio/Video Clips                            net folklore has often claimed that ad blocking software pro-
             0.5%       50   Government/Legal                             tects your computer from XSS vulnerabilities common in ad
             0.4%       46   Software Downloads
             0.4%       43   Religion                                     networks [19]. Because we found that many of both the target
             0.4%       43   Pornography                                  web pages and the vulnerable scripts were located on domains
             0.4%       39   Adult/Mature Content
             0.4%       37   Alternative Spirituality/Belief
                                                                          that hosted advertising, we tested how much protection a
             0.3%       31   Email                                        normal user who uses an ad blocker would have from such
             0.3%       28   Social Networking                            vulnerabilities. For this analysis, we used the adblockparser
             0.3%       28   Personal Sites
             0.2%       24   Malicious Sources/Malnets                    Python library [6] to simulate what scripts would not be
             0.2%       21   Office/Business Applications                 executed if the user was running ad blocking software that
             0.2%       21   Auctions                                     obeyed the rules defined in the Adblock EasyList, a popular
             0.2%       18   Phishing
             0.1%       14   Humor/Jokes                                  rule list of advertising content to block [3]. We counted a
             0.1%       13   Suspicious                                   vulnerability as being blocked if the Adblock EasyList would
             0.1%       13   Charitable Organizations
             0.1%        8   Scam/Questionable/Illegal
                                                                          block either the script or the entire target URL when the target
             0.1%        7   Web Hosting                                  URL is loaded inside an iframe and not as the main frame. We
             0.1%        6   Intimate Apparel/Swimsuit                    found that, of the 3,219 unique vulnerabilities, 2,039 (63%)
            <0.1%        5   Weapons
            <0.1%        5   Placeholders                                 would have been blocked by this simulated configuration of
            <0.1%        5   Gambling                                     Adblock.
            <0.1%        4   Web Ads/Analytics
            <0.1%        4   Personals/Dating
            <0.1%        3   Nudity                                       B. Effectiveness of static-analysis tools
            <0.1%        2   Military
            <0.1%        2   Chat (IM)/SMS
                     10325   Total
                                                                              We next examine whether the vulnerabilities we found
                                                                          could be detected at development time using off-the-shelf
TABLE IV: Categories of top level domains that contain an                 static-analysis tools. We find that most could not, although
iframe with a DOM XSS vulnerability. The count column                     static-analysis tools sometimes found additional bugs.
shows the number of top level pages in a category that                        More specifically, with our dataset of confirmed vulnerabil-
contained a frame with a vulnerability. The percent shows the             ities IV-A, we tested static-analysis tools to evaluate their abil-
percent of top level pages with that category.                            ity to find the same vulnerabilities that the dynamic analysis
                                                                          found. To target JavaScript, dynamic analysis traditionally is
                                                                          seen as having fewer false positives [27]; however, static analy-
                                                                          sis is often more helpful for programmers during development
vast majority of vulnerabilities are in the developers’ own               because of the lack of customized analysis for adding new
scripts (or at least scripts hosted locally on their domains). The        code—developers can set up a static-analysis toolchain once
fraction is smaller than reported in prior work, which found              to automatically check new code. In addition, static analysis
that 22% of code attributable purely to an error by a third               can be more complete—able to detect vulnerabilities in code
party [35]. This difference could be the result of our different          that was not executed on a particular run of the program.
methodology for confirming DOM XSS vulnerabilities.                       The majority of the vulnerabilities that were caught in our
                                                                          experiment only by static-analysis tools were in this category.
         c) Vulnerability attribution by script: We additionally
examined the scripts in the entire stack trace for each vulnera-                  a) Overlapping vulnerabilities: We compared the rates
bility. The goal of this analysis was to determine whether some           at which different tools, described in Section III-D, found
scripts occurred in stack traces of vulnerabilities particularly          the vulnerabilities that we had previously compiled using the
often. Such scripts could be good candidates for adding                   dynamic analysis. We found that the tools we tested usually
encoding functions, or for other remediation, as that would               failed to detect the DOM XSS vulnerabilities from our dataset.

                                                                     10
                    % of detected vulnerabilities   # of reported issues                   Tool         False positive %   # of reported issues
       Esflow       0%                              4                                      Esflow                    95%                     19
       ScanJS       8%                              2700                                   ScanJS                  100%                   3764
       Burp Suite   10%                             39                                     Burp Suite                 0%                     36

TABLE V: The percent of vulnerabilities detected by the                         TABLE VI: Empirical false positive rate computed from a ran-
dynamic analysis that were detected by different static-analysis                dom sample of 20 reported errors over 50 randomly sampled
tools out of a total of 50 web pages with known vulnerabilities.                web pages.



The full results comparing different tools are provided in                      analyzed the scripts on those pages with each of the tested
Table V. Notably, while Burp Suite, the most promising tool,                    static-analysis tools. Each tool would report findings on the
had a low rate of finding the same errors as the dynamic                        pages related to DOM XSs. We randomly sampled 20 of those
analysis, it pointed out many potential issues not found by                     findings, except for esflow, which only reported 19 findings.
the dynamic analysis. We next describe these findings in more                   We then manually examined each finding, and the piece of
detail.                                                                         code that it referred to, to determine whether that piece of
                                                                                code could be exploitable. In doing so we aimed to simulate
    We randomly sampled 50 of the 3,219 unique bugs we                          how a developer assessing the same code and reviewing the
found using our dynamic analysis. Then, for the two tools                       output of the tool would categorize the bug.
that scanned JavaScript code, we downloaded the web page                            Our guiding criteria for manually counting true and false
where the vulnerability was located, and all the accompanying                   positives in the tools’ output was to look for flows from
JavaScript, and used the downloaded JavaScript as input to                      exploitable sources (e.g., URLs, cross-origin messages) to
the tools. We included any JavaScript embedded in HTML                          exploitable sinks (e.g., document.write, eval) without
in addition to externally loaded JavaScript. Because the tool                   encoding that would render the flow benign. Thus, we counted
was examining the web page statically, we were not able                         flows as true positives even if the identified block of code was
to include JavaScript that is dynamically loaded during the                     not executed during the page load during which our dynamic
execution of the page. For Burp Suite, we loaded the web page                   analysis detected a vulnerability. This may happen because the
in the Chromium web browser and connected Burp Suite to the                     function is dead code, or because that particular page load did
browser via a proxy. In this way, all the JavaScript requested                  not happen to execute the vulnerable function. We believe this
by the browser was analyzed by Burp Suite’s static-analysis                     method of measuring false positives is a conservative estimate,
tool. Therefore, it was able to access external scripts that were               because in reality some of the identified vulnerabilities may be
dynamically loaded during execution.                                            in dead code. We also did not include findings that were not
     We counted a tool as successfully identifing one of these                  related to DOM XSS vulnerabilities—for example, warnings
vulnerabilities if it output any error message related to DOM                   about bad coding practices—as either false positives or false
XSS referring to the code where the sink for the vulnerability                  negatives. We aimed to measure the number of actionable
was located. For Burp Suite and esflow, we manually reviewed                    vulnerabilities that could be detected by our tested static-
all messages and counted how many referred to the exact line                    analysis tools.
number and character offset of the sink that was vulnerable.                        Deciding whether a “bug” reported by a static-analysis tool
For ScanJS, we counted messages that referred to the same                       is exploitable was a judgment call. We believe that any bias in
script location (line number and script name) as the vulnerable                 the judgment is likely to be biased towards marking something
sink, provided that they warned of a potential XSS vulnerabil-                  as non-exploitable when it could be exploited, because it is
ity. We explicitly terminated the analysis of any program that                  easier to show how a piece of code might be dangerous,
took longer than one hour. This affected four of the 50 web                     but much harder to confirm that code is safe in all cases.
pages tested with esflow. In practice, we believe that this is                  In practice, we believe this closely matches how an engineer
realistic in that static-analysis tools must give results within a              reading the output of such a tool would label the output.
reasonable time to be useful to developers. We do not count
as matches cases in which the tool detects a vulnerability that
was not a part of our dataset.                                                  C. Qualitative trends in DOM XSS vulnerabilities

       b) False positive rates: We compared the false positive                      To gain greater insight into the causes that give rise to
rates of the tools by sampling tool output and manually                         DOM XSS vulnerabilities, we manually, qualitatively analyzed
deciding whether the particular snippets of code that the tool                  two subsets of the vulnerabilities detected by our dynamic
flagged could be exploitable. We found Burp Suite to have no                    analysis. First, we randomly selected from the unique vulner-
false positives, while the other tools had many false positives.                abilities; however, we noticed that a large portion of these
Table VI shows the results for all tools.                                       vulnerabilities was semantically very similar, despite being
                                                                                unique bugs according to our uniqueness criteria (script lo-
    We randomly sampled 50 out of all the URLs that we                          cation, hosting domain, and context; also used in previous
visited in our dataset. We randomly sampled from all URLs,                      work [22]). Therefore, we also selected a separate subsample
and not just URLs for which we did not confirm vulnerabilities,                 of vulnerabilities, in which we first randomly selected 20
so that our results for false positive rates would not be biased                domains on which vulnerabilities had been found, and then
towards websites that are more secure, and therefore more                       selected a random vulnerability on each domain. This allowed
likely to have false positives than true positives. We then                     us to get a sample that is conceptually more representative

                                                                           11
of the types of bugs that occur across different domains,                                                          By domain   By unique bug
and hence of the types of problems that are likely to be                        Simple concatenation                       8               1
encountered by different organizations. A summary of the                        Simple except for variable usage           4              18
                                                                                Spans multiple functions                   8               1
trends we observed is located in Table VII.
                                                                                Custom templating                          3               0
       a) Vulnerability complexity: First, we found that some                   Custom filtering                           1               0
bugs were extremely simple, such as concatenating the entire                    Dynamically generated code                 2               0

URL into an HTML or JavaScript execution function. Exam-
ples of why this happened were creating a form where the                 TABLE VII: Description of types of vulnerability qualities
form submission attached a return URL for the current page,              observed during qualitative coding of bugs. We randomly
or passing the web page’s URL as a query parameter for the               sampled our vulnerability dataset in two ways, by domain
source of an iframe. In addition to simple concatenation, we             and by unique vulnerabilities; each sample contained a total
also found cases where the URL was stored in a non-local                 of 20 vulnerabilities. “Simple concatenation” refers to bugs
variable that could be assigned to in code that was far away             that were a simple concatenation of the entire source with
from the sink (e.g., in a different file or function).                   HTML or JavaScript markup. “Multiple functions” refers to
                                                                         vulnerabilities that spanned multiple functions. “Simple except
        b) Failed mitigation behaviors: In addition, for eight           for variable usage” refers to bugs where a variable with the
of the forty vulnerabilities the relevant code was more com-             source value was concatenated with HTML or JavaScript code.
plex and spanned multiple functions. Three of those eight                Custom templating refers to code that attempted to use a
utilized custom template processing that did not perform                 custom templating library, but without encoding. Dynamically
encoding based on the context in the template, resulting                 generated code refers to instances where code involved in
in insecure templating code. Another vulnerability was due               the bug was dynamically generated, and would generally be
to an attempt to perform custom, but highly incomplete,                  outside of the abilities of static analysis.
filtering—removing all instances of <script> tags, but still
leaving open many other ways for an exploit to occur, for
example, by using event handler code like <img src=x
onerror='INJECTION'/>. For two other vulnerabilities,                    target website but is redirected to a phishing website via
code involved in the flow was dynamically generated using the            assignment to document.location in JavaScript. A victim
eval function, meaning that such code would typically not                might assume that they were on a benign website because the
be visible to static-analysis tools.                                     hostname in the URL they clicked on was benign. We speculate
                                                                         that these other types of flows might be similar to the types of
    We did not observe any failed attempts to use custom                 flows we study here and would be a good avenue for future
encoding functions. Combined with the fact that many of the              work.
bugs were shallow—a finding echoed by [35]—this suggests
that perhaps engineers were not aware that URLs could contain                We sampled only a subset of the web pages on the Internet,
characters that could be used to inject markup.                          and on the pages we sampled, we did not exercise much
                                                                         dynamic functionality—for example, by clicking on web-
    When manually reproducing vulnerabilities, we also ob-               page elements or entering text—nor were we able to visit
served cases where complex control-flow paths must be fol-               web pages behind log-in barriers. On one hand, this allowed
lowed to execute the vulnerable piece of code. For example, we           our analysis to scale to large numbers of vulnerabilities and
could not reproduce one specific vulnerability until realizing           websites, but on the other, the vulnerabilities we detected may
that the vulnerable code was only executed if the screen width           not be representative of all vulnerabilities. Nonetheless, we
was larger than 1,024 pixels, as it had been in our original data        found many vulnerabilities through our analyses. Our manual
collection. In another case, the vulnerable section of code was          analysis of vulnerabilities may also exhibit similar biases: We
executed on some page loads but not on others. We discuss                performed a more in-depth analysis only of a subset of our
code coverage further in Section VI.                                     results. This subset was by necessity small so that it would
                                                                         be feasible to manually analyze. We do not suggest that the
                      V.   L IMITATIONS                                  examined vulnerabilities are representative of our dataset, but
                                                                         we analyzed them in depth to give greater insight into at least
    Despite being less straightforward to automatically exploit
                                                                         some vulnerabilities.
in the context of a live website, other types of flows besides
the ones we focused on (URL to HTML and JavaScript flows)                    Due to slight differences in methodology, the comparison
may also be vulnerable. For example, we observed (during                 of our results to previous work may not be perfectly accu-
manual analysis) a flow from a cookie source to an HTML                  rate. Differences in results may be due to implementation
sink that could be exploitable by a second flow from a URL               differences, although for the parts of methodology that are
source into a cookie sink on the same web page. The page                 shared between our work and Lekies et al.’s [22], we tried to
could be exploited by crafting a special URL, from which                 reproduce previous methodology faithfully.
content would flow through the document’s cookie into the
HTML sink. Other work has observed XSS vulnerabilities                                              VI.     D ISCUSSION
that derive from cookie sources and could be exploitable by
web attackers [39]. Vulnerabilities that exploit the JavaScript              We performed this study to measure the prevalence of
postMessage API have also been reported [33]. Location                   DOM XSS vulnerabilities, evaluate and inform the design of
sinks can be leveraged to create more potent phishing websites,          static-analysis tools, and assess the viability of other methods
in which an attacker may craft a URL that points to the                  for preventing DOM XSS vulnerabilities. We first discuss

                                                                    12
how the raw results of our measurement study compare to                  traces of the exploits of different vulnerabilities were generally
previous work that used similar methodology to measure XSS               composed of different scripts. We interpret this to mean that
vulnerabilities (Section VI-A), teasing out which differences            most DOM XSS vulnerabilities are due to custom code, and
are the result of methodology and which reflect a change in              not library code that is shared by many domains.
the prevalence of DOM XSS vulnerabilities. We then leverage
our quantitative and qualitative analyses of the sources and                 One way to prevent DOM XSS vulnerabilities is to detect
nature of DOM XSS vulnerabilities to discuss the weaknesses              them before the software is released. We believe that a promis-
of some suggested countermeasures (Section VI-B). Finally,               ing direction for finding DOM XSS vulnerabilities at scale is
we further interpret the results of our examination of static-           using techniques that analyze larger portions of the program
analysis tools and suggest how these tools could be improved             space. The problem of code coverage of dynamic analysis
to catch more DOM XSS vulnerabilities (Section VI-C).                    techniques is not new or specific to DOM XSS vulnerabilities;
                                                                         however, it can be a bigger hurdle for large-scale analysis of
A. Comparing measurements on DOM XSS vulnerabilities                     web applications than for traditional programs. Running many
                                                                         versions of a web application may require a large amount of
    Our methodology for detecting DOM XSS vulnerabilities                network bandwidth for reloading web pages, which can make
replicates and builds on Lekies et al.’s [22]. We extend Lekies          it difficult to scale. Solutions that avoid reloading the page to
et al.’s methodology by adding another method for determining            explore more sections of the program should be explored, as
whether a bug is exploitable, namely, inserting a potential              well as methods to force execution down alternate program
exploit into query key-value pairs rather than just at the end of        paths. In particular, work on fuzzing parameters for traditional
the URL. When inserting the injection at the end of the URL,             XSS [17] and on forcing JavaScript execution through different
we find that a roughly similar fraction of flows is vulnerable as        code paths [20] holds promise.
reported by Lekies et al. [22]. However, using both methods
of inserting the injection, we identify 83% more confirmed                   Our analysis also provides additional evidence of the risks
vulnerabilities than when just inserting the exploit at the end.         of developing custom versions of common design patterns.
This suggests that previous work, as well as our own, may                While using design patterns for templated HTML—a prac-
substantially undercount the number of vulnerable flows.                 tice analogous to parameterized SQL queries—is generally a
                                                                         good approach to preventing DOM XSS vulnerabilities, it is
    Our methodology differed from that of Lekies et al., in              important to correctly implement the details. For example,
that we visited twice as many top-level domains, but fewer               we observed three instances of bespoke HTML template
subpages for each domain (see Section III-A). We believe                 implementations that did not apply encoding functions to
this is the main cause of different findings for the number              the values of the templates. In general, custom templating
of domains that have at least one vulnerability. Previous work           implementations can be error prone, because differences in
found 9.6% of domains to have at least one vulnerability, while          context can be easy to overlook. For example, to be safe from
we found 3.8% of domains to have one. Interesting, this shows            XSS, a value in a templated HTML statement that is inside
that vulnerabilities are not systemic, i.e., a domain that has at        a script tag must first have encoding applied for the HTML
least one vulnerability is not likely to have that vulnerability         parser and then for the JavaScript parser.
(or different ones) on a preponderance of pages. Since some
parts of pages hosted on the same domain are often shared                C. Static-analysis tools
across most pages, this implies that DOM XSS vulnerabilities
are usually not in this shared content.                                      We next further interpret the results of running the static-
                                                                         analysis tools on a sample of vulnerable scripts (see Sec-
    Where our methodology and that of Lekies et al. are                  tion IV-B). These results suggest that many vulnerabilities may
most directly comparable—when relying only on the simpler                currently escape both static and dynamic analyses. We also
method of confirming vulnerabilities and examining the ra-               leverage our results to suggest ways to extend static-analysis
tio of vulnerabilities to number tainted flows or to number              tools to catch more bugs.
of pages visited—our results are generally similar, although
overall our results suggest an increase in the number of                     In Section IV-B, we measured the false positive rate of
vulnerabilities over time. In our work, we find more flows               different static-analysis tools and the rate at which tools
per page—on average, 92.6 flows per page compared to                     correctly identified vulnerabilities from our dataset of known
an average of 48.5 flows per page in Lekies et al.’s work.               vulnerabilities using dynamic taint tracking. For the false
Additionally, normalizing by the number of flows we found                positive rate, we empirically sampled the tools output and
more vulnerabilities: We found 0.04% of flows to be vulner-              manually decided whether a tool’s finding was a false positive
able, while Lekies et al. reported 0.03%. Normalizing by the             or a true positive. However, we were unable to empirically
number of pages visited, we also found more vulnerabilities:             measure the false negative rate overall. This is because it was
1,754 vulnerabilities on 44,722 pages (3.9%); previous work              not feasible for us to know all possible vulnerabilities in non-
found 6,167 vulnerabilities on 504,275 web pages (1.2%). We              contrived application. Instead, we measure the rate at which
speculate that this difference is because JavaScript programs            static-analysis tools can detect known bugs that are detected
are becoming more complex, and as a consequence DOM XSS                  with a different methodology.
vulnerabilities are becoming more frequent.
                                                                             Our analysis of Burp Suite, the best-performing static-
                                                                         analysis tool we tested, showed low false-positive rates but also
B. Preventing DOM XSS
                                                                         an inability to detect most of the vulnerabilities identified by
    In Section IV-A, we showed that the unique vulnerabilities           the dynamic analysis. Together, these two measurements imply
typically did not involve many of the same scripts: the stack            that the static-analysis tools were detecting largely different

                                                                    13
vulnerabilities that our analysis. The dataset of vulnerabilities           Measurement
with which we tested static-analysis tools, however, was lim-
ited to vulnerabilities detected through our dynamic analysis.              • Our key-value pair injection method in conjunc-              Sec. IV-A
In our test, we visited a large number of web pages but did not               tion with prior method found 83% more vulner-
                                                                              abilities than found using only prior method of
attempt to exercise much of the web application’s functionality,
                                                                              injection [22].
for example, by clicking on fields, entering data into forms,               • We identified what has changed and what remains              Sec. VI-A
or sending messages to pages. It is likely that such activities               the same in DOM XSS over a 4-year span by
would reveal more vulnerabilities. In addition, in our dataset,               building on top of a prior experiment.
we found many of the vulnerabilities to be shallow, in that they
involved a straightforward concatenation of data from a source              XSS trends
into the parameter to a sensitive sink function. This is similar            • We found more tainted flows overall and a higher             Sec. VI-A
to prior findings [35]. Indeed, it could be that the majority of              rate of vulnerable flows than previous work, which
vulnerabilities are more complex and would be better detected                 suggests that DOM XSS is getting worse.
by static-analysis tools. Given that we know that there are                 • Vulnerabilities are concentrated on a small num-             Sec. IV-A
many bugs that escape either analysis, we speculate that there                ber of iframe owners and script hosting sites.
may be many more bugs that escape both analyses.                            • 83% of vulnerabilities are due to code hosted on             Sec. IV-A
                                                                              advertising and analytics domains.
    ScanJS generally appears to identify poor coding practices              What contributes to XSS
that lead to DOM XSS vulnerabilities, rather than detecting                 • DOM XSS vulnerabilities are likely not systemic              Sec. VI-A
such vulnerabilities. Indeed, many of the suggestions that                    within domains.
the tool gives revolve around the use of certain functions                  • Vulnerabilities are often in unique, custom code,            Sec. IV-A
being dangerous (e.g., document.write or eval). While                         not in shared libraries.
ScanJS unfortunately did not detect many vulnerabilities on                 • Incorrectly implemented bespoke HTML templat-                Sec. IV-C
our dataset, we believe it to be useful for, e.g., enforcing coding           ing, a defense against XSS, introduces XSS vul-
standards.                                                                    nerabilities.
                                                                            XSS prevention
    Based on our experiments, we can make some recommen-
dations for improving static-analysis tools. One area where                 • Ad blocking would block many of the vulnerabil-              Sec. IV-A
static-analysis tools could improve is the ability to track flows             ities and is an effective client-side protection tool.
                                                                            • Incorrectly implemented templating leads to vul-             Sec. VI-B
across function boundaries. We found a non-negligible number                  nerabilities and possibly false sense of security.
of such vulnerabilities (20% in the domain sampling setting                 • The three popular (low-cost or free) static-analysis         Sec. VI-C
in Section IV-C) and tracking such flows can be difficult                     tools we tested are not effective at finding the
statically, especially when there are many branches. Another                  vulnerabilities found using our dynamic tool; how-
aspect of static-analysis tools that could use improvement is                 ever, Burp often finds vulnerabilities not found by
the ability to track flows that go through objects. For example,              our tool.
a tainted string is sometimes stored as the key or value in a
JavaScript object and later used in a computation. Finally, one                                Fig. 7: Summary of findings.
constraint of static-analysis tools that is especially limiting in
JavaScript is the inability to analyze dynamically generated
code. A hybrid static-analysis tool that analyzes new code
before it is executed in the browser might be better able to                                       ACKNOWLEDGMENTS
detect such vulnerabilities.
                                                                              The authors would like to thank Cara Bloom for providing
                                                                           comments on a draft of this work. This work was supported
                                                                           in part by gifts from John & Claire Bertucci, by CyLab at
                      VII.   C ONCLUSION                                   Carnegie Mellon University via a CyLab Presidential Fel-
                                                                           lowship, and by the National Science Foundation via grant
    We studied how to detect and prevent DOM XSS vulner-                   CNS1704542.
abilities in JavaScript code. In this work, we improved on
the methodology to confirm DOM XSS vulnerabilities, finding
                                                                                                         R EFERENCES
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                                                                                           • document.write, and document.writeln
                                                                                           • Assignment to the src attribute of a script, em-
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       2010, pp. 111–131.                                                                    ment (element.src = “...”), and assignment using
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                                                                                           • Assignment to innerHTML, and outerHTML, and
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[24]   N. Nikiforakis, L. Invernizzi, A. Kapravelos, S. Van Acker, W. Joosen,
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[26]   ——, “DOM based XSS.” [Online]. Available: https://www.owasp.org/
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[27]   ——, “Static code analysis.” [Online]. Available: https://www.owasp.
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[29]   ——, “DexterJS: robust testing platform for DOM-based XSS vulner-
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[30]   N. Patnaik and S. Sahoo, “JavaScript static security analysis made easy
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[31]   G. Richards, S. Lebresne, B. Burg, and J. Vitek, “An analysis of the
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