---
type: Article
title: Detecting and Exploiting Second Order Denial-of-Service Vulnerabilities in Web Applications
description: "Second-order DoS: the attacker first seeds a database with many cheap junk rows, then sends one request whose cost grows with those rows, exhausting server CPU on very little bandwidth. A static analysis tool, Torpedo, pairs two taint analyses with symbolic execution to find such flaws and generate attack inputs, reporting 37 in six widely used PHP applications."
resource: "https://dl.acm.org/doi/10.1145/2810103.2813680"
tags: [article, webseclist-reference, dos, algorithmic-complexity, static-analysis, php, database, tooling, owasp-a04-2021]
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    resource: "https://dl.acm.org/doi/10.1145/2810103.2813680"
    title: Detecting and Exploiting Second Order Denial-of-Service Vulnerabilities in Web Applications
    author: Oswaldo Olivo, Isil Dillig, Calvin Lin
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authors:
  - Oswaldo Olivo
  - Isil Dillig
  - Calvin Lin
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---

# Detecting and Exploiting Second Order Denial-of-Service Vulnerabilities in Web Applications

**Detecting and Exploiting Second Order Denial-of-Service Vulnerabilities in Web Applications** - Oswaldo Olivo, Isil Dillig, Calvin Lin, Publisher not stated.

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## Content

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--- page 1 ---

Detecting and Exploiting Second Order Denial-of-Service
Vulnerabilities in Web Applications
Oswaldo Olivo Isil Dillig Calvin Lin
{olivo, isil, lin}@cs.utexas.edu
Department of Computer Science
The University of Texas at Austin
ABSTRACT
This paper describes a new class of denial-of-service (DoS)
attack, which we refer to as
Second Order DoS
attacks.
These attacks consist of two phases, one that pollutes a
database with junk entries and another that performs a
costly operation on these entries to cause resource exhaus-
tion. The main contribution of this paper is a static anal-
ysis for detecting second-order DoS vulnerabilities in web
applications. We have implemented our analysis in a tool
called
Torpedo
, and we show that
Torpedo
can success-
fully detect second-order DoS vulnerabilities in widely used
web applications written in PHP. Once our tool discovers a
vulnerability, it also performs symbolic execution to gener-
ate candidate attack vectors. We evaluate
Torpedo
on six
widely-used web applications and show that it uncovers 37
security vulnerabilities, while reporting 18 false positives.
Categories and Subject Descriptors
F.3.2 [
Semantics of Programming Languages
]: Pro-
gram analysis.
Keywords
Static analysis; Program Analysis; Denial-of-Service; Web
Applications; Second-Order Vulnerabilities.
1. INTRODUCTION
Web applications form the backbone of the modern In-
ternet and provide a plethora of useful services, including
banking, commerce, education, blogging, and social net-
working. Since web applications do not require the user
to install any software beyond a standard web browser, they
are enormously popular. Unfortunately, this growing popu-
larity has also made web applications a desirable target for
many kinds of security exploits, including denial-of-service
(DoS) attacks.
DoS attacks, which can render websites inaccessible and
can cause signicant nancial damage to website owners,
Permission to make digital or hard copies of all or part of this work for personal or
classroom use is granted without fee provided that copies are not made or distributed
for prot or commercial advantage and that copies bear this notice and the full cita-
tion on the rst page. Copyrights for components of this work owned by others than
ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or re-
publish, to post on servers or to redistribute to lists, requires prior specic permission
and/or a fee. Request permissions from Permissions@acm.org.
CCS'15,
October 12–16, 2015, Denver, Colorado, USA.
c

2015 ACM. ISBN 978-1-4503-3832-5/15/10 ...$15.00.
DOI: http://dx.doi.org/10.1145/2810103.2813680.
come in two 
avors.
Network-based DoS attacks
require an
attacker to 
ood a target server with many requests, thereby
saturating server resources and rendering the target web ser-
vice unavailable. In contrast,
application-level DoS attacks
take advantage of an underlying vulnerability in the web
application and either cause the server to crash or exhaust
its computational resources. These application-level DoS at-
tacks are typically more dangerous and cannot be prevented
using standard network-level defense mechanisms [19, 2].
In this paper, we address the issue of application-level
DoS attacks that cause excessive CPU usage. In particu-
lar, we identify a new type of DoS attack, which we refer
to as Second Order DoS attacks, because like recent work
on second-order XSS and SQLI vulnerabilities [10], these at-
tacks consist of two phases: In the rst step, the attacker
uses a bot to pollute the database with junk entries. In the
second step, the attacker performs some expensive compu-
tation over the junk entries in the database, rendering the
application unavailable for a considerable amount of time.
These second-order DoS attacks are made possible by the
presence of lurking security vulnerabilities in web applica-
tions. Specically, the rst phase of the attack is feasible
because the application does not employ an appropriate de-
fense mechanism, such as a
CAPTCHA
, that prevents users
from inserting database entries through a bot. Similarly,
the second part of the attack is possible because the appli-
cation does not sanitize the retrieved database entries (e.g.,
by bounding their size). Furthermore, such DoS attacks
cannot be prevented using standard network-based defense
mechanisms: Since the inserted database entries are typi-
cally small in size and temporally separated, second-order
DoS attacks use low-bandwidth and can evade detection by
techniques that monitor anomalous network trac.
A key contribution of this paper is a static analysis for
automatically identifying second-order DoS vulnerabilities.
Our method consists of two consecutive taint analyses for
detecting the vulnerability, followed by a symbolic execution
phase for attack vector generation. The goal of our rst
static analysis is to infer
tainted database attributes:
In this
context, a database attribute
A
is said to be tainted if a
query on
A
can yield an unbounded number of database
entries. The second phase of our analysis takes these tainted
database attributes as input and checks for the existence of
an 
(
n
) computation over them. If these conditions are met,
the application contains a second-order DoS vulnerability.
In particular, the attacker can now taint a database attribute
A
by inserting many entries that share the same value for
A
, and he can then issue a carefully crafted query
Q
that

--- page 2 ---

triggers an expensive (at least linear-time) computation over
the results of
Q
. Once our taint analysis detects a potential
second-order DoS vulnerability, we also perform backwards
symbolic execution to generate candidate attack vectors in
order to help developers understand, conrm, and x the
vulnerability.
We have implemented our technique in a tool called
Tor-
pedo
, which analyzes PHP programs. Our evaluation on
several widely-used PHP applications shows that
Torpedo
can uncover serious security vulnerabilities. To summarize,
this paper makes the following contributions:

We argue that the notion of second-order vulnerabilities|
well-known in the context of XSS and SQLI attacks|
is also applicable in the context of denial-of-service
attacks. We give a precise denition of
second-order
DoS vulnerabilities
, and we explain how attackers can
exploit them to cause CPU exhaustion while evading
detection by network-based defense mechanisms.

We present a novel static analysis for automatically de-
tecting second-order DoS vulnerabilities. Unlike pre-
vious work that can assume that sanitizers exist as
pre-dened functions, our technique is based on new
expanded notions of
taint
and
sanitization
that take
into account the state of the database and its impact
on CPU usage.

We describe a backwards symbolic execution algorithm
for generating candidate attack vectors. This tech-
nique allows us to assess the impact of the uncovered
security vulnerabilities without requiring a human to
manually generate inputs.

We empirically demonstrate that when applied to a set
of widely-used PHP applications,
Torpedo
can nd
37 security vulnerabilities with a false detection rate
of 33%.
2. BACKGROUND
In this section, we provide relevant background on PHP
and relational databases.
2.1 Background on PHP Scripts
PHP is one of the most popular programming languages
for web development, with approximately 82% of server-
side scripts implemented using PHP [25]. Specically, PHP
makes it convenient to create
dynamic web pages
that inter-
act with the user and customize page content based on user
preferences. There are two key reasons why PHP is so popu-
lar for web application development: (1) HTML integration,
and (2) native support for relational databases.
HTML integration.
One of the most useful features of
PHP is the way it allows programmers to handle HTML
forms. Specically, when a user lls out an HTML form,
it is possible to invoke a PHP script with the user data
stored in so-called
superglobals
that are available in every
scope. Two of the most commonly used PHP superglobals
are
$_GET
and
$_POST
, both of which are mappings from
keys to values (called
arrays
in PHP terminology). If a web
form contains an input eld named
x
which is sent using
the HTTP POST (resp. GET) method, then
$_POST["x"]
(resp.
$_GET["x"]
) holds the value of the user input for
eld
x
. For instance, consider the following HTML form:
<form action="example.php" method="get">
Name: <input type="text" name="name">
<input type="submit"> </form>
and the corresponding PHP script called \example.php":
echo $_GET["name"];
Here, when the user enters their name into the
name
eld
of the above HTML form and clicks submit, a PHP script
called \example.php" gets executed. Furthermore, since the
web form species the data submission method to be HTTP
GET, the user input is stored in the superglobal variable
$_GET["name"]
. Thus, the net eect of the above script is
to simply print out the name entered into the web form.
Database support.
Another attractive feature of PHP is
its native support for databases. The most popular database
system used with PHP is MySQL, which is an open-source,
cross-platform relational database. Certain built-in PHP
commands allow scripts to connect to a MySQL database
and request content that is typically displayed on a webpage.
For the purposes of this paper, the most relevant command
is the
mysqli_query
function, which takes as input a string
corresponding to the database query. For instance, consider
the following PHP code:
$name = $_GET["name"];
$query = "SELECT * FROM Customers WHERE Name=$name";
$result = $mysqli->query($query);
This code selects from the
Customers
database exactly those
people whose name matches the user input. Insertions into
the database are performed in a similar way, also using the
mysqli_query
function.
2.2 Relational Databases
In relational databases, such as MySQL, data is organized
into
tables
(or
relations
) of rows and columns where there
is a unique key associated with each row. In this model,
each row is a
tuple
representing a single data item, and each
column is a labeled
attribute
of the tuple. Given a relation
R
with set of attributes
A
and a formula
'
such that vars(
'
)

A
, a selection operation

'
(
R
) selects all tuples in
R
that
satisfy condition
'
. Similarly, given a set
A
0
and a relation
R
with attributes
A
such that
A
0

A
, a projection operation

A
0
(
R
) yields a new relation
R
0
that includes all rows of
R
but only those columns whose name is in
A
0
. Hence, the
following MySQL query:
SELECT Author FROM Papers
WHERE title = "X" AND author="Y"
corresponds to the operation

author
(

'
(
papers
)) where
'
represents the formula
title
= \
X
"
^
author
= \
Y
".
In the remainder of this paper, we refer to any set of tuples
retrieved from relation
R
as a
view
of
R
. Hence, the result
of any MySQL query of the form:
SELECT ... FROM MyTable WHERE ...
corresponds to a view of
MyTable
. Note that every relation
R
is also a view of itself. Given some view
R
, we write
j
R
j
to denote the number of tuples in
R
.

--- page 3 ---

3. DEFINING SECOND ORDER DENIAL-
OF-SERVICE VULNERABILITIES
In this section, we rst give a precise denition of
second-
order DoS vulnerabilities
and then discuss some common
mechanisms that programmers employ for avoiding such se-
curity holes.
Definition
1.
(Second-Order DoS Vulnerability)
Let
P
be a program using a database table
R
, and let
V
R
be
a view of
R
. We say that
P
contains a second-order DoS
vulnerability if:
1. The quantity
j
V
R
j
can be controlled by a bot
2. The worst-case resource usage of
P
is

(
j
V
R
j
)
As explained in this denition, there are two necessary
conditions that enable a second-order DoS attack. First,
the application must allow a bot to control the result size
of some query on database table
R
. Second, the resource
usage of the application must be at least linear in the size of
this attacker-controlled view of
R
. If the application satises
both of these conditions, then an attacker can insert junk
entries into
R
in a way that drives
j
V
R
j
to
1
in the limit.
Furthermore, since the worst-case resource usage of the ap-
plication is proportional to
j
V
R
j
, the attacker can then craft
inputs that trigger this excessive resource usage behavior.
In practice, there are several ways to avoid second-order
DoS vulnerabilities in web applications. The most common
way to protect against second-order DoS attacks is to per-
form some sort of Turing test before inserting any user input
into the database. Hence, in this context,
CAPTCHA
s and
other similar mechanisms (e.g., text message verication)
provide a form of sanitization that prevents bots from pol-
luting a database.
However, performing a Turing test is not the only way to
defend web applications against second-order DoS attacks.
For example, another form of sanitization is to require ad-
ministrator credentials or to bound the size of a view
V
R
be-
fore performing computation whose resource usage behavior
depends on
j
V
R
j
. For example, consider a web application
that iterates over a collection obtained using the following
database query:
$res = SELECT * FROM Papers WHERE Author=$author
Here, if the application disallows the insertion of more
than 10 papers by the same author into the database, then
the worst-case resource usage of the application will be bound
by a constant and will therefore not be susceptible to a
second-order DoS attack.
4. STATIC ANALYSIS
In this section, we describe our algorithm for statically de-
tecting second-order DoS vulnerabilities. As shown schemat-
ically in Figure 1, our approach consists of two consecutive
static taint analyses:

Phase I:
The goal of the rst phase is to identify
tainted database attributes
. We say that an attribute
K
of some database table
R
is tainted if
j

'
K
(
R
)
j
can
be controlled by a bot, where
'
K
is a condition involv-
ing attribute
K
. Hence, our rst static analysis deter-
mines which user inputs can reach which attributes of
Figure 1: Schematic illustration of our approach.
Here, squiggly arrows indicate 
ows between dier-
ent resources.
Binop
 2 f
+
;

;
==
;
! =
; <; >; :::
g
Expr
e
:=
c
j
v
j
e
1

e
2
j
e
1
[
e
2
]
j
count
(
e
)
Cond  :=
K
=
v
j

1
AND 
2
j

1
OR 
2
Stmt
S
:=
v
:=
e
j
S
1
;
S
2
j
f
(
e
1
; : : : ; e
k
)
j
if (
e
) then
S
1
else
S
2
j
foreach (
v
1
as
v
2
)
S
j
INSERT (
v
1
; :::; v
n
) INTO
R
j
v
:= SELECT (
K
1
; :::;
K
n
)
FROM
R
WHERE 
Figure 2: Language used for describing our analysis
a database table without being sanitized. In this con-
text, a sanitizer is a piece of code that prevents a bot
from arbitrarily increasing the size of

'
K
(
R
).

Phase II:
In the second phase of our analysis, we start
with tainted database attributes inferred in Phase I
and then perform taint propagation to identify query
results whose sizes may be arbitrarily large. Our anal-
ysis then issues a warning if the number of executions
of a loop is controlled by such a
tainted query result
.
In the rest of this section, we will use the simplied lan-
guage of Figure 2 to formally describe our static analyses.
In particular, we consider a simple PHP-like language that
has built-in support for database operations, such as IN-
SERT and SELECT. Expressions in our simplied language
include constants (1, \xyz",
f
1
;
2
;
3
g
; : : :
), variables, and bi-
nary operations
e
1

e
2
where
 2 f
+
;

;

;
=
;

; :::
g
. In
addition, we allow array reads
e
1
[
e
2
] to model reading from
PHP superglobals, such as $GET
and $POST
. Finally, the
expression
count
(
e
) yields the size of collection
e
.
Continuing with the grammar of Figure 2, statements in-
clude assignments
v
:=
e
, composition
S
1
;
S
2
, if statements,
and loops of the form foreach(
v
1
as
v
2
)
S
where
v
1
is a col-
lection (i.e., array or map), and
v
2
is bound to each element
v
1
. In what follows, we will use function calls
f
(
e
1
; : : : ; e
k
)
to model various kinds of sanitizers. To simplify our presen-
tation, we only consider the two most important database
operations, namely INSERT and SELECT
1
. Database inser-
tion operations have the syntax
INSERT (
v
1
; : : : ; v
k
) INTO
R1
Our actual implementation handles most MYSQL com-
mands, not just
INSERT
and
SELECT
.

--- page 4 ---

Phase IUser 
input(DB, attr)Phase II(DB, attr)Loop
Query
result

--- page 5 ---

where
R
is the name of a database table and (
v
1
; : : : ; v
k
) is
a tuple to be inserted into
R
. Selection operations have the
syntax:
SELECT (
K
1
; : : : ;
K
n
) FROM
R
WHERE 
Here, each
K
i
is the name of an attribute of table
R
and  is
a condition used for ltering relevant tuples in
R
. Note that
condition  is a boolean combination of atomic predicates
of the form
K
=
v
where
K
is the name of an attribute and
v
is a variable.
4.1 Phase I Analysis
As mentioned earlier, the rst phase of our algorithm per-
forms static taint analysis to identify tainted database at-
tributes. Here, taint sources correspond to user inputs, and
sinks are database insertions. Our analysis distinguishes be-
tween two classes of sanitizers:

Full sanitizers:
Such sanitizers protect the applica-
tion against bots. Examples of full sanitizers include
Turing tests (e.g.,
CAPTCHAs
or SMS verication)
as well as administrative credential checks. We refer
to these checks as full sanitizers because they sanitize
every
input received by the application henceforth.

Conditional sanitizers:
These checks sanitize a par-
ticular variable
v
for some attribute
K
of database ta-
ble
R
. Specically, if
v
is
conditionally sanitized
for
(
R
;
K
), this means that the value stored in variable
v
cannot occur an unbounded number of times in at-
tribute
K
of table
R
. The following PHP function
exemplies such a conditional sanitizer:
cond_sanitize(v) {
$rows = SELECT * FROM Contacts where name = $v;
if(count($rows) == 0) return true;
return false;
}
This function returns true i attribute
name
of ta-
ble
Contacts
does not already contain value
v
. Since
this function is used to prevent insertion of duplicate
names in the
Contacts
table, it sanitizes
v
for context
(
Contacts
;
name
). These kinds of conditional sanitiz-
ers are ubiquitous in real code.
Since our analysis needs to dierentiate between full and
conditional sanitizers, our taint analysis is somewhat non-
standard. We describe our Phase I static analysis in Figure 3
using judgments of the form:
b;

`
S
:
b
0
;

0
;

Here,
b
is a boolean value, referred to as a
bot checker
, in-
dicating whether we have encountered a full sanitizer in the
code analyzed so far. Environment , called the
conditional
taint environment
, maps each program variable to a propo-
sitional formula

and is used to reason about conditional
sanitization. Specically, formula

is used to represent all
contexts under which a variable is tainted and is formed
according to the following grammar:

:=
true
j R
K
j :

j

1
^

2
j

1

2
Here,
R
K
is a boolean variable representing context (
R
;
K
).
Hence, if (
v
) =
R
K
, this means that
v
is tainted under
context (
R
;
K
). On the other hand, if (
v
) =
:R
K
^:R
0
K
0
,
then
v
is tainted in all contexts except (
R
;
K
) and (
R
0
;
K
0
).
Going back to the judgment
b;

`
S
:
b
0
;

0
;
, we use a
set  to keep track of tainted database attributes (
R
;
K
).
Hence, the judgment
b;

`
S
:
b
0
;

0
;
 means the follow-
ing: Assuming we analyze statement
S
in an environment
where
b
indicates the presence/absence of a full sanitizer
and  indicates conditional taint information, the analysis
of statement
S
produces a new bot checker
b
0
, a new condi-
tional taint environment 
0
and a set  of tainted database
attributes. Thus, for a program
P
, if our analysis produces
the judgment
false
;
[ ]
`
P
:
b;

;

then the set  gives us all the tainted database attributes
inferred by phase I.
(
Input
)

0
= [
v
7!
true
]b;

`
v
:=
userinput
() :
b;

0
;
;
(
Asn:
1)
e
62
dom()b;

`
v
:=
e
:
b;

;
;
(
Asn:
2)
e
2
dom()b;

`
v
:=
e
:
b;
[
v
7!
(
e
)]
;
;
(
Stz:
1)b;

`
fullsanitizer
() :
true
;

;
;
(
Stz:
2)

0
= [
v
7!
((
v
)
^ :R
K
)]b;

`
condsanitizer
(
v;
R
;
K
) :
b;

0
;
;
(
Insert
)
Attributes
(
R
) = (
K
1
; : : : ;
K
n
)
 =
f
(
R
;
K
i
)
j
b
=
false
^
(
v
i
)
6) :R
K
i
gb;

`
INSERT (
v
1
; :::; v
n
) INTO
R
:
b;

0
;

(
Seq
)
b;

`
S
1
:
b
1
;

1
;

1
b
1
;

1
`
S
2
:
b
2
;

2
;

2b;

`
S
1
;
S
2
:
b
2
;

2
;

1
[

2
(
If
)
b;

`
S
1
:
b
1
;

1
;

1
b;

`
S
2
:
b
2
;

2
;

2

0
= 
1
t

2

0
= 
1
[

2b;

`
if(
e
) then
S
1
else
S
2
:
b
1
^
b
2
;

0
;

0
Figure 3: Phase I static analysis
Let us now consider the rules from Figure 3 in more detail.
According to the rst rule labeled
Input
, a call to function
userinput
is a taint source; hence variable
v
is uncondition-
ally tainted after this statement. The next two rules describe
taint propagation for assignments
v
:=
e
and cause variable
v
be to become tainted under the same contexts as
e
.
The next two rules, labeled
Stz 1
and
Stz 2
, describe the
analysis of full and conditional sanitizers, respectively. Ac-
cording to
Stz 1
, the analysis of full sanitizers simply sets
the bot checker to
true
.
2
The second rule labeled
Stz 22
The careful reader may wonder why we do not analyze full
sanitizers by simply setting  to be the empty map. While
this strategy can be made sound, it would be imprecise be-

--- page 6 ---

analyzes conditional sanitizers that bound the number of
occurrences of
v
that can appear in attribute
K
of table
R
. Since variable
v
is now sanitized for context (
R
;
K
),
we only propagate taint for
v
when
:R
K
is true. Even
though we model conditional sanitizers using the function
call
condsanitizer
(
v;
R
;
K
), our analysis automatically in-
fers PHP/SQL expressions that perform such conditional
sanitization. By contrast, our analysis requires manual an-
notations for full sanitizers (please see Section 6).
The rule labeled
Insert
describes the analysis of database
insertions, which correspond to taint sinks. To understand
this rule, suppose that we are performing an insertion into
database table
R
which has attributes
K
1
; : : : ;
K
n
. Now,
if we have previously performed full sanitization, we know
that this insertion is not being performed by a bot. Hence,
if
b
is
true
, then
j

'
K
(
R
)
j
is not controlled by a bot, and
(
R
;
K
) should not become tainted. Similarly, if we have
performed conditional sanitization to restrict the number of
occurrences of value
v
i
in the
K
i
'th attribute of
R
, then
j

'
K
i
(
R
)
j
is bounded; hence, (
R
;
K
i
) is not tainted. Thus,
our analysis considers an insertion to be a sink for (
R
;
K
i
)
only when
b
is false and (
v
i
)
6) :R
K
i
(i.e., it is possible
that
v
i
is tainted under context (
R
;
K
i
)).
The last two rules of Figure 3 summarize taint propaga-
tion for sequences and if statements. In the
Seq
rule, observe
that we take the union of 
1
and 
2
because a database at-
tribute (
R
;
K
) is tainted if it is either tainted in
S
1
or
S
2
.
Finally, let us consider taint propagation for a conditional
statement of the form if(
e
) then
S
1
else
S
2
. Here, we can
only be sure that a full sanitization has been performed if
it has been performed in both branches; thus, our analysis
takes the
conjunction
of
b
1
and
b
2
. On the other hand, since
we want to overapproximate tainted database attributes, we
propagate the union of 
1
and 
2
. Similarly, since we also
want to be conservative about taint information for vari-
ables, we compute the join (
t
) of 
1
and 
2
, dened as
follows:
(
1
t

2
)(
v
) =
8
<
:

1
(
v
) if
v
62
dom(
2
)

2
(
v
) if
v
62
dom(
1
)

1
(
v
)

2
(
v
) otherwise
In other words, this join operation ensures that variable
v
is
tainted if it is tainted in either branch.
Observe that the rules from Figure 3 omit the analysis
of loops and selection operations because (1) our analysis
unrolls loops a xed number of times, and (2) selection op-
erations are eectively no-ops for the rst analysis.
4.2 Phase II Analysis
The second phase of our algorithm performs a dierent
kind of static taint analysis to infer 
(
n
) computation over
tainted query results (views)
. For the Phase II analysis,
taint sources are elements of set  (i.e., tainted database
attributes) inferred by the Phase I analysis. On the other
hand, taint sinks are loops that iterate over collections. Un-
like the Phase I analysis where we need to dierentiate be-
tween two classes of sanitizers, the notion of sanitization for
the Phase II analysis is more straightforward: Specically,
we say that a collection
v
is sanitized if its size is bounded.
The taint propagation rules for Phase II are described in
Figure 4 using judgments of the form:cause the program may apply full sanitization before asking
the user for input.

;

`
S
: 
0
;
E
Here,  is the output of the rst static analysis (i.e., tainted
database attributes), and
E
is a boolean variable indicating
whether a vulnerability has been encountered. The set  is a
set of variables that correspond to tainted query results. Es-
sentially, our phase II analysis propagates taint arising from
selection operations and issues a warning when the number
of loop iterations depends on a tainted variable
v
2
.
Let us now consider the rules from Figure 4 in more detail.
The rst rule for assignments
v
:=
e
simply propagates taint
to
v
if
e
is tainted. The second rule analyzes sanitizers that
perform some bounds checking on the size of a collection
v
.
In this case, since the size of collection of
v
is bounded, we
simply remove
v
from the set of tainted variables . While
Figure 4 models sanitizers using a function call
sanitize(v)
,
our implementation automatically infers sanitization expres-
sions that perform bounds checking on the size of collections.
The most interesting aspect of Phase II is the analysis of
selection operations. Here, given a set  of tainted database
attributes, we need to infer whether the result of a selection
query is also tainted. Unsurprisingly, this depends on the
expression  used in the WHERE clause of the query. For
this purpose, our analysis utilizes the helper rules shown in
Figure 5. Given tainted attributes  and a database table
R
, these rules decide whether to propagate taint or not. In
particular, given a query whose WHERE clause is , the
judgment 
;
R `
 :
true
indicates that taint should be
propagated to the result of the query.
The rst two rules in Figure 5 deal with the base case
where  is an atomic predicate of the form
K
=
v
. In this
case, if (
R
;
K
) is not tainted (i.e., (
R
;
K
)
62
), then the
result of the query cannot be unbounded; hence, 
;
R `
K
=
v
:
true
if and only if (
R
;
K
)
2
. If the WHERE
clause involves AND, then the result is tainted i both 
1
and 
2
are tainted. In contrast, 
1
OR 
2
yields true i

;
R `

i
:
true
for some
i
2 f
1
;
2
g
.
Based on this discussion, let us go back to the
Select
rule
from Figure 4. As expected, the query result
v
becomes
tainted if and only if 
;
R `
 :
true
; hence, we only add
v
to set  under this condition. Since the rules
Seq
and
If
are
similar to taint propagation from the rst phase, we do not
describe them in detail.
In Figure 4, the last rule for loops describes the analysis
of
sinks
. In particular, since the loop iterates over collection
v
1
, the CPU usage of the program is 
(
count
(
v
1
)).
3
Fur-
thermore, if
v
1
2
, we know that the size of
v
1
may be
unbounded, so the analysis issues a warning if
v
1
2
. Note
that this rule also propagates taint for the loop body.
5. ATTACK VECTOR GENERATION
So far, we have described a static analysis for identify-
ing second-order DoS vulnerabilities. However, our static
analysis has two main limitations: First, it can have false
positives. Second, even when the tool reports a true pos-
itive, it can be hard to understand the conditions under
which the detected vulnerability can be exploited. Hence,
to help programmers understand and conrm the warnings3
Unless there is a
break
or
return
statement, in which case
the attacker should insert values in the rst phase that don't
trigger these statements. In our experience, we don't nd
this to be an obstacle for the attacker.

--- page 7 ---

(
Assign
)

0
=

[ f
v
g
if
e
2

 if
e
62

;

`
v
:=
e
: 
0
;
false
(
Sanitize
)
;

`
sanitize(v)
: 
nf
v
g
;
false
(
Select
)

;
R `
 :
c

0
=

[ f
v
g
if
c
=
true
 if
c
=
false
;

`
v
:= SELECT (
K
1
; :::;
K
n
) FROM
R
WHERE  : 
0
;
false
(
Seq
)

;

`
S
1
: 
1
;
E
1

;

1
`
S
2
: 
2
;
E
2
;

`
S
1
;
S
2
: 
2
;
E
1
_ E
2
(
If
)

;

`
S
1
: 
1
;
E
1

;

`
S
2
: 
2
;
E
2
;

`
if(
e
) then
S
1
else
S
2
: 
1
[

2
;
E
1
_ E
2
(
Loop
)

0

;

0
`
S
: 
0
;
E
;

`
foreach(
v
1
as
v
2
)
S
: 
0
;
(
v
1
2
)
_ E
Figure 4: Inference rules describing the second phase of static analysis
(
Base
1)
(
R
;
K
)
2

;
R ` K
=
v
:
true
(
Base
2)
(
R
;
K
)
62

;
R ` K
=
v
:
false
(
AND
)

;
R `

1
:
c
1

;
R `

2
:
c
2
;
R `

1
AND 
2
:
c
1
^
c
2
(
OR
)

;
R `

1
:
c
1

;
R `

2
:
c
2
;
R `

1
OR 
2
:
c
1
c
2
Figure 5: Helper rules for SELECT
generated by the tool, we have also developed an
attack vec-
tor generation engine
. In the context of second-order DoS
vulnerabilities, an
attack vector
consists of the following:

Component 1:
A set
S
of tuples inserted into the
database, together with other user inputs that are needed
to trigger these insertion operations

Component 2:
A particular database query that
causes the application to perform some expensive com-
putation over
S
(again, along with other user inputs
that are necessary for triggering this behavior)
As shown schematically in Figure 6, our approach to au-
tomated attack generation is based on backwards symbolic
execution and constraint solving. Specically, given a pair of
program locations

0
; 
1
associated with sources and sinks,
Figure 6: Illustration of attack vector generation
we perform backwards symbolic execution to collect a set of
constraints

describing the conditions under which execu-
tion will reach from

0
to

1
. We then use an SMT solver
to nd a satisfying assignment

to

and use

to generate
a candidate attack vector.
5.1 Backwards Symbolic Execution
Given source and sink locations

0
; 
1
, the goal of our
symbolic execution is to generate a constraint

that de-
scribes the conditions under which control will reach from

0
to

1
. This analysis is described in Figure 7 using judg-
ments of the following shape:
; b; 
0
; 
1
`
S
:

0
; b
0
Here,

0
and

1
are the source and sink locations respec-
tively and
b
is a boolean value indicating whether we have
reached the source. Given condition

, formula

0
repre-
sents the constraint under which control will reach

1
start-
ing from the current statement
S
. Hence, if our analysis

--- page 8 ---

ConstraintsBackwards
symb. executionSatisfyingassignmentProgram
locationInput!

--- page 10 ---

produces the judgment:
false
;
false
; 
0
; 
1
`
P
:
;then

yields the condition under which

1
is reachable from

0
in program
P
.
Let us now consider the rules from Figure 6 in more de-
tail. According to rule 1, if we encounter a sink statement at
program point

1
, we know that

1
is unconditionally reach-
able from this statement; hence, we propagate
true
. On the
other hand, if we encounter a source at program point

0
, we
have reached the desired source; hence, we set the boolean
variable
b
to
true
to indicate that we should stop computing
weakest preconditions.
Continuing with rule (3) for assignment
v
:=
e
, we use the
standard rule for weakest precondition computation by sub-
stituting
e
for
v
in constraint

. However, if we have already
reached the source (i.e,
b
is true), we do not need to com-
pute weakest preconditions; hence, the generated constraint
is (
b
!

)
^
(
:
b
!

[
e=v
]). Rule (4) for composition (
S
1
;
S
2
)
also computes weakest preconditions in the standard way.
Rule (5) for conditionals is a bit more involved. First, we
compute the weakest precondition of

with respect to the
then and else branches. Now, if we have encountered the
source

0
in either branch, we need to stop propagating the
weakest precondition; hence the new value of boolean
b
0
is
b
1
b
2
. Assuming we have not yet encountered the desired
source, the new precondition is computed as (
e
^

1
)
(
:
e
^

2
). To see why this is correct, consider two cases: If there
is sink

1
is in the then branch, then condition
e
needs to
be true for control to reach

1
; hence, we conjoin
e
with

1
.
On the other hand, if the desired sink is in the else branch,
:
e
needs to hold for control to reach

1
. Note that at least
one of

1
and

2
is guaranteed to be false because the sink
location cannot be in both branches simultaneously.
The last rule describes the analysis of
SELECT
statements.
This rule is similar to the assignment rule, except that we
now substitute
v
with a more complex term
t
that involves
set comprehensions. In particular, term
t
is a set that con-
tains all tuples in
R
satisfying condition .
5.2 Using Constraints to Generate Inputs
We now describe how to use the constraints from Sec-
tion 5.1 to generate attack vectors. As in Section 4, the
attack vector generation consists of two phases: In the rst
phase, the input to the analysis is a (user input, database
insertion) pair discovered to be a feasible source-sink 
ow
in the Phase I static analysis of Section 4.1. Similarly, for
the second phase of attack vector generation, the input is a
(database selection, loop) pair that is deemed to be a feasi-
ble source-sink 
ow according to the Phase 2 static analysis
(Section 4.2).
The second phase of attack vector generation is simpler
than the rst phase because we only need to compute a sin-
gle input. For this purpose, we get a satisfying assignment

to the constraint generated using backwards symbolic ex-
ecution. The input values given by

, together with the
database query for the sink, are now used to generate the
second component of the attack vector.
The rst phase of attack vector generation is a bit more in-
volved since we need to generate a
sequence
of tuples, rather
than a single input. A key challenge here is that the con-
straint

generated using symbolic execution can refer to
database
R
, which evolves as we insert new tuples into the
database. To address this challenge, we employ an iterative
algorithm that repeatedly instantiates constraint

with re-
spect to the actual tuples inserted into the database. In
particular, given a set variable
R
used in constraint

, we
rst initialize it to the empty set and get a satisfying as-
signment

0
for

[
;
=
R
]. This assignment

0
is now used to
generate a concrete tuple
t
to insert into the database. In
the next iteration, we instantiate
R
with the set
f
t
g
and ask
for a new satisfying assignment

1
to

[
f
t
g
=
R
]. This process
continues until we have inserted a suciently large number
of tuples into the database.
Example
1.
We illustrate attack vector generation using
a realistic code pattern commonly found in PHP programs:
L1: x := $_POST["a"]; y := $_POST["b"]; z := $_POST["c"];
if (z == "1") {
v := SELECT (k1, k2) from R where k2 = y;
if(count(v)==0)
L2: INSERT (x, y) INTO R;
}
Our goal is to generate a sequence of tuples that can reach
the database insertion at program point
L2
starting from pro-
gram location
L1
. Using backwards symbolic execution, we
rst generate the following constraint

:
$POST
[\
c
"] =
1
^
count
(
f
(
e:
K
1
; e:
K
2
)
j
e
2 R ^
e:
K
2
= $POST
[\
b
"]
g
) = 0
To generate the rst tuple, we instantiate
R
with
;
, which
yields
$_POST["c"] = "1"
. Hence, the values of
$_POST["a"]
and
$_POST["b"]
are unconstrained, but
$_POST["c"]
must
be
"1"
; so suppose we generate the input
"aa", "bb", "1".
In the next iteration, we instantiate
R
with
f
("aa", "bb")
g
in

. This new constraint now tells us that, in addition to
$_POST["c"] = "1"
, we need
$_POST["b"]
6
=
"bb"
. Hence,
we now pick the next input to be
"aa", "bc", "1".
In
the next iteration, we instantiate
R
with the set
f
("aa",
"bb"), ("aa", "bc")
g
, which tells us that
$_POST["c"] =
"1"
^
$_POST["b"]
6
=
"bb"
^
$_POST["b"]
6
=
"bc"
. This
process continues until we have inserted suciently many
tuples into the database.
5.3 Constraint Solving
As described in the previous subsections, the formulas we
need to solve for attack vector generation belong to the fol-
lowing constraint language :
Term
t
:=
c
j
x
j
f
(
t
)
j f
x
j
x
2
S
^

g
Formula

:= true
j
false
j
t
1
op
t
2
j

1
^

2
j

1

2
j :

j

1
!

2
Here,
c
is a constant,
x
is a variable,
f
is an uninterpreted
function, and
S
is a set. If we exclude
set comprehension
terms
of the form
f
x
j
x
2
S
^

g
from this constraint lan-
guage, then our formulas would belong to the standard rst
order theory of equality with uninterpreted functions (and
linear arithmetic) and could be directly solved using o-the-
shelf SMT solvers. Unfortunately, to allow the computation
of weakest preconditions in the presence of database queries,
our analysis also needs to introduce set comprehension terms
which are not supported by standard SMT solvers. For this
purpose, we employ a customized decision procedure that
overapproximates satisability by performing a transforma-
tion and using o-the-shelf SMT solvers. In particular, our
algorithm consists of the following steps:

--- page 11 ---

(1)

=

1; b; 
0
; 
1
`
sink
@

:
true
; b
(2)

=

0; b; 
0
; 
1
`
source
@

:
;
true
(3)

0
= (
b
!

)
^
(
:
b
!

[
e=v
]); b; 
0
; 
1
`
v
:=
e
:

0
; b
(4)

0
; b
0
; 
0
; 
1
`
S
1
:

00
; b
00
; b; 
0
; 
1
`
S
2
:

0
; b
0; b; 
0
; 
1
`
S
1
;
S
2
:

00
; b
00
(5)
; b; 
0
; 
1
`
S
1
:

1
; b
1
; b; 
0
; 
1
`
S
2
:

2
; b
2
b
0
=
b
1
b
2

0
= (
e
^

1
)
(
:
e
^

2
); b; 
0
; 
1
`
if(
e
) then
S
1
else
S
2
: (
b
0
!

)
^
(
:
b
0
!

0
)
; b
0
(6)
t
=
f
(
x:
K
1
; : : : ; x:
K
n
)
j
x
2 R ^
[
x:
K
i
=
K
i
]
g

0
= (
b
!

)
^
(
:
b
!

[
t=x
]); b; 
0
; 
1
`
v
:= SELECT (
K
1
; :::;
K
n
) FROM
R
WHERE  :

0
; b
Figure 7: Backward symbolic execution rules for generating attack vector constraints. Statements whose
preconditions are not met (or are not shown in the gure) are assumed to be no-ops.
1. Replace each set comprehension term
t
i
2

with a
fresh variable
x
i
and generate the formula

0
=

[
x
i
=t
i
]
and the mapping  :
f
x
i
7!
t
i
g
2. Let (
x
i
) be
f
x
j
x
2
S
i
^

i
g
. Now, generate the
constraint:

00
= (
^
x
i
2
dom
()
(
count
(
x
i
) = 0
!
^
e
ij
2
S
i
:

i
[
e
ij
=x
]))
3. Use an o-the-shelf SMT solver to get a satisfying as-
signment to

0
^

00
It is easy to see that our procedure overapproximates satis-
ability: In particular, we construct

0
by replacing set com-
prehension terms with fresh variables. Second, observe that
count
(
x
i
) = 0 implies that
x
i
must be the empty set; hence
if
x
i
represents a set comprehension term
f
x
j
x
2
S
i
^

i
g
,
we know that

i
must evaluate to false for
all
elements in
set
S
i
, which is expressed using

00
.
Since our procedure overapproximates satisability, it is
possible that the inputs generated using our technique do
not trigger the desired source-sink 
ow in reality. How-
ever, we have not observed this overapproximation to be
a problem in practice. Specically, the overwhelming ma-
jority of the set comprehension terms
t
i
appear in the form
count
(
t
) = 0; and, under this restriction, it can be shown
that

0
^

00
is
equisatisable
to the original constraint

.
6. IMPLEMENTATION
Torpedo
consists of approximately 4,000 lines of PHP
code. We use Nikic's PHP parser [22] to obtain an initial
AST and then construct our own CFG representation for
each function. Since an SMT solver (recall Section 5) is
needed to automatically generate attack vectors,
Torpedo
uses the Z3 SMT solver [33] and its string solving plug-
in [34] for nding satisfying assignments to constraints. For
interprocedural analysis,
Torpedo
conceptually performs
function inlining by \gluing together" the CFGs of callees at
method invocation sites.
Internally,
Torpedo
consists of four dierent modules,
namely, (1) static taint analysis, (2) symbolic execution en-
gine, (3) sanitization inference, and (4) an engine for infer-
ring database schemas. Since we have already described the
taint analyzer and symbolic execution engine in detail, we
now brie
y outline the design of modules (3) and (4).
Sanitizer Inference Engine
.
To infer sanitizers,
Tor-
pedo
uses a combination of manual annotations and auto-
mated static analysis. For the Phase I static analysis from
Section 4.1,
Torpedo
requires manual annotations of full
sanitizers, since automated inference of Turing tests is be-
yond the scope of static analysis. Hence, we have man-
ually annotated
CAPTCHA
routines, as well as methods
that check for website administrator credentials. However,
Torpedo
does perform static analysis to infer conditional
sanitizers that impose a bound on the size of data structures.
Specically,
Torpedo
rst statically analyzes the source
code to generate constraints on collection sizes (for Phase
II) and on the number of occurrences of keys in database
tables (for Phase I).
Torpedo
then uses an SMT solver to
check if the generated constraints imply an upper bound on
the size of some data structure of interest. Hence, a state-
ment
S
is considered to be a sanitizer if the size of a data
structure is unbounded before
S
but becomes bounded after
S
.
Database Schema Inference
.
Recall from Section 4 that
our static analysis needs to know the attributes for a given
database table, so
Torpedo
performs a pre-analysis that
infers the schema for each database table. Specically, af-
ter parsing all les in the application,
Torpedo
looks for

--- page 12 ---

ApplicationFilesLOC# TP# FPSCARF191686110OpenConf13022,88970HotCRP10348,144811Gallery50562,69910osCommerce70286,69353Wordpress479261,56454Total1938483,6753718 Table 1: Summary of our experimental results.
\TP" indicates true positives (i.e., real vulnerabil-
ities), and \FP" denotes false positives. Applicationn
=25,000n
=50,000n
=75,000n
=100,000SCARF6m32s22m53sT OT OOpenConf2m26s17m49sT OT OHotCRP7m46s26m33sT OT OGallery1m57s6m12s14m8s29m47sosCommerce7m16s15m35s33m17sT OWordpress46s2m11s8m37s21m53s Table 2: Amount of time the server is unresponsive
for dierent numbers (
n
) of entries inserted into the
database during the rst phase.
T O
means that the
application becomes unresponsive for more than one
hour. This data only includes a subset of the uncov-
ered vulnerabilities.
CREATE TABLE
instructions in the source code, and it records
the ordered set of attributes associated with each table name.
Since database queries in PHP can be generated dynamically
through the use of string variables,
Torpedo
can only over-
approximate the set of string values provided to the queries.
As we discuss later, this source of imprecision is one of the
main causes of false positives.
7. EVALUATION
We evaluate
Torpedo
by applying it to six server-side
web applications written in PHP. Specically, our bench-
marks include HotCRP (a widely-used conference manage-
ment software), WordPress (a popular blogging application),
Gallery (a photo management application), SCARF (a re-
search discussion forum), osCommerce (an online store man-
agement software), and OpenConf (another conference man-
agement system). In total, we use
Torpedo
to analyze
483,675 lines of PHP code. We perform our experiments on
a MacBook Air laptop with Mac OSX 10.9.3, a 2 GHz Intel
Core i7 processor, and 8 GB of RAM.
Table 7 summarizes our experimental results, showing that
Torpedo
nds a total of 37 vulnerabilities across six appli-
cations and only reports 18 false positives. On average, we
see that
Torpedo
has a 33% false detection rate.
Discussion of true positives.
For the true vulnerabilities
detected by our tool, we use
Torpedo
's attack vector gener-
ation capability to conrm that the uncovered vulnerability
can be exploited to launch a DoS attack. Specically, we
devise a bot to insert a large number of junk entries into a
given database and then issue a query that triggers an 
(
n
)
computation over these entries. As expected, the severity
of the DoS attack is proportional to the number of entries
inserted during the rst phase. Table 2 shows the number of
database entries inserted during the rst phase against the
amount of time the server is unresponsive during the second
phase. For example, for a vulnerability in HotCRP, when we
insert 75,000 entries into the database in the rst phase, we
can bring down the server for more than an hour by issuing
a
single
query in the second phase.
Upon manual inspection of the true vulnerabilities, we
nd that the second phase of the attack does not necessarily
need to be carried out by a bot. In fact, all of the running
times reported in Table 2 are caused by a single database
query, so automation of the second phase is not a prereq-
uisite for the DoS attack. By contrast, since the uncovered
DoS attacks typically involve the insertion of thousands of
entries into the database, automation is crucial to the rst
phase of the attack.
Another interesting aspect of the vulnerabilities is that
a few tainted database attributes typically lead to several
security vulnerabilities in the same application. In other
words, many of the source-sink 
ows identied by
Tor-
pedo
's Phase II taint analysis share the same source. For
example, the 8 dierent vulnerabilities found in HotCRP in-
volve two distinct tainted database attributes. This obser-
vation suggests that several vulnerabilities within the same
application can be prevented by a single x that blocks the
rst phase of the attack (e.g., by employing some kind of
Turing test).
Finally, we observe that the severity of the uncovered vul-
nerability is proportional not only to the number of database
entries inserted in the rst phase of the attack but also to
the
kind
of sink encountered in the second phase. In particu-
lar, 
(
n
) computations that involve network operations, le
I/O or database manipulation typically lead to more serious
vulnerabilities. For example, one of the vulnerabilities in
osCommerce involves sending emails to all registered users,
which can lead to the collapse of the server's network for
hours.
Discussion of false positives.
We now discuss the root
causes of the false positives reported by
Torpedo
. Man-
ual inspection of all false alarms reveals that there are only
two root causes: (1) incomplete sanitizer inference, and (2)
incomplete database query resolution. In particular, all 11
false positives in HotCRP are due to missed detection of san-
itizers, and the remaining 7 false alarms in osCommerce and
WordPress are caused by imprecise string analysis used for
database schema detection.
Torpedo
fails to identify some
of the sanitizers in HotCRP because the constraints gener-
ated for sanitizer inference are overapproximate: Since
Tor-
pedo
heuristically drops some interprocedural path condi-
tions for scalability reasons, the SMT solver may decide that
the overapproximate constraint is satisable even though the
exact constraint is in fact unsatisable. We note that all
false positives in HotCRP can be eliminated using a few
simple annotations that explicitly identify sanitizers missed
by
Torpedo
. Incomplete database query resolution occurs
when
Torpedo
is unable to identify the string values of the
database name and/or attributes in a dynamic database
query, and this over-approximation results in false positives.
We believe the remaining 8 false positives in osCommerce
and Wordpress can be eliminated by employing a more pre-
cise string analysis for inferring the tables and attributes of
database queries.

--- page 13 ---

Lasting Damage to Applications.
While the results in
Table 2 focus on the damage of a specic second-phase at-
tack, the impact of the rst phase can often be much more
signicant: Once the database has been polluted, the ap-
plication is often primed for multiple possible second-phase
attacks, becoming virtually unusable. For example, imag-
ine a conference submission site whose database has been
populated with an enormous number
n
of spurious papers.
This database is unlikely to be useful for the review process
because the conference chair would have to be careful to
not trigger the high-complexity behavior in the application.
Alternatively, the conference chair could try to cleanse the
database. In OpenConf, the program chair might try to 
ag
for withdrawal all submissions with no uploaded les. This
natural reaction to the attack unfortunately triggers the sec-
ond phase of the attack. In general, a careful attacker can
perform a dictionary attack that makes it dicult to distin-
guish malicious from benign entries, complicating the task
of automatically cleansing the tables without removing le-
gitimate entries.
In the remainder of this section, we describe two repre-
sentative vulnerabilities uncovered by
Torpedo
and outline
how an attacker can exploit these vulnerabilities to launch
a second-order DoS attack.
7.1 Exploit in HotCRP
One of the vulnerabilities uncovered by
Torpedo
is in the
HotCRP conference management application. This vulner-
ability arises due to an interaction between three HotCRP
features, namely account creation, paper registration, and
merging of accounts.
To understand the vulnerability and how it can be ex-
ploited, we rst observe that HotCRP allows a registered
user to add an
unrestricted
number of papers to an un-
derlying database called
Paper
. Furthermore, it is possi-
ble, although not trivial, to automatically pollute this
Paper
database by ensuring that certain conditions are met (for ex-
ample,
$_REQUEST
[\p"] is set to \new",
$_POST
[\submitnal"]
and
$_POST
[\submitpaper"] are both set to \1", the hidden
formid
value, which is actually leaked from the cookie, is
valid, and so on).
Second, let us consider the HotCRP functionality that
allows users to merge dierent accounts, shown in Figure 9.
This merge operation rst retrieves the set
S
of all papers
associated with one account, and then, for each paper in
S
,
it performs an update operation on the
Paper
database to
modify the corresponding author information. Thus, when
merging an account
A
with another account
B
, the amount
of work that is performed is directly proportional to the
number of papers associated with
A
's account.
Thus, to launch a DoS attack on HotCRP, an attacker can
implement a bot that performs the following steps:
1. It registers a large number
m
of bogus user accounts.
4
2. For each user account, it then registers a large number
n
of papers by providing inputs that pass the paper
registration lters.4
Even though HotCRP disallows the registration of multi-
ple accounts associated with the same email address, the at-
tacker can still generate arbitrarily many HotCRP accounts
because some email services, including Yahoo, do not pre-
vent bots from creating accounts.
...
if ($Me->is_empty())
$Me->escape();
...
if (isset($_REQUEST["merge"]) && check_post()) {
if (!$_REQUEST["email"])
...
else if (!$_REQUEST["password"])
...
else {
$MiniMe = Contact::find_by_email($_REQUEST["email"]);
if (!$MiniMe)
...
else if
(!$MiniMe->check_password($_REQUEST["password"]))
...
else if ($MiniMe->contactId == $Me->contactId) {
...
} else if (!$MiniMe->contactId || !$Me->contactId)
...
else {
...
$result = $Conf->qe("select paperId,
authorInformation
from Paper where authorInformation like '%\t" .
sqlq_for_like($MiniMe->email) . "\t%'");
$qs = array();
while (($row = edb_row($result))) {
$row[1] = str_ireplace("\t"
. $MiniMe->email .
"\t", "\t" .
$Me->email . "\t", $row[1]);
$qs[] ="update Paper set authorInformation='"
.sqlq($row[1]) . "' where paperId=$row[0]";
}
...
Figure 8: Code snippet showing merging of user ac-
counts functionality in HotCRP.
3. Finally, it merges account
i
with account
i
+1 for each
i
2
[1
; m

1], again by generating inputs that pass
HotCRP's checks that (unsuccessfully) attempt to pre-
vent illicit account merging.
Observe that this attack causes the server to perform work
whose complexity is (
m

n
), where
m
is the number of ac-
counts and
n
is the number of papers per account. Further-
more, since
m
and
n
can both be made arbitrarily large, this
attack can feasibly cause HotCRP to become unavailable for
signicant periods of time. For example, when
m
= 5 and
n
= 25
;
000, the bot we created was able to bring down
HotCRP for more than an hour on our local server.
5
7.2 Exploit in osCommerce
We now describe a vulnerability uncovered by
Torpedo
in the osCommerce application. Since osCommerce provides
infrastructure for online stores, DoS attacks involving os-
Commerce directly cost money to businesses that use this
application. An interesting aspect of the vulnerability found
in osCommerce is that the second phase of the attack is only
indirectly
triggered by the attacker. Thus, the point of this
example is to illustrate that second-order DoS attacks can
be serious even if the second phase is not under the direct
control of the attacker.5
For the HotCRP results in Table 2, we use
m
= 1.

--- page 14 ---

if (isset($HTTP_POST_VARS['action'])
&& ($HTTP_POST_VARS['action'] == 'process')
&& isset($HTTP_POST_VARS['formid'])
&& ($HTTP_POST_VARS['formid'] == $sessiontoken)) {
...
if (strlen($firstname)
< ENTRY_FIRST_NAME_MIN_LENGTH) {
$error = true;
$messageStack->add('create_account',
ENTRY_FIRST_NAME_ERROR);
}
...
if (strlen($email_address) <
ENTRY_EMAIL_ADDRESS_MIN_LENGTH) {
$error = true;
$messageStack->add('create_account',
ENTRY_EMAIL_ADDRESS_ERROR);
}
...
} else {
$check_email_query = tep_db_query(
"select count(*) as total from "
. TABLE_CUSTOMERS .
" where customers_email_address = '" .
tep_db_input($email_address) . "'");
$check_email = tep_db_fetch_array
($check_email_query);
if ($check_email['total'] > 0) {
$error = true;
$messageStack->add('create_account',
ENTRY_EMAIL_ADDRESS_ERROR_EXISTS);
}
}
...
if ($error == false) {
...
tep_db_perform(TABLE_CUSTOMERS, $sql_data_array);
...
Figure 9: Code snippet showing user registration
functionality in osCommerce
The vulnerability in osCommerce arises from an inter-
action between two features, namely account creation and
email subscription. Let us rst consider account creation.
The key point here is that osCommerce does not employ
a mechanism that prevents bots from registering spurious
user accounts. As shown in the code snippet of Figure 9, os-
Commerce uses a database relation called
TABLE_CUSTOMERS
that stores information about all registered users. When
a user lls out an HTML form to create a new account,
the code performs checks to ensure that certain conditions
are met, for instance, that the customer's rst name and
email address are a certain minimum length, that there are
no other users with the same email address, etc. However,
these checks are not sucient to rule out the possibility that
the web form is being lled out by a bot. In fact, the ap-
plication does not even check that the user has entered a
valid (i.e., existing) email address. As a result, it is fairly
straightforward to create a bot that registers many spurious
users and pollutes the
TABLE_CUSTOMERS
database.
The next feature relevant to the attack is an email sub-
scription feature that noties users when certain events oc-
cur. For example, a user can subscribe to a
product category
,
which noties the user when a new product is added to that
category (e.g., electronics or groceries). Similarly, users can
subscribe to individual products so that osComerce can no-
tify them of changes to the inventory (e.g., when a certain
product is re-stocked). Since the code implementing this
subscription feature does not protect itself against bots, it
is possible for an attacker to subscribe a huge number of
spurious accounts to all possible categories and products.
Hence, each time there is a minor change in the inventory,
the application will send an enormous number of email mes-
sages to all of the spurious users registered by the attacker.
At rst sight, this exploit may seem insignicant because
the amount of work performed upon each inventory change
is only
linear
in the number of subscribed users. However,
when we perform experiments to evaluate the impact of this
kind of attack, we nd that we can bring down our own
server for over 10 minutes by registering only 40,000 users
and subscribing them to a product. If the website becomes
unavailable for over 10 minutes every time there is a mi-
nor change to the inventory, customers are unlikely to enjoy
their online shopping experience. Thus, even this innocuous-
looking attack makes websites based on osCommerce quite
unusable for all practical purposes.
Moreover, we nd that after polluting the database, the
application's administrator becomes essentially helpless, as
many of the application's administrative features become
unusable due to their long setup or execution times. The
panel for displaying user proles becomes too slow to use.
Sending a general newsletter or new product announcements
can take hours or even collapse the network, preventing the
legitimate users from receiving the message. Personalized
emails to specic users can become almost impossible to
send due to the need to navigate a vast amount of junk
entries. Of course, the administrator likely has no idea which
operations have been aected by the attack, further adding
to his despair. Unfortunately, as mentioned earlier, it can
be extremely dicult to automatically cleanse the database
in the presence of a sophisticated rst-phase attack.
8. RELATED WORK
We now place our work in the context of prior work, start-
ing with DoS attacks and then considering static analyses
for other security purposes.
Defending Against Network-Based DoS Attacks.
Most mechanisms for defending against DoS attacks are
deployed at the network level to monitor network behavior,
identify anomalous trac, and set up rewalls that block
the attack [11, 1, 27, 21, 20, 29, 17, 8, 15, 32, 28, 23]. Al-
though these techniques are capable of preventing some DoS
(and DDoS) attacks, they are limited to a specic underly-
ing model of anomalous trac and can suer from scalability
problems. Furthermore, they sometimes raise false alarms
that prevent legitimate users from accessing the applica-
tion. In general, distinguishing between DoS attacks and
sudden high-volume user trac (
ash crowds) is an open
problem [13]. A more detailed survey of network-layer DoS
prevention mechanisms can be found elsewhere [19, 2].
More importantly, network-based defense measures are
only activated while the attack is in progress, and they are

--- page 15 ---

incapable of diagnosing application-specic performance is-
sues that can be exploited by low-bandwidth attacks, includ-
ing the second-order DoS attacks considered in this paper.
Defending Against Application-Level DoS Attacks.
Typical application-level DoS vulnerabilities cause the soft-
ware to crash or become unresponsive. Particularly danger-
ous are the cases where a small amount of data sent by
an attacker can cause the application to shut down (
ping of
death
[5, 14]), enter an innite loop, or trigger a super-linear
recursion call-stack (
inputs of coma
[6, 26]).
Dynamic analyses for the detection of application-level
DoS vulnerabilities try to generate inputs that either ex-
hibit worst-case execution times or enter non-terminating
loops [4, 3, 12]. Dynamic analyses can be dicult to scale
to large programs and cannot always generate inputs that
uncover such worst-case behaviors.
Static analyses have been used to identify high-complexity
code whose behavior is dependent on user input and can
thus be manipulated by an attacker [6, 26]. Such analyses
have been able to uncover some simple classes of algorithmic
complexity attacks, but they cannot automatically identify
more subtle cases of algorithmic complexity vulnerabilities,
such as improperly implemented hash functions [9]. In par-
ticular, detection of such vulnerabilities requires knowledge
about input distributions, which is hard to reason about
statically.
Recent work on static analysis has focused on extreme
cases of DoS vulnerabilities: detection of super-linear recur-
sion call-stacks [6] and innite loops [26]. Our work detects
DoS vulnerabilities that stem from polynomial loops that
can be manipulated by the attacker, instead of the extreme
cases of superlinear recursion and innite loops. More im-
portantly, our work focuses on high resource usage behavior
that is triggered by certain kinds of database queries and
where the query result is controlled by the attacker.
Other Static Analysis-Based Defenses.
Second-order vulnerabilities involving SQL injections (SQLI)
and cross-site scripting (XSS) have been known for some
time, but a static analysis for detecting these attacks has
only recently been proposed [10]. Our work is inspired in
part by this recent work and shares a similar overall frame-
work that consists of two connected taint analyses. How-
ever, since we target DoS vulnerabilities rather than XSS
and SQLI, our notions of taint and sanitization are dier-
ent; thus, the details of the detection algorithms also dier
substantially. First, our analysis must detect multiple po-
tential insertions into database tables and analyze their per-
formance impact. Second, our analysis needs to dierentiate
between full and conditional sanitizers, whereas conditional
sanitization is not relevant in the context of XSS and SQLI
vulnerabilities. Third, unlike the method of Dahse and Holz,
our technique must perform automated inference to identify
conditional sanitizers. Finally, another contribution of this
paper over previous work is a novel symbolic execution al-
gorithm for generating candidate attack vectors.
Xie and Aiken [31] implement a symbolic execution algo-
rithm for SQL injections. The idea is to detect unsanitized
variables that reach SQL queries using semantic analysis of
path constraints. Their symbolic execution engine is similar
to ours, but we must solve the additional problem of relat-
ing insertions to extractions. In addition, our engine also
generates the attack vectors.
Livshits and Lam describe a 
ow-analysis for detecting
XSS and SQL injection vulnerabilities in Java [18]. Wasser-
mann and Su use static analysis to identify XSS vulnerabil-
ities on code using weak sanitization [30]. These approaches
tackle a dierent security vulnerability and do not reason
about database interactions.
Automatic Generation of Attack Vectors.
Kiezun et al. [16] describe a method of generating attack
vectors for XSS attacks and SQL injections. Specically,
they use dynamic symbolic execution to generate concrete
inputs that trigger execution paths involving sensitive nodes.
Sen et al. [24] and Chaudhuri & Foster [7] use similar dy-
namic symbolic execution methods for Javascript and Ruby-
on-Rails respectively. Since our approach is static, it has
the potential to report more false positives, but a key ad-
vantage is that it does not depend on an input-generation
mechanism or a mutation library.
9. CONCLUSIONS
In this paper, we have introduced the notion of second-
order DoS attacks and presented static analyses (1) for de-
tecting their underlying application-level vulnerabilities and
(2) for generating attack vectors to exploit these vulnera-
bilities. We have used these techniques to detect 37 secu-
rity vulnerabilities across six open-source web applications,
while admitting 18 false positives. Our experiments show
that these vulnerabilities can be exploited by performing a
tractable number of insertions and can render the applica-
tion unresponsive for hours.
More broadly, this work expands the threat model: Whereas
taintedness traditionally is concerned with specic user in-
put values, second-order DoS attacks are also concerned with
tainted database entries whose presence might lead to some
expensive future operation. In general, as threat models
continue to expand, so does the motivation for more sophis-
ticated static analyses that can defend against new attacks.
Acknowledgments.
This work was funded in part by AFRL Award FA8750-
15-2-0096 and NSF grants CNS-1138506 and DRL-1441009.
We thank the anonymous referees, Will Robertson, and Tom
Dillig for helpful comments on earlier drafts.
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