String Analysis for Dependable Input
Validation
Tevfik Bultan
Verification Lab
Department of Computer Science
University of California, Santa Barbara
bultan@cs.ucsb.edu
http://www.cs.ucsb.edu/~vlab
VLab String Analysis Publications
With my students Fang Yu and Muath Alkhalaf
•Verifying Client-Side Input Validation Functions Using String Analysis
[ICSE’12]
•Patching Vulnerabilities with Sanitization Synthesis [ICSE’11]
•Relational String Verification Using Multi-Track Automata [IJFCS’11],
[CIAA’10].
•String Abstractions for String Verification [SPIN’11]
•Stranger: An Automata-based String Analysis Tool for PHP [TACAS’10]
•Generating Vulnerability Signatures for String Manipulating Programs
Using Automata-based Forward and Backward Symbolic Analyses
[ASE’09]
•Symbolic String Verification: Combining String Analysis and Size
Analysis [TACAS’09]
•Symbolic String Verification: An Automata-based Approach [SPIN’08]
Web Software Everywhere
• Commerce, entertainment, social interaction
• We will rely on web apps more in the future
• Web apps + cloud will make desktop apps obsolete
Road Block: Dependability
• Web applications are not dependable!
• As web applications are becoming increasingly dominant
– and as their use in safety critical areas is increasing
• their dependability is becoming a critical issue
• Web applications are especially notorious for security vulnerabilities
– Their global accessibility makes them a target for many malicious
users
Vulnerabilities in Web Applications
• There are many well-known security vulnerabilities that exist in many
web applications. Here are some examples:
– Malicious file execution: where a malicious user causes the
server to execute malicious code
– SQL injection: where a malicious user executes SQL commands
on the back-end database by providing specially formatted input
– Cross site scripting (XSS): causes the attacker to execute a
malicious script at a user’s browser
• These vulnerabilities are typically due to
– errors in user input validation or
– lack of user input validation
Why Is Input Validation Error-prone?
• Extensive string manipulation:
– Web applications use extensive string manipulation
• To construct html pages, to construct database queries in SQL,
etc.
– The user input comes in string form and must be validated and
sanitized before it can be used
• This requires the use of complex string manipulation functions
such as string-replace
– String manipulation is error prone
String Related Vulnerabilities
String related web application vulnerabilities as a
percentage of all vulnerabilities (reported by CVE)
50%
File Inclusion
XSS
SQL Injection
45%
40%
35%
30%
25%
20%
15%
10%
5%
0%
2001 2002 2003 2004 2005 2006 2007 2008 2009
OWASP Top 10 in 2007:
1. Cross Site Scripting
2. Injection Flaws
OWASP Top 10 in 2010:
1. Injection Flaws
2. Cross Site Scripting
String Related Vulnerabilities


String related web application vulnerabilities occur when:

a sensitive function is passed a malicious string input from the
user

This input contains an attack

It is not properly sanitized before it reaches the sensitive function
String analysis: Discover these vulnerabilities automatically
XSS Vulnerability

A PHP Example:
1:<?php
<script ...
2: $www = $_GET[”www”];
3: $l_otherinfo = ”URL”;
4: echo ”<td>” . $l_otherinfo . ”: ” . $www . ”</td>”;
5:?>

The echo statement in line 4 is a sensitive function

It contains a Cross Site Scripting (XSS) vulnerability
Is It Vulnerable?

A simple taint analysis can report this segment vulnerable using taint
propagation
1:<?php
tainted
2: $www = $_GET[”www”];
3: $l_otherinfo = ”URL”;
4: echo ”<td>” . $l_otherinfo . ”: ” .$www. ”</td>”;
5:?>

echo is tainted → script is vulnerable
How to Fix it?


To fix the vulnerability we added a sanitization routine at line s
Taint analysis will assume that $www is untainted and report that the
segment is NOT vulnerable
1:<?php
tainted
2: $www = $_GET[”www”];
3: $l_otherinfo = ”URL”;
untainted
s: $www = ereg_replace(”[^A-Za-z0-9 .-@://]”,””,$www);
4: echo ”<td>” . $l_otherinfo . ”: ” .$www. ”</td>”;
5:?>
Is It Really Sanitized?
1:<?php
<script ...
2: $www = $_GET[”www”];
3: $l_otherinfo = ”URL”;
s: $www = ereg_replace(”[^A-Za-z0-9 .-@://]”,””,$www);
4: echo ”<td>” . $l_otherinfo . ”: ” .$www. ”</td>”;
5:?>
Sanitization Routines are Erroneous

The sanitization statement is not correct!
ereg_replace(”[^A-Za-z0-9 .-@://]”,””,$www);
– Removes all characters that are not in { A-Za-z0-9 .-@:/ }
– .-@ denotes all characters between “.” and “@” (including “<”
and “>”)
– “.-@” should be “.\-@”

This example is from a buggy sanitization routine used in
MyEasyMarket-4.1 (line 218 in file trans.php)
String Analysis



String analysis determines all possible values that a string expression
can take during any program execution
Using string analysis we can identify all possible input values of the
sensitive functions

Then we can check if inputs of sensitive functions can contain
attack strings
How can we characterize attack strings?

Use regular expressions to specify the attack patterns

Attack pattern for XSS: Σ∗<scriptΣ∗
Vulnerabilities can be Tricky
• Input <!sc+rip!t ...> does not match the attack pattern
– but it matches the vulnerability signature
– and it can cause an attack
•
•
•
•
•
•
1:<?php
2: $www = <!sc+rip!t ...>;
3: $l otherinfo = ”URL”;
s: $www = ereg replace(”[^A-Za-z0-9 .-@://]”,””, <!sc+rip!t...>);
4: echo ”<td>” . $l otherinfo . ”: ” . <script ...> .”</td>”;
5:?>
String Analysis


If string analysis determines that the intersection of the attack pattern
and possible inputs of the sensitive function is empty

then we can conclude that the program is secure
If the intersection is not empty, then we can again use string analysis
to generate a vulnerability signature

characterizes all malicious inputs

Given Σ∗<scriptΣ∗ as an attack pattern:

The vulnerability signature for $_GET[”www”] is
Σ∗<α∗sα∗cα∗rα∗iα∗pα∗tΣ∗
where α { A-Za-z0-9 .-@:/ }
Automata-based String Analysis
• Finite State Automata can be used to characterize sets of string values
• We use automata based string analysis
– Associate each string expression in the program with an automaton
– The automaton accepts an over approximation of all possible
values that the string expression can take during program
execution
• Using this automata representation we symbolically execute the
program, only paying attention to string manipulation operations
Input Validation Verification Stages
Application/
Scripts
Parser/
Taint Analysis
Attack
Patterns
(Tainted) Dependency
Graphs
Reachable Attack
Strings
Vulnerability Analysis
Vulnerability
Signature
Signature Generation
Sanitization
Statements
Patch Synthesis
Combining Forward & Backward Analyses




Convert PHP programs to dependency graphs
Combine symbolic forward and backward symbolic reachability
analyses
Forward analysis

Assume that the user input can be any string

Propagate this information on the dependency graph

When a sensitive function is reached, intersect with attack pattern
Backward analysis

If the intersection is not empty, propagate the result backwards to
identify which inputs can cause an attack
Front
End
Forward
Analysis
PHP
Program
Backward
Analysis
Vulnerability
Signatures
Attack
patterns
Dependency Graphs
Given a PHP program,
first construct the:
Dependency graph
$_GET[www],
“URL”,
3
1:<?php
$l_otherinfo, 3
2: $www = $ GET[”www”];
3: $l_otherinfo = ”URL”;
4: $www = ereg_replace(
”[^A-Za-z0-9 .-@://]”,””,$www
);
5: echo $l_otherinfo .
”: ” .$www;
6:?>
“”, 4
[^A-Za-z0-9 .-@://], 4
“: “, 5
preg_replace, 4
str_concat, 5
$www, 4
str_concat,
echo,
5
5
Dependency
Graph
2
$www, 2
Forward Analysis
• Using the dependency graph we conduct vulnerability analysis
• Automata-based forward symbolic analysis that identifies the possible
values of each node
– Each node in the dependency graph is associated with a DFA
• DFA accepts an over-approximation of the strings values that
the string expression represented by that node can take at
runtime
• The DFAs for the input nodes accept Σ∗
– Intersecting the DFA for the sink nodes with the DFA for the attack
pattern identifies the vulnerabilities
• Uses post-image computations of string operations:
– postConcat(M1, M2)
returns M, where M=M1.M2
– postReplace(M1, M2, M3)
returns M, where M=replace(M1, M2, M3)
Forward Analysis
Forward = Σ*
Attack Pattern = Σ*<Σ*
$_GET[www],
“URL”,
“”, 4
[^A-Za-z0-9 .-@://], 4
3
Forward = URL
“: “, 5
$l_otherinfo,
3
$www, 2
Forward = ε
Forward = [^A-Za-z0-9 .-@/]
2
Forward = Σ*
preg_replace, 4
Forward = :
Forward = URL
Forward = [A-Za-z0-9 .-@/]*
str_concat, 5
$www, 4
Forward = [A-Za-z0-9 .-@/]*
Forward = URL:
str_concat,
5
Forward = URL: [A-Za-z0-9 .-@/]*
echo,
L(Σ*<Σ*)
∩
5
L(URL:
.-@/]*) = .-@/]*
Forward[A-Za-z0-9
= URL: [A-Za-z0-9
L(URL: [A-Za-z0-9 .-;=-@/]*<[A-Za-z0-9 .-@/]*)
≠Ø
Resulting Automaton
U
R
L
:
[A-Za-z0-9 .-;=-@/]
[A-Za-z0-9 .-@/]
Space
<
URL: [A-Za-z0-9 .-;=-@/]*<[A-Za-z0-9 .-@/]*
Symbolic Automata Representation
• We use the MONA DFA Package for automata manipulation
– [Klarlund and Møller, 2001]
• Compact Representation:
– Canonical form and
– Shared BDD nodes
• Efficient MBDD Manipulations:
– Union, Intersection, and Emptiness Checking
– Projection and Minimization
• Cannot Handle Nondeterminism:
– We used dummy bits to encode nondeterminism
Symbolic Automata Representation
Explicit DFA
representation
Symbolic DFA
representation
Widening
• String verification problem is undecidable
• The forward fixpoint computation is not guaranteed to converge in the
presence of loops and recursion
• We compute a sound approximation
– During fixpoint we compute an over approximation of the least
fixpoint that corresponds to the reachable states
• We use an automata based widening operation to over-approximate
the fixpoint
– Widening operation over-approximates the union operations and
accelerates the convergence of the fixpoint computation
Widening
Given a loop such as
1:<?php
2: $var = “head”;
3: while (. . .){
4:
$var = $var . “tail”;
5: }
6: echo $var
7:?>
Our forward analysis with widening would compute that the value of the
variable $var in line 6 is (head)(tail)*
Backward Analysis
• A vulnerability signature is a characterization of all malicious inputs
that can be used to generate attack strings
• We identify vulnerability signatures using an automata-based backward
symbolic analysis starting from the sink node
• Pre-image computations on string operations:
– preConcatPrefix(M, M2)
returns M1 and where M = M1.M2
– preConcatSuffix(M, M1)
returns M2, where M = M1.M2
– preReplace(M, M2, M3)
returns M1, where M=replace(M1, M2, M3)
Backward Analysis
Forward = Σ*
Backward = [^<]*<Σ*
$_GET[www],
node 3
“URL”,
2
node 6
“”, 4
[^A-Za-z0-9 .-@://], 4
3
$www, 2
Forward = URL
Forward = [^A-Za-z0-9 .-@/]
Forward = ε
Forward = Σ*
Backward = Do not care
Backward = Do not care
Backward = Do not care
Backward = [^<]*<Σ*
“: “, 5
$l_otherinfo, 3
Forward = URL
preg_replace, 4
Vulnerability Signature = [^<]*<Σ*
Forward = :
Forward = [A-Za-z0-9 .-@/]*
Backward = Do not care
Backward =
[A-Za-z0-9 .-;=-@/]*<[A-Za-z0-9 .-@/]*
Backward = Do not care
node 10
$www, 4
str_concat, 5
Forward = [A-Za-z0-9 .-@/]*
Forward = URL:
node 11
Backward =
[A-Za-z0-9 .-;=-@/]*<[A-Za-z0-9 .-@/]*
Backward = Do not care
str_concat, 5
Forward = URL: [A-Za-z0-9 .-@/]*
Backward =
URL: [A-Za-z0-9 .-;=-@/]*<[A-Za-z0-9 .-@/]*
node 12
echo, 5
Forward = URL: [A-Za-z0-9 .-@/]*
Backward =
URL: [A-Za-z0-9 .-;=-@/]*<[A-Za-z0-9 .-@/]*
Vulnerability Signature Automaton
Σ
<
[^<]
Non-ASCII
[^<]*<Σ*
Vulnerability Signatures
• The vulnerability signature is the result of the input node, which
includes all possible malicious inputs
• An input that does not match this signature cannot exploit the
vulnerability
• After generating the vulnerability signature
– Can we generate a patch based on the vulnerability signature?
The vulnerability signature automaton for the running example
<
[^<]
Σ
Patches from Vulnerability Signatures
• Main idea:
– Given a vulnerability signature automaton, find a cut that separates
initial and accepting states
– Remove the characters in the cut from the user input to sanitize
<
Σ
[^<]
min-cut is {<}
• This means, that if we just delete “<“ from the user input, then the
vulnerability can be removed
Patches from Vulnerability Signatures
• Ideally, we want to modify the input (as little as possible) so that it does
not match the vulnerability signature
• Given a DFA, an alphabet cut is
– a set of characters that after ”removing” the edges that are
associated with the characters in the set, the modified DFA does
not accept any non-empty string
• Finding a minimal alphabet cut of a DFA is an NP-hard problem (one
can reduce the vertex cover problem to this problem)
– We use a min-cut algorithm instead
– The set of characters that are associated with the edges of the min
cut is an alphabet cut
• but not necessarily the minimum alphabet cut
Automatically Generated Patch
Automatically generated patch will make sure that no string that matches
the attack pattern reaches the sensitive function
<?php
if (preg match(’/[^ <]*<.*/’,$ GET[”www”]))
$ GET[”www”] = preg replace(<,””,$ GET[”www”]);
$www = $_GET[”www”];
$l_otherinfo = ”URL”;
$www = ereg_replace(”[^A-Za-z0-9 .-@://]”,””,$www);
echo ”<td>” . $l_otherinfo . ”: ” .$www. ”</td>”;
?>
Experiments
• We evaluated our approach on five vulnerabilities from three open
source web applications:
(1) MyEasyMarket-4.1: A shopping cart program
(2) BloggIT-1.0: A blog engine
(3) proManager-0.72: A project management system
• We used the following XSS attack pattern:
Σ∗<scriptΣ∗
Forward Analysis Results
• The dependency graphs of these benchmarks are simplified based on
the sinks
– Unrelated parts are removed using slicing
Input
Results
#nodes
#edges
#sinks
#inputs
Time(s)
Mem (kb)
#states/#
bdds
21
20
1
1
0.08
2599
23/219
29
29
1
1
0.53
13633
48/495
25
25
1
2
0.12
1955
125/1200
23
22
1
1
0.12
4022
133/1222
25
25
1
1
0.12
3387
125/1200
Backward Analysis Results
• We use the backward analysis to generate the vulnerability signatures
– Backward analysis starts from the vulnerable sinks identified during
forward analysis
Input
Results
#nodes
#edges
#sinks
#inputs
Time(s)
Mem (kb)
#states/#
bdds
21
20
1
1
0.46
2963
9/199
29
29
1
1
41.03
1859767
811/8389
25
25
1
2
2.35
5673
20/302,
20/302
23
22
1
1
2.33
32035
91/1127
25
25
1
1
5.02
14958
20/302
Alphabet Cuts
• We generate alphabet cuts from the vulnerability signatures using a
min-cut algorithm
Input
Results
#nodes
#edges
#sinks
#inputs
Alphabet
Cut
21
20
1
1
{<}
29
29
1
1
{S,’,”}
25
25
1
2
Σ,Σ
23
22
1
1
{<,’,”}
25
25
1
1
{<,’,”}
Vulnerability
signature
depends on
two inputs
• Problem: When there are two user inputs the patch will block
everything and delete everything
– Overlooks the relations among input variables (e.g., the
concatenation of two inputs contains < SCRIPT)
Relational String Analysis
• Instead of using multiple single-track DFAs use one multi-track DFA
– Each track represents the values of one string variable
• Using multi-track DFAs:
– Identifies the relations among string variables
– Generates relational vulnerability signatures for multiple user inputs
of a vulnerable application
– Improves the precision of the path-sensitive analysis
– Proves properties that depend on relations among string variables,
e.g., $file = $usr.txt
Multi-track Automata
• Let X (the first track), Y (the second track), be two string variables
• λ is a padding symbol
• A multi-track automaton that encodes X = Y.txt
(t,λ)
(a,a), (b,b) …
(x,λ)
(t,λ)
Relational Vulnerability Signature
• We perform forward analysis using multi-track automata to generate
relational vulnerability signatures
• Each track represents one user input
– An auxiliary track represents the values of the current node
– We intersect the auxiliary track with the attack pattern upon
termination
Relational Vulnerability Signature
• Consider a simple example having multiple user inputs
<?php
1: $www = $_GET[”www”];
2: $url = $_GET[”url”];
3: echo $url. $www;
?>
• Let the attack pattern be Σ∗ < Σ∗
Relational Vulnerability Signature
• A multi-track automaton: ($url, $www, aux)
• Identifies the fact that the concatenation of two inputs contains <
(a,λ,a),
(b,λ,b),
…
(λ,a,a),
(λ,b,b),
…
(λ,a,a),
(λ,b,b),
…
(<,λ,<)
(λ,<,<)
(λ,<,<)
(a,λ,a),
(b,λ,b),
…
(λ,a,a),
(λ,b,b),
…
(λ,a,a),
(λ,b,b),
…
Relational Vulnerability Signature
• Project away the auxiliary variable
• Find the min-cut
• This min-cut identifies the alphabet cuts {<} for the first track ($url) and
{<} for the second track ($www)
(a,λ),
(b,λ),
…
(λ,a),
(λ,b),
…
(λ,a),
(λ,b),
…
(a,λ),
(b,λ),
…
(<,λ)
(λ,<)
(λ,a),
(λ,b),
…
(λ,<)
min-cut is {<},{<}
(λ,a),
(λ,b),
…
Patch for Multiple Inputs
• Patch: If the inputs match the signature, delete its alphabet cut
<?php
if (preg match(’/[^ <]*<.*/’, $ GET[”url”].$ GET[”www”]))
{
$ GET[”url”] = preg replace(<,””,$ GET[”url”]);
$ GET[”www”] = preg replace(<,””,$ GET[”www”]);
}
1: $www = $ GET[”www”];
2: $url = $ GET[”url”];
3: echo $url. $www;
?>
Technical Issues
• To conduct relational string analysis, we need to compute
”intersection” of multi-track automata
– Intersection is closed under aligned multi-track automata
• λs are right justified in all tracks, e.g., abλλ instead of aλbλ
– However, there exist unaligned multi-track automata that are not
describable by aligned ones
– We propose an alignment algorithm that constructs aligned
automata which over or under approximate unaligned ones
Other Technical Issues
• Modeling Word Equations:
– Intractability of X = cZ:
• The number of states of the corresponding aligned multi-track
DFA is exponential to the length of c.
– Irregularity of X = YZ:
• X = YZ is not describable by an aligned multi-track automata
• We propose a conservative analysis
– We construct multi-track automata that over or under-approximate
the word equations
Composite Analysis
• What I have talked about so far focuses only on string contents
– It does not handle constraints on string lengths
– It cannot handle comparisons among integer variables and string
lengths
• We extended our string analysis techniques to analyze systems that
have unbounded string and integer variables
• We proposed a composite static analysis approach that combines
string analysis and size analysis
Size Analysis
• Size Analysis: The goal of size analysis is to provide properties about
string lengths
– It can be used to discover buffer overflow vulnerabilities
• Integer Analysis: At each program point, statically compute the
possible states of the values of all integer variables.
– These infinite states are symbolically over-approximated as linear
arithmetic constraints that can be represented as an arithmetic
automaton
• Integer analysis can be used to perform size analysis by representing
lengths of string variables as integer variables.
An Example
• Consider the following segment:
1: <?php
2:
$www = $ GET[”www”];
3:
$l otherinfo = ”URL”;
4:
$www = ereg replace(”[^A-Za-z0-9 ./-@://]”,””,$www);
5:
if(strlen($www) < $limit)
6:
echo ”<td>” . $l otherinfo . ”: ” . $www . ”</td>”;
7:?>
• If we perform size analysis solely, after line 4, we do not know the
length of $www
• If we perform string analysis solely, at line 5, we cannot check/enforce
the branch condition.
Composite Analysis
• We need a composite analysis that combines string analysis with size
analysis.
– Challenge: How to transfer information between string automata
and arithmetic automata?
• A string automaton is a single-track DFA that accepts a regular
language, whose length forms a semi-linear set
– For example: {4, 6} ∪ {2 + 3k | k ≥ 0}
• The unary encoding of a semi-linear set is uniquely identified by a
unary automaton
• The unary automaton can be constructed by replacing the alphabet of
a string automaton with a unary alphabet
Arithmetic Automata
• An arithmetic automaton is a multi-track DFA, where each track
represents the value of one variable over a binary alphabet
• If the language of an arithmetic automaton satisfies a Presburger
formula, the value of each variable forms a semi-linear set
• The semi-linear set is accepted by the binary automaton that projects
away all other tracks from the arithmetic automaton
Connecting the Dots
• We developed novel algorithms to convert unary automata to binary
automata and vice versa
String
Automata
Unary Length
Automata
Binary Length
Automata
Arithmetic
Automata
• Using these conversion algorithms we can conduct a composite
analysis that subsumes size analysis and string analysis
Stranger: A String Analysis Tool
Stranger is available at:
www.cs.ucsb.edu/~vlab/stranger
Pixy Front End
Parser
Dependency
Graphs
PHP
program
Attack
patterns
Symbolic String Analysis
String
Analyzer
String/Automata
Operations
Stranger
Automata
CFG
DFAs
Dependency
Analyzer
–
–
Automata Based
String Manipulation
Library
Vulnerability
Signatures
+ Patches
MONA Automata
Package
Uses Pixy [Jovanovic et al., 2006] as a PHP front end
Uses MONA [Klarlund and Møller, 2001] automata package for
automata manipulation
Case Study



Schoolmate 1.5.4

Number of PHP files: 63

Lines of code: 8181
Forward Analysis results
Time
Memory
Number of XSS
sensitive sinks
Number of XSS
Vulnerabilities
22 minutes
281 MB
898
153
After manual inspection we found the following:
Actual Vulnerabilities
False Positives
105
48
Case Study – False Positives

–
Why false positives?
– Path insensitivity: 39
 Path to vulnerable program point is not feasible
– Un-modeled built in PHP functions : 6
– Unfound user written functions: 3
– PHP programs have more than one execution entry point
We can remove all these false positives by extending our analysis to a
path sensitive analysis and modeling more PHP functions
Case Study - Sanitization


We patched all actual vulnerabilities by adding sanitization routines
We ran stranger the second time
–
Stranger proved that our patches are correct with respect to the
attack pattern we are using
Related Work: String Analysis
• String analysis based on context free grammars: [Christensen et al.,
SAS’03] [Minamide, WWW’05]
• String analysis based on symbolic/concolic execution: [Bjorner et al.,
TACAS’09]
• Bounded string analysis : [Kiezun et al., ISSTA’09]
• Automata based string analysis: [Xiang et al., COMPSAC’07]
[Shannon et al., MUTATION’07]
• Application of string analysis to web applications: [Wassermann and
Su, PLDI’07, ICSE’08] [Halfond and Orso, ASE’05, ICSE’06]
Related Work
• Size Analysis
– Size analysis: [Hughes et al., POPL’96] [Chin et al., ICSE’05] [Yu
et al., FSE’07] [Yang et al., CAV’08]
– Composite analysis: [Bultan et al., TOSEM’00] [Xu et al.,
ISSTA’08] [Gulwani et al., POPL’08] [Halbwachs et al., PLDI’08]
• Vulnerability Signature Generation
– Test input/Attack generation: [Wassermann et al., ISSTA’08]
[Kiezun et al., ICSE’09]
– Vulnerability signature generation: [Brumley et al., S&P’06]
[Brumley et al., CSF’07] [Costa et al., SOSP’07]
THE END