CS 267: Automated Verification Lectures 16: String Analysis Instructor: Tevfik Bultan

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

String Related Vulnerabilities String related web application vulnerabilities as a percentage of all vulnerabilities (reported by CVE) OWASP Top 10 in 2007: 1.Cross Site Scripting 2.Injection Flaws OWASP Top 10 in 2010: 1.Injection Flaws 2.Cross Site Scripting

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 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 2: $www = $_GET[”www”]; 3: $l_otherinfo = ”URL”; 4: echo ” ”. $l_otherinfo. ”: ”. $www. ” ”; 5:?> The echo statement in line 4 is a sensitive function It contains a Cross Site Scripting (XSS) vulnerability <script...

Is It Vulnerable? A simple taint analysis can report this segment vulnerable using taint propagation 1:<?php 2: $www = $_GET[”www”]; 3: $l_otherinfo = ”URL”; 4: echo ” ”. $l_otherinfo. ”: ”.$www. ” ”; 5:?> echo is tainted → script is vulnerable tainted

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 2: $www = $_GET[”www”]; 3: $l_otherinfo = ”URL”; s: $www = 4: echo ” ”. $l_otherinfo. ”: ”.$www. ” ”; 5:?> tainted untainted

Is It Really Sanitized? 1:<?php 2: $www = $_GET[”www”]; 3: $l_otherinfo = ”URL”; s: $www = 4: echo ” ”. $l_otherinfo. ”: ”.$www. ” ”; 5:?> <script …>

Sanitization Routines can be Erroneous The sanitization statement is not correct! ; – Removes all characters that are not in { } denotes all characters between “. ” and ” (including “ ”) – ” 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 does not match the attack pattern –but it matches the vulnerability signature and it can cause an attack 1:<?php 2: $www = $_GET[”www”]; 3: $l_otherinfo = ”URL”; s: $www = 4: echo ” ”. $l_otherinfo. ”: ”.$www. ” ”; 5:?> <!sc+rip!t …>

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 ∉ { }

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 StagesParser/ Taint Analysis Vulnerability Analysis Signature Generation Attack Patterns Application/ Scripts Vulnerability Signature (Tainted) Dependency Graphs Patch Synthesis Sanitization Statements Reachable Attack Strings

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 FrontEnd ForwardAnalysis BackwardAnalysis Attack patterns PHP Program Vulnerability Signatures

Dependency Graphs Given a PHP program, first construct the: Dependency graph 1:<?php 2: $www = $ GET[”www”]; 3: $l_otherinfo = ”URL”; 4: $www = ereg_replace( ); 5: echo $l_otherinfo. ”: ”.$www; 6:?> echo, 5 str_concat, 5 $www, 4 “”, 4 preg_replace, 4 4 $www, 2 $_GET[www], 2 “: “, 5 $l_otherinfo, 3 “URL”, 3 str_concat, 5 Dependency Graph

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 echo, 5 str_concat, 5 $www, 4 “”, 4 preg_replace, 4 4 $www, 2 $_GET[www], 2 “: “, 5 $l_otherinfo, 3 “URL”, 3 str_concat, 5 Forward = URL: Forward = Forward = Σ* Forward = ε Forward = Forward = Σ* Forward = : Forward = URL Forward = URL: L(URL: Attack Pattern = Σ*<Σ* ∩ ≠ Ø L(URL: = L(Σ*<Σ*)

Result Automaton U R L : Space < URL:

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 echo, 5 str_concat, 5 $www, 4 “”, 4 preg_replace, 4 4 $www, 2 $_GET[www], 2 “: “, 5 $l_otherinfo, 3 “URL”, 3 str_concat, 5 Forward = URL: Backward = URL: Forward = URL: Backward = URL: Forward = Backward = Forward = Backward = Forward = Σ* Backward = [^<]*<Σ* Forward = ε Backward = Do not care Forward = Backward = Do not care Forward = Σ* Backward = [^<]*<Σ* Forward = : Backward = Do not care Forward = URL Backward = Do not care Forward = URL Backward = Do not care Forward = URL: Backward = Do not care node 3node 6 node 10 node 11 node 12 Vulnerability Signature = [^<]*<Σ*

Vulnerability Signature Automaton [^<]*<Σ* < [^<] Σ Non-ASCII

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 This means, that if we just delete “<“ from the user input, then the vulnerability can be removed [^<] < Σ min-cut is {<}

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 = echo ” ”. $l_otherinfo. ”: ”.$www. ” ”; ?>

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 ∗ <script Σ ∗

Forward Analysis Results The dependency graphs of these benchmarks are simplified based on the sinks –Unrelated parts are removed using slicing InputResults #nodes#edges#sinks#inputsTime(s)Mem (kb)#states/# bdds / / / / /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 InputResults #nodes#edges#sinks#inputsTime(s)Mem (kb)#states/# bdds / / /302, 20/ / /302

Alphabet Cuts We generate alphabet cuts from the vulnerability signatures using a min-cut algorithm 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) InputResults #nodes#edges#sinks#inputsAlphabet Cut {<} 29 11{S,’,”} Σ, Σ {<,’,”} 25 11{<,’,”} Vulnerability signature depends on two inputs

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 (a,a), (b,b) … (t, λ )(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,<) ( λ, a,a), ( λ, b,b), … ( λ, a,a), ( λ, b,b), … ( λ,<,<) ( λ, a,a), ( λ, b,b), … ( λ, a,a), ( λ, b,b), … (a, λ, a), (b, λ, 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 ) ( λ, a), ( λ, b), … ( λ, a), ( λ, b), … ( λ,<) ( λ, a), ( λ, b), … ( λ, a), ( λ, b), … (a, λ ), (b, λ ), … min-cut is {<},{<}

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: $www = ereg 5: if(strlen($www) < $limit) 6: echo ” ”. $l otherinfo. ”: ”. $www. ” ”; 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 Using these conversion algorithms we can conduct a composite analysis that subsumes size analysis and string analysis String Automata Unary Length Automata Binary Length Automata Arithmetic Automata

Stranger: A String Analysis Tool – Uses Pixy [Jovanovic et al., 2006] as a PHP front end – Uses MONA [Klarlund and Møller, 2001] automata package for automata manipulation Parser DependencyAnalyzer String Analyzer Analyzer MONA Automata Package Automata Based String Manipulation Library Library CFG Dependency Graphs Symbolic String Analysis DFAs Pixy Front End String/Automata Operations Stranger Automata Vulnerability Signatures + Patches PHP program Attack patterns Stranger is available at:

Case Study Schoolmate Number of PHP files: 63 Lines of code: 8181 Forward Analysis results After manual inspection we found the following: Actual VulnerabilitiesFalse Positives TimeMemory Number of XSS sensitive sinks Number of XSS Vulnerabilities 22 minutes281 MB898153

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

Recent Work Client-side input validation analysis [ICSE 2012]: –String analysis for JavaScript –Dynamic slicing to extract the validation code –Using regular expressions for specification of input validation policy Max and min policies Differential string analysis for input validation [ISSTA 2012]: –Analyzing and comparing client- and server-side input validation functions –General security policy: Server-side input validation should always be stronger than client-side input validation

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], [Saxena et al., S&P 2010] Bounded string analysis : [Kiezun et al., ISSTA’09] Automata based string analysis: [Xiang et al., COMPSAC’07] [Shannon et al., MUTATION’07], [Balzarotti et al., S&P 2008], [Hooimeijer et al., Usenix’11] 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]

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