Eliminating Web Software Vulnerabilities with Automated Verification Tevfik

Eliminating Web Software Vulnerabilities with Automated Verification Tevfik Bultan Verification Lab Department of Computer Science University of California, Santa Barbara bultan@cs. ucsb. edu http: //www. cs. ucsb. edu/~vlab

University of California at Santa Barbara

Verification Lab (VLab) at UCSB • Application of automated verification techniques to software – Automated verification of web applications • Checking input validation, sanitization, string analysis (PHP) • Checking navigation correctness (MVC farmeworks) • Checking data models (Ruby on Rails) – Automated verification of web services • Modular testing and verification of web services (WSDL) • Formal modeling and analysis of choreography and orchestration (WS-CDL, WS-BPEL) – Automated verification of access control policies • Policy composition (XACML) – Automated verification of concurrency • Analyzing concurrency, deadlock detection (Java)

VLab Publications on String Analysis • Relational String Verification Using Multi-Track Automata [Yu, Bultan, Ibarra CIAA’ 10] • Stranger: An Automata-based String Analysis Tool for PHP [Yu, Alkhalaf, Bultan TACAS’ 10] • Generating Vulnerability Signatures for String Manipulating Programs Using Automata-based Forward and Backward Symbolic Analyses [Yu, Alkhalaf, Bultan ASE’ 09] • Symbolic String Verification: Combining String Analysis and Size Analysis [Yu, Bultan, Ibarra TACAS’ 09] • Symbolic String Verification: An Automata-based Approach [Yu, Bultan, Cova, Ibarra SPIN’ 08]

Web software • Web software is becoming increasingly dominant • Web applications are used extensively in many areas: – Commerce: online banking, online shopping, … – Entertainment: online music & videos, … – Interaction: social networks • We will rely on web applications more in the future: – Health records • Google Health, Microsoft Health. Vault – Controlling and monitoring of national infrastructures: • Google Powermeter • Web software is also rapidly replacing desktop applications – Could computing + software-as-service • Google Docs, Google …

One Major Road Block • Web applications are not trustworthy! • Web applications are notorious for security vulnerabilities – Their global accessibility makes them a target for many malicious users • As web applications are becoming increasingly dominant – and as their use in safety critical areas is increasing • their trustworthiness is becoming a critical issue

Web applications are not secure • 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

Web Application Vulnerabilities

Web Application Vulnerabilities • The top two vulnerabilities of the Open Web Application Security Project (OWASP)’s top ten list in 2007 – Cross Site Scripting (XSS) – Injection Flaws (such as SQL Injection) • The top two vulnerabilities of the OWASPs top ten list in 2010 – Injection Flaws (such as SQL Injection) – Cross Site Scripting (XSS)

Why are web applications 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 <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, e. g. , [Huang et al. WWW 04], 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 = preg_replace(”[^A-Za-z 0 -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 = preg_replace(”[^A-Za-z 0 -9. -@: //]”, ””, $www); 4: echo ”<td>”. $l_otherinfo. ”: ”. $www. ”</td>”; 5: ? >

Sanitization Routines can be Erroneous The sanitization statement is not correct! preg_replace(”[^A-Za-z 0 -9. -@: //]”, ””, $www); – – – Removes all characters that are not in {A-Za-z 0 -9. -@: /} “. -@” denotes all characters between “. ” and “@” (including “<” and “>”) “. -@” should have been “. -@” This example is from a buggy sanitization routine used in My. Easy. Market-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∗

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-z 0 -9. -@: /}

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 = preg replace(”[^A-Za-z 0 -9. -@: //]”, ””, <!sc+rip!t. . . >); 4: echo ”<td>”. $l otherinfo. ”: ”. <script. . . >. ”</td>”; 5: ? >

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

Symbolic Automata Representation • We use the MONA DFA Package for automata manipulation – [Klarlund and Møller, 2001] • Compact Representation: – The transition relation of the DFA is represented as a multi-terminal BDD (MBDD) • Exploits the MBDD structure in the implementation of DFA operations – Union, Intersection, and Emptiness Checking – Projection and Minimization • Cannot Handle Nondeterminism: – We extended the alphabet with dummy bits to encode nondeterminism

Symbolic Automata Representation Explicit DFA representation Symbolic DFA representation

String Analysis Stages Construct dependency graphs for the PHP programs 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 = preg_replace( ”[^A-Za-z 0 -9. -@: //]”, ””, $www ); 5: echo $l_otherinfo. ”: ”. $www; 6: ? > [^A-Za-z 0 -9. -@: //], 4 “”, 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: – post. Concat(M 1, M 2) returns M, where M=M 1. M 2 – post. Replace(M 1, M 2, M 3) (language-based replacement) returns M, where M=replace(M 1, M 2, M 3)

Forward Analysis Forward = Σ* Attack Pattern = Σ*<Σ* $_GET[www], “URL”, “”, 4 [^A-Za-z 0 -9. -@: //], 4 3 Forward = URL “: “, 5 $l_otherinfo, 3 $www, 2 Forward = ε Forward = [^A-Za-z 0 -9. -@/] 2 Forward = Σ* preg_replace, 4 Forward = : Forward = URL Forward = [A-Za-z 0 -9. -@/]* str_concat, 5 $www, 4 Forward = [A-Za-z 0 -9. -@/]* Forward = URL: str_concat, 5 Forward = URL: [A-Za-z 0 -9. -@/]* echo, L(Σ*<Σ*) ∩ 5 L(URL: . -@/]*) =. -@/]* Forward[A-Za-z 0 -9 = URL: [A-Za-z 0 -9 L(URL: [A-Za-z 0 -9. -; =-@/]*<[A-Za-z 0 -9. -@/]*) ≠Ø

Intersection Result Automaton U R L : [A-Za-z 0 -9. -; =-@/] [A-Za-z 0 -9. -@/] Space < URL: [A-Za-z 0 -9. -; =-@/]*<[A-Za-z 0 -9. -@/]*

Widening • String verification problem is undecidable in general – Two string variables, equality checks and concatenation is enough to get to undecidability • 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 operation and accelerates the convergence of the fixpoint computation

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 • Uses pre-image computations on string operations: – pre. Concat. Prefix(M, M 2) returns M 1 and where M = M 1. M 2 – pre. Concat. Suffix(M, M 1) returns M 2, where M = M 1. M 2 – pre. Replace(M, M 1, M 2) returns M 3, where M=replace(M 1, M 2, M 3)

Backward Analysis Forward = Σ* Backward = [^<]*<Σ* $_GET[www], node 3 “URL”, 2 node 6 [^A-Za-z 0 -9. -@: //], 4 3 “”, 4 $www, 2 Forward = URL Forward = [^A-Za-z 0 -9. -@/] Forward = ε Forward = Σ* Backward = Do not care Backward = [^<]*<Σ* “: “, 5 $l_otherinfo, Forward = URL 3 preg_replace, 4 Vulnerability Signature = [^<]*<Σ* Forward = : Forward = [A-Za-z 0 -9. -@/]* Backward = Do not care Backward = [A-Za-z 0 -9. -; =-@/]*<[A-Za-z 0 -9. -@/]* Backward = Do not care node 10 $www, 4 str_concat, 5 Forward = [A-Za-z 0 -9. -@/]* Forward = URL: node 11 Backward = Do not care str_concat, Backward = [A-Za-z 0 -9. -; =-@/]*<[A-Za-z 0 -9. -@/]* 5 Forward = URL: [A-Za-z 0 -9. -@/]* Backward = URL: [A-Za-z 0 -9. -; =-@/]*<[A-Za-z 0 -9. -@/]* node 12 echo, 5 Forward = URL: [A-Za-z 0 -9. -@/]* Backward = URL: [A-Za-z 0 -9. -; =-@/]*<[A-Za-z 0 -9. -@/]*

Vulnerability Signature Automaton Σ [^<] < Not 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 = preg_replace(”[^A-Za-z 0 -9. -@: //]”, ””, $www); echo ”<td>”. $l_otherinfo. ”: ”. $www. ”</td>”; ? >

Experiments • We evaluated our approach on five vulnerabilities from three open source web applications: (1) My. Easy. Market-4. 1: A shopping cart program (2) Blogg. IT-1. 0: A blog engine (3) pro. Manager-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 reduced based on the sinks – Unrelated parts are removed 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 23 22 1 1 {<, ’, ”} 25 25 1 1 {<, ’, ”} Σ, Σ Vulnerability signature depends on two inputs • Problem: When there are two user inputs the patch will block everything and delete everything – Cannot interpret the relations among input variables (e. g. only block when 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 string 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 (λ, t) (a, a), (b, b) … (λ, x) (λ, t)

Relational Vulnerability Signature • Performs 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 – Intersects 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, <) (λ, <, <) (a, λ, a), (b, λ, 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), … (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 proposed an alignment algorithm that constructs aligned automata which over or under approximate unaligned ones

Other Technical Issues • Modeling Word Equations: – Intractability of X = c. Z • 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 proposed a conservative analysis – Constructs 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 = preg replace(”[^A-Za-z 0 -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 + 3 k | 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 PHP program CFG Dependency Graphs – Symbolic String Analysis String Analyzer String/Automata Operations Stranger Automata Based String Manipulation Library DFAs Dependency Analyzer – Attack patterns String Analysis Report (Vulnerability Signatures) 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] • Application of string analysis to web applications: [Wassermann and Su, PLDI’ 07, ICSE’ 08] [Halfond and Orso, ASE’ 05, ICSE’ 06] • Automata based string analysis: [Xiang et al. , COMPSAC’ 07] [Shannon et al. , MUTATION’ 07] • String analysis based on symbolic/concolic execution: [Bjorner et al. , TACAS’ 09] • Bounded string analysis : [Kiezun et al. , ISSTA’ 09]

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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