SMT Solvers for Software Security (USENIX WOOT’12)

At WOOT’12 a paper co-written by Julien Vanegue, Rolf Rolles and I will be presented under the title “SMT Solvers for Sofware Security”. An up-to-date version can be found in the Articles/Presentation section of this site.

In short, the message of this paper is “SMT solvers are well capable of handling decision problems from security properties. However, specific problem domains usually require domain specific modeling approaches. Important limitations, challenges, and research opportunities remain in developing appropriate models for the three areas we discuss – vulnerability discovery, exploit development, and bypassing of copy protection”. The motivation for writing this paper is to discuss these limitations, why they exist, and hopefully encourage more work on the modeling and constraint generation sides of these problems.

A quick review of the publication lists from major academic conferences focused on software security will show a massive number of papers discussing solutions based on SMT technology. There is good reason for this 1) SMT-backed approaches such as symbolic/concolic execution have proved powerful tools on certain problems and 2) There are an increasing number of freely available frameworks.

The primary domain where SMT solvers have shone, in my opinion, is in the discovery of bugs related to unsafe integer arithmetic using symbolic/concolic execution. There’s a fairly obvious reason why this is the case; the quantifier free, fixed size, bitvector logic supported by SMT solvers provides direct support for the precise representation of arithmetic at the assembly level. In other words, one does not have to do an excessive amount of work when modeling the semantics of a program to produce a representation suitable for the detection of unsafe arithmetic. It suffices to perform a near direct translation from the executed instructions to the primitives provided by SMT solvers.

The exploit generation part of the paper deals with what happens when one takes the technology for solving the above problem and applies it to a new problem domain. In particular, a new domain in which the model produced simply by tracking transformations and constraints on input data no longer contains enough data to inform a solution. For example, in the case of exploit generation, models that do not account for things like the relationship between user input and memory layout. Obviously enough, when reasoning about a formula produced from such a model a solver cannot account for information not present. Thus, no amount of computational capacity or solver improvement can produce an effective solution.

SMT solvers are powerful tools and symbolic/concolic execution can be an effective technique. However, one thing I’ve learned over the past few years is that they don’t remove the obligation and effort required to accurately model the problem you’re trying to solve. You can throw generic symbolic execution frameworks at a problem but if you’re interested in anything more complex than low level arithmetic relationships you’ve got work to do!

Misleading the Public for Fun and Profit

Sometimes I read a research paper, usually in the area where computer science meets application, and it’s obvious that the authors are far overstating the practical impact of the work. This can be due to the researchers simply not having any exposure to the practical side of the field in which they are investigating and thus accidentally (through ignorance) overstate their claims. Alternatively it can be a purposeful and deliberate attempt to mislead and posture in front of a readership that hopefully won’t know any better.

The first case is presumably simple ignorance but is still lamentable. The obvious solution here is to avoid making such claims at all. If the research cannot stand on its own then perhaps it is not worthwhile? Researchers (both academic and industrial) have a habit of jumping on problems they underestimate, throwing a variety of techniques at them, hoping one sticks and then calling the problem solved. This typically occurs when they are not actually required to solve the problem correctly and robustly but merely as a ‘prototype’. They then get pilloried by anyone who actually has to solve the problem properly and almost always because of a disparity between claims made and the real impact rather than issues with methodology, recording or technical aspects.

The second case is far more insidious and unfortunately I think not uncommon. In academic research it can be easy to impress by combining cutting edge, but not necessarily original, research with a practical problem, sort-of solving parts of it and like before declaring it solved. Often followed quickly by phrases involving ‘game changing’, ‘paradigm shifting’ and so forth. Personally, I think this is a serious problem in the research areas that are less theoretical and more practical. Often the investigators refuse to accept they aren’t actually aware of the true nature of the problem they are dealing with or how it occurs in the real world. Egotistically this is difficult as they are often lauded by their academic peers and therefore surely must grasp the trivialities of the practical world, no? At this point a mixture of ego, need to impress and lack of ethics combine to give us papers that are at best deluded and at worst downright wrong.

Regardless of whether a paper ends up making such claims mistakenly for the first or the second reason the result is the same. It cheapens the actual value of the research, results in a general loss of respect for the capabilities of academia, deludes the researchers further and causes general confusion as to where research efforts should be focused. Worse still is when attempts to overstate the impact are believed by both the media and other researchers resulting in a complete distortion between the actual practical and theoretical value of the research and it’s perceived impact.

Now, on to the paper that has reminded me of this most recently: The latest paper from David Brumleys group at CMU titled AEG: Automatic Exploit Generation. I was looking forward to reading this paper as it was the area I worked on during my thesis but quite honestly it’s incredibly disappointing at best and has serious factual issues at worst. For now let’s focus on the topic at hand ‘overstating the impact of academic research cheapens it and spreads misinformation‘. With the original Patch-Based Exploit Generation paper we had all sorts of stories about how it would change the way in which patches had to be distributed, how attackers would be pushing buttons to generate their exploits in no time at all and in general how the world was about to end. Naturally none of this happened and people continued to use PatchDiff. Unfortunately this is more of the same.

Near the beginning of the most recent paper we have the following claim “Our automatic exploit generation techniques have several immediate security implications. First, practical AEG fundamentally changes the perceived capabilities of attackers“. This statement is fundamentally flawed. It assumes that practical AEG is currently possible on bugs that people actually care about. This is patently false. I’ve written one of these systems. Did it generate exploits? Yes it did. Is it going to pop any program running on a modern operating system with the kinds of vulnerabilities we typically see? Nope. That would require at a minimum another 2 years of development and at that point I would expect a system that is usable by a skilled exploit writer as an augmentation of his skillset rather than a replacement. The few times I did use the tool I built for real exploits it was in this context rather than full blown exploit generation. The system discussed in the mentioned paper has more bells and whistles in some areas and is more primitive in others and it is still an unfathomable distance from having any impact on a realistic threat model.

Moving on, “For example, previously it has been believed that it is relatively difficult for untrained attackers to find novel vulnerabilities and create zero-day exploits. Our research shows this assumption is unfounded“. It’s at this point the distance between the authors of this paper and the realities of industrial/government/military vulnerability detection and exploit development can be seen. Who are the people we are to believe have this view? I would assume the authors themselves do and then extrapolated to the general exploit creating/consuming community. This is an egotistical flaw that has been displayed in many forays by academia into the vulnerability detection/exploit generation world.

Let’s discuss this in two parts. Firstly, in the context of the exploits discussed in this paper and secondly in the context of exploits seen in the real world.

In the case of the bug classes considered in the paper this view is entirely incorrect. Anyone who looks at Full Disclosure can regularly see low hanging bugs being fuzzed and exploited in a cookie cutter style. Fuzz the bug, overwrite the SEH chain, find your trampoline, jump to your shellcode bla bla bla rinse and repeat, start a leet h4x0r group and flood Exploit DB. All good fun, no useful research dollars wasted. The bugs found and exploited by the system described are of that quality. Low hanging, fuzzable fruit. The ‘training’ involved here is no more than would be required to set up, install and debug whatever issues come up in the course of running the AEG tool. In our most basic class at Immunity I’ve seen people who’ve never seen a debugger before writing exploits of this quality in a couple of days.

For more complex vulnerabilities and exploits that require a skilled attacker this AEG system doesn’t change the threat model. It simply doesn’t apply. A fully functional AEG tool that I can point at Firefox and press the ‘hack’ button (or any tool that had some sort of impact on real threats. I’d be happy with exploit assistance rather than exploit generation as long as it works) would of course, but we are a long, long way from that. This is not to say we won’t get there or that this paper isn’t a step in the right direction but making the claim now is simply laughable. To me it just reeks of a research group desperate to shout ‘FIRST!’ and ignoring the real issues.

A few more choice phrases for your viewing pleasure:

Automated exploit generation can be fed into signature generation algorithms by defenders without requiring real-life attacks” – Fiction again. This would be possible *if* one had a usable AEG system. The word I presume they are looking for is *could*, “could be fed into”.

In order to extend AEG to handle heap-based overflows we would need to also consider heap management structures, which is a straight-forward extension” – Again, this displays a fundamental ignorance of what has been required to write a heap exploit for the past six or so years. I presume they heard about the unlink() technique and investigated no further. Automatic exploit generation of heap exploits requires one to be able to discover and trigger heap manipulation primitives as well as whatever else must be done. This is a difficult problem to solve automatically and one that is completely ignored.

In reference to overflows that smash local variables and arguments that are dereferenced before the function returns and therefore must be valid – “If there is not enough space to place the payload before the return address, AEG can still generate an exploit by applying stack restoration, where the local variables and function arguments are overwritten, but we impose constraints that their values should remain unchanged. To do so, AEG again relies on our dynamic analysis component to retrieve the runtime values of the local variables and arguments” – It’s at this point that I start to wonder if anyone even reviewed this thing. In any program with some amount of heap non-determinism, through normal behaviour or heap base randomisation, this statement makes no sense. Any pointers to heap allocated data passed as arguments or stored as local variables will be entirely different. You may be lucky and end up with that pointer being in an allocated heap region but the chances of it pointing to the same object are rather slim in general. Even in the context of local exploits where you have much more information on heap bases etc. this statement trivialises many problems that will be encountered.


With the above paper I have two main issues. One is with the correctness of some of the technical statements made and the other is with distortion between reality and the stated impact and generality of the work. For the technical issues I think the simple observation that they are there is enough to highlight the problem. The flawed statements on impact and generality are more problematic as they display a fundamental corruption of what a scientific paper should be.

I have a deep respect for scientific research and the ideals that I believe it should embody. Much of this research is done by university research groups and some of the papers produced in the last century are among humanities greatest intellectual achievements. Not all papers can be revolutionary of course but even those that aren’t should aim to uphold a level of scientific decorum so that they may contribute to the sum of our knowledge. In my opinion this single idea should be at the heart of any university researcher being funded to perform scientific investigation. A researcher is not a journalist nor a politician and their papers should not be opinion pieces or designed to promote themselves at the expense of facts. There is nothing wrong with discussing perceived impact of a paper within the paper itself but these statements should be subjected to the same scientific rigour that the theoretical content of the paper is. If one finds themselves unqualified (as in the above paper) to make such statements then they should be excluded. Facts are all that matter in a scientific paper, distorting them through ignorance is incompetence, distorting them on purpose is unethical and corrupt.

Game Over! Thank you for playing Academia

I’ve recently finished my Msc dissertation, titled “Automatic Generation of Control Flow Hijacking Exploits for Software Vulnerabilities“. A PDF copy of it is available here should you feel the need to trawl through 110 or so pages of prose, algorithms, diagrams and general ramblings. The abstract is the following:

Software bugs that result in memory corruption are a common and dangerous feature of systems developed in certain programming languages. Such bugs are security vulnerabilities if they can be leveraged by an attacker to trigger the execution of malicious code. Determining if such a possibility exists is a time consuming process and requires technical expertise in a number of areas. Often the only way to be sure that a bug is in fact exploitable by an attacker is to build a complete exploit. It is this process that we seek to automate. We present a novel algorithm that integrates data-flow analysis and a decision procedure with the aim of automatically building exploits. The exploits we generate are constructed to hijack the control flow of an application and redirect it to malicious code.

Our algorithm is designed to build exploits for three common classes of security vulnerability; stack-based buffer overflows that corrupt a stored instruction pointer, buffer overflows that corrupt a function pointer, and buffer overflows that corrupt the destination address used by instructions that write to memory. For these vulnerability classes we present a system capable of generating functional exploits in the presence of complex arithmetic modification of inputs and arbitrary constraints. Exploits are generated using dynamic data-flow analysis in combination with a decision procedure. To the best of our knowledge the resulting implementation is the first to demonstrate exploit generation using such techniques. We illustrate its effectiveness on a number of benchmarks including a vulnerability in a large, real-world server application.

The implementation of the described system is approx. 7000 lines of C++. I probably won’t be releasing the code as I’m fairly sure I signed over my soul (and anything I might create) to the University earlier in the year. The two core components are a data-flow/taint analysis library and higher level library that uses the previous API to perform data-flow/taint analysis over x86 instructions (as given to us by Pin). Both of these components are useful in their own right so I think I’m going to do a full rewrite (with added GUI + DB) and open source the code in the next couple of months. Hopefully they’ll prove useful for others working on dynamic analysis problems.

Exploit generation, a specialisation of testing?

It sounds like a silly question, doesn’t it? Nobody would consider exploit development to be a special case of vulnerability detection. That said, all research on exploit generation that relies on program analysis/verification theory (From now on assume these are the projects I’m discussing. Other approaches exist based on pattern matching over program memory but they are riddled with their own problems.) has essentially ridden on the coat-tails of research and tools developed for test-case generation. The almost standard approach to test-case generation consists of data flow analysis in combination with some sort of decision procedure. We then generate formulae over the paths executed to create inputs that exercise new paths. This is also the exact approach taken by all exploit generation projects.

There are pros and cons to this relationship. For instance, some activities are crucial to both test-case generation and exploit generation, e.g., data flow and taint analysis. Algorithms for these activities are almost standardised at this stage and when we work on exploit generation we can basically lift code from test generation projects. Even for these activities though there are sufficient differences and opportunities presented by exploit generation that it is worth doing some re-engineering. For example, during my research I extending the taint analysis to reflect the complexity of the instructions involved in tainting a location. When building a formula to constrain a buffer to shellcode we can then use this information to pick the locations that result in the least complex formulae. An exploit only needs a single successful formula (usually) so we can pick and choose the locations we want to use; testing on the other hand typically requires exhaustive generation and thus this optimisation hasn’t been previously applied because the benefits are less evident (but still might be a decent way of increasing the number of test cases generated in a set time frame).

The two problems share other similarities as well. In both cases we find ourselves often dissatisfied with the results of single path analysis. When generating an exploit the initial path we analyse might not be exploitable but there may be another path to the same vulnerability point that is. Again in this case we can look to test case generation research for answers. It is a common problem to want to focus on testing different sub-paths to a given point in a program and so there are algorithms that use cut points and iterative back-tracking to find relevant paths. So with such research available one might begin to think that exploit generation is a problem that will be inadvertently ‘solved’ as we get better at test case generation.


With test case generation all test cases are essentially direct derivatives from the analysis of a previous test case. We build a formula that describes a run of the program, negate a few constraints or add on some new ones, and generate a new input. Continue until boredom (or some slightly more scientific measure). What I am getting at is that all the required information for the next test is contained within the path executed by a previous test. Now consider an overflow on Windows where we can corrupt the most significant byte of a function pointer that is eventually used. If you decide to go down the ‘heap spray’ route to exploit this vulnerability you immediately hit a crucial divergence from test case generation. In order to successfully manipulate the structure of a programs heap(s) we will almost always require information that is not contained in the path executed to trigger the vulnerability initially. Discovering heap manipulation primitives is a problem that requires an entirely different approach to the test case generation approach of data flow analysis + decision procedure over a single path. It is also not a problem that will likely ever be solved by test case generation research as it really isn’t an issue in that domain. Whole classes of vulnerabilities relating to memory initialisation present similar difficulties.

What about vulnerability classes that fit slightly better into the mould carved out by test generation research? One of the classes I considered during my thesis was write-4-bytes-anywhere style vulnerabilities. Presuming we have a list of targets to overwrite in such cases (e.g. the .dtors address) this is a solvable problem. But what if we only control the least significant byte (or word) and can’t modify the address to equal one of the standard targets? Manually one would usually see what interesting variables fall within the controllable range, looking for those that will be at a static offset from the pointer base. But what is an ‘interesting variable’? Lets assume there are function pointers within that range. How do we automatically detect them? Well we’d need to monitor the usage of all byte sequences within the range we can corrupt. It’s a problem we can approach using data flow/taint analysis but once you start to consider that solution it starts to look a lot like a multi-path analysis problem but over a single path. We are no longer considering just data that is definitely tainted by user input, we are considering data that might be, and as we can only control a single write we have different ‘paths’ depending on what bytes we choose to modify….. and we’re doing this analysis over a single concrete path? Fun.

I guess the core issue is that test-case generation and exploit generation are close enough that we can get adequate results by applying the algorithms developed for the former to the latter. To get consistently good results though we need to consider the quirks and edge cases presented by exploit generation as a separate problem. Obviously there are many useful algorithms from test case generation research that can be applied to exploit generation but to apply these blindly misses opportunities for optimisations and improvements (e.g. the formula complexity issue mentioned). On the other hand there are problems that will likely never be considered by individuals working on test case generation; these problems will require focused attention in their own right if we are to begin to generate exploits for certain vulnerability classes.

Automatic exploit generation: Lessons learned so far

Here are a couple of thoughts that are bouncing around in my head as I come to the concluding stages of my v1 prototype. I’ve made a number of design decision in the initial implementation that I now see issues with, but hopefully by documenting them v2 will be better!

Using in-process analysis tools might not be such a good idea: Early on I decided to use dynamic analysis to gather information about taint data propagation and path conditions. Due to previous work (such as catchconv) using dynamic binary instrumentation frameworks, like Valgrind, I pretty much immediately decided I would do the same. After writing a couple of basic apps for Valgrind, Pin and DynamoRio, I eventually settled on Pin due to its cross platform support and C++ codebase. One critical factor I ignored is that these tools really aren’t designed with malicious code in mind. So, when you do things like trash a stored instruction pointer it can really confuse the DBI tool.

Other problems can occur if the vulnerability ends up writing over several hundred megabytes of junk in the application address space. This can lead to difficult to debug problems, where the memory in use by the injected analysis client is being corrupted, as well as that of the application under test.

More basic, but just as time consuming, problems stem from the fact that these in-process analysis clients are rather difficult to debug once something goes wrong. The three frameworks mentioned vary in their support for debugging and error logging, but in general it is exceedingly annoying to debug anything non-trivial. Simple segfaults have eaten hours of my time and often you are left resorting to printf based ‘debugging’.

The final issue I’ve come across is obvious, but should still be mentioned. Complex runtime instrumentation, such as dataflow analysis, really effect the responsiveness and runtime of the application. My current code, which is admittedly incredibly unoptimised, can increase the runtime of ls from milliseconds to about 20 seconds. This isn’t much of an issue if you don’t need to interact with the application to trigger the vulnerability, but in a case where some buttons need to be clicked or commands entered, it can become a significant inconvenience.

Assisted may be better than automated: The idea of this project is to investigate what vulnerability classes are automatically exploitable, and to develop a prototype that can show the results. I’ve achieved this goal for a sufficient variety of vulnerabilities and shown that automation is in fact possible.

There is a but here though; to continue this project would require constant attention and coding to replace the human effort in exploit generation each time a new class of vulnerability comes along, or a change in exploit technique. As I’ve moved from basic stack overflows to considering more complicated scenarios, the differences in exploit types become more time consuming to encode. Because of this, I intend (when I implement v2 of the tool in the coming months) to move away from complete automation. By putting the effort into providing a decent user interface, it will be possible to inform an exploit writer of the results of data flow and constraint analysis and have them make an educated judgement on the type of exploit to attempt, and specify some parameters. Working from this point of view should make the entire tool much less effort to port between operating systems also.

Information on memory management is very important: This is an obvious point for anyone that has had to write heap exploits in the last 5 years or so. It is near impossible to automatically generate a Linux heap exploit without having some information on the relationship between user input and the structure of the processes heap. When manually writing an exploit we will often want to force the program to allocate large amounts of memory, and the usual way to do this involves jumping into the code/disassembly and poking around for a while until you find a memory allocation dependent on the size of some user supplied field, or a loop doing memory allocation with a user influenceable bound.

Essentially, to have a solution that takes care of both scenarios we need a way to infer relationships between counters and program input. The first paper to discuss how to do this using symbolic execution was published in March of this year, and is a good read for anyone considering implementing this kind of tool.

As I hadn’t added loop detection, or other required functionality described in that paper, my current tool is unable to do the analysis described. I consider this a rather annoying drawback, and it will be among my highest priorities for v2. Hacky solutions are possible, such as modelling the result of strlen type functions on user input, but this would miss a number of scenarios and is in general quite an ugly approach.

Extending to new vulnerability classes

One of the things I really want to support is automatic generation of exploits for modern heap based vulnerabilities. At the moment I have other features to implement so this has gotten pushed back for the time being. In the meantime, I wanted to see how hard it was to extend my current functionality from stack overflows that trash the EIP to other vulnerability/exploit combinations. So, yesterday I went and found an example from an wargame I used play. It contains a pretty silly vulnerability, as follows:

(The aim here was to see how hard it was to extend my current code, not to see how complicated I could make a test case. The array pointed to by input is controllable by the user and 256 bytes in size. The function some_func is some benign function that just exits the program)

void func_ptr_smash(char *input)
    void (*func_ptr)(int);
    char buffer[248];
    func_ptr = &some_func;
    strcpy(buffer, input);

    (*func_ptr) (z);

Extending the tool turned out to be pretty simple. In a stack smash that overwrites the stored EIP we attempt to generate a query that expresses the constraint memLocation == trampolineAddr, where memLocation is the value in ESP at the ret instruction, and trampolineAddr is the address of some usable trampoline.

Modifying this to handle a function pointer overwrite can be done in a couple of ways, depending on what parts of the address space are randomised and how generic we want the solution to be. The most straight forward solution is simply to treat a function pointer overwrite like a slight twist on the previous situation. Essentially, instead of a ret instruction popping a tainted value into the EIP, which we can then redirect to a trampoline, we have a call instruction where the argument is tainted and can be sused to redirect to a trampoline. So, instead of generating a constraint on the value of ESP we have to express the constraint on whatever register/memory location the call instruction uses as an argument.

Another potential approach is usable if some non-randomised data locations exist that we can use as a shellcode buffer. Once again the same data flow analysis can be used to find the location of a suitable home for shellcode in these areas. In this case we avoid the requirement for a register to contain the address of one of these buffers and can just jump right into it by generating a constraint that specifies the operand to the call is equal to the static memory address of our shellcode.

Here is an example run of the tool in which we use the latter method. I tested it on Ubuntu 8.04 which has a non-randomised heap by default and thus we can hardcode the address of shellcode buffers on the heap. The vulnerable program was compiled with -O0 -fno-stack-protector -D_FORTIFY_SOURCE=0, otherwise gcc would have repositioned the overflow buffer and optimised the call so that the address is calculated at compile time.

In conclusion, my current approach was easily extendible in this case due to the similarity between a function pointer overwrite and smashing the stored EIP. Both cases essentially only differ at the point where the tainted memory location or register is moved to the EIP. They are detectable in exactly the same way and have the same symptom; namely, the attempted movement of tainted data into the EIP register. I would hypothesise that any vulnerability* with the same symptom can be dealt with in a similar way. So then we must ask, what other symtoms are there? Well, what can cause a program to crash? We have seen the case where the program attempts to execute data at an unmapped memory location, so that leaves invalid reads and writes.

Exploiting vulnerabilities detected via an invalid read/write

Old glibc heap exploits are a simple example of those that would be detectable as a result of an invalid write. I won’t go into the details of the method but the unlink macro essentially has the following effect, where next->fd and next->bk are under our control:

 *( next->fd + 12 ) = next->bk
 *( next->bk + 8 ) = next->fd

In this case the vulnerability will probably be discovered when the application tries the first write. This is a crucial difference between the earlier vulnerabilities and this one when considering how to automatically generate an exploit. Detecting the potential for an exploit is still simple – when an instruction writes memory we can simply check the destination operand to see if it is tainted**. The problem now becomes ‘how do we automatically determine a useful location to write?’. Assuming all data sources are randomised our options are limited somewhat. Depending on the protections in place the DTORS/GOT might be usable. Other than that (and depending on what the value we are corrupting actually points to) we could potentially just change the lower bytes of the location being written and attempt to modify some useful program variable on the heap***. This has the disadvantage of requiring some sort of input from the user, as determining what is a useful variable would seem to be mostly application specific.

If the location being written is on the stack we could potentially modify the lower bytes to change a stored EIP/EBP and then proceed in the same fashion as before. To automate this we could note the value of the ESP when a call instruction occurs and calculate the difference between this value and the location of the variable being written.

To sum these options up we have two potential output types. The first is a direct exploit; It writes the DTORS/GOT or changes the lower bytes of a stack variable to modify a stored EIP and may or may not be possible depending on the protections in place and the location being written. The second is a new program input that may lead to another crash at a different location. It is basically another fuzz input except with potentially some program variables corrupted. In this case, the result is that the program can continue execution and we hope that it hits another exploitable crash further on****.

For a read from an invalid address we also have a couple of options. If the variable being read into is later used for something such as memory allocation or as a bound on a loop/function involved in moving memory we might attempt to control this value. To do this automatically would require some form of static analysis to determine if the variable was ever used in such a context (or perhaps multiple runs of dynamic analysis). Once again, as in the write case, we also have the option to just manipulate the destination read in such a way that it is any valid address and hope that another vulnerability is later triggered. Unlike the write case this is pretty trivial though as we can just read from any address in the .text section.

* Obviously this doesn’t apply to certain vulnerability classes. It applies to most I can think of that we will exploit by somehow changing the execution pointer. Not trust problems, many race conditions, other design flaws etc.
** Some slightly more complicated analysis might be required here as sometimes a destination operand in a write can be legitimately tainted but restricted to the bounds of some safe chunk of data
*** We could also change the metadata of some other chunks on the heap but right now (3am in the morning) I can’t think of an obvious way to leverage this for code execution
**** In some cases the address written might be constrained in such a way that a heap spray is required to ensure it is mapped. Same idea applies for reads. Another potential problem is that all writable data stores might be randomised. In this case heap spraying could again be useful.

Morphing shellcode using CFGs and SAT

A friend of mine is working on a project that involves building a metamorphic engine for x86 assembly. One of the core parts of such a project is a context free grammar describing valid mutations for a given instruction. To use one of his examples, an instruction to put v in r can be modelled in a BNF style grammar as follows:

put_v_in_r(v1,r1) := pushl_v(v1) popl_r(r1) | movl_v_r(v1,r1)

This could be quite useful in the process of automatic exploit generation. I expect the user to provide shellcode expressing what they want the exploit to do, but what if that shellcode is constrained by conditionals in the program? e.g. the shellcode is \x41\x42\x43\x44 but there is a conditional in the program that causes it to abort if the byte \x41 is detected in the input stream.

One solution in this situation, is to simply ask the user for different shellcode, but in the presence of complex modifications and conditions it quickly becomes impossible to provide any kind of meaningful feedback on what they should do to pass the filters. How about an automated solution? We have the conditions in propositional form and, due to the other project mentioned, we also have access to a grammar of potential shellcode mutations. If we can combine the two into a new propositional formula, describing the effect of mutating the shellcode using this grammar and the conditions from the program, we might be able to use the power of SMT/SAT solvers to brute force a solution! If a solution is found then we can preserve the effects of the original shellcode, as well as passing the filters.

The main difficulty in implementing this solution comes from encoding the grammar in propositional form. The typical solution to encoding a transition relation as a propositional formula involves iteratively applying the transition relation to existing states until a fixed point is reached. That is, starting with our original shellcode we would expand the first non-terminal to one or more potential shellcodes. We then expand these in the same fashion, and so on until no further new states are added; we then have the set of all potential shellcodes given the starting shellcode and the provided grammar. Obviously, there can be problems storing the states if the number grows exponentially on each expansion, but this is a common verification problem and there are a number of approaches to resolve it, varying from “hope it doesn’t happen” to using a compact storage mechanism like binary decision diagrams. We can then extract the states that contain no non-terminals, i.e. they are a valid x86 instruction stream, conjoin this with the path condition and ask our SAT/SMT solver to enumerate the shellcodes that satisfy these conditions.

There is a bit of a snag with this fixed point approach though. What if our grammar contains an expansion A ->* aB , which states that A expands to, some terminal, a and, some non-terminal, B in one or more steps, and also the rule B ->* A? In this case we are no longer guaranteed to reach a fixed point, as we can enter an infinite loop. The obvious solution is to transform our grammar into one that doesn’t contain such rules. We can do this by setting an upper bound, k, on the number of such recursive iterations allowed and including these expansions as new non-terminals. This new grammar has lost some of the potential outcomes of the original but it can now be processed using our fixed point approach. It should be noted that this upper bound on the number of self-recursions isn’t quite as artificial or as limiting as it may seem. There will always be some upper bound on the size of the buffer used for shellcode and thus it may be practical, in some cases, to use quite a low value of k.

(In fact, for a real world implementation it is well worth considering how to involve the length of the buffer we intend to use as we perform the fixed point computation. There is no reliable way to favour shorter shellcodes that also satisfy the program constraints, but one optimisation would be to exclude any shellcodes that have already exceeded the length limit from future expansions.)