Thoughts, musings, knowledge, etc. about digital forensics. As well as how computer science, IT (information technology) and IS (information security) relate.
I was at a training class last year and the instructor made a good point about the TV show CSI (Crime Scene Investigation). While the actual techniques/methods/etc. the show uses may not always be accurate with respect to real life (some are, some aren’t), the characters do perform a lot of experiments. If you don’t know the answer to a question, you can do some research and hope there is an answer somewhere, or you can perform some experimentation yourself.
One thing that I see on a fairly regular basis is confusion between deductive and inductive reasoning. Both types of reasoning play different roles in investigations/forensics/science/etc. The difference between the two is sometimes hard to define. Here are two common defintions:
1. With deductive reasoning, the conclusions are contained, whether explicit or implicit, in the premises. With inductive reasoning, the conclusions go beyond what is contained in the premises.
2. The conclusions arrived at using (correct) deductive logic are necessarily true, meaning they must be true. The conclusions arrived at using inductive logic, are not necessarily true, although they may be.
An example might clarify things (taken from a philosophy class I took years ago):
In this case, since I studied, I got an A on the exam. The conclusion (I got an A on the exam) is contained implicitly in 1 and 2. For the geeks in us, here is a proof:
With inductive reasoning however:
Just because I got an A on the exam doesn’t imply I studied, I could have cheated. For the geeks in us, here is an (incorrect) proof:
The key in these examples in is parts 1 and 2. With deductive reasoning we had B and followed the If chain [(IF B then C) ^ B yields C]. With the inductive reasoning we have no B. In terms of logic this is confusing an “if” statement with an “if and only if”, where the former requires one direction of truth and the latter requires two directions of truth.
So how does this play into investigations/forensics/etc.? The idea is to be careful the the conclusions drawn. For instance, (relating back to the blog post about context) if an examiner finds the string “hacker” on a hard disk, the hit doesn’t necessarily mean that a “hacker” was on the system, nor does it necessarily mean that “hacker” tools were used. The data around the string would (hopefully) provide more context. Although even the presence of “hacker” tools doesn’t mean that the suspect actually used them, nor does it necessarily mean that the suspect even introduced them to the system. These types of questions are often raised with “The Trojan Defense”.
One (common) misunderstanding of deductive and inductive reasoning is with our legal system. Our legal system depends heavily on inductive reasoning (inferences). For instance take the case with Keith Jones testifying at the UBS trial. Keith Jones testified about what was found on UBS systems, various different sources of logs (e.g. WTMP logs, provider logs, etc.) and his analysis of the information. Does this prove with 100% certainty that the suspect (Duronio) actually committed the crime? No it doesn’t. However with a substantial amount of evidence, a jury could reach the conclusion that the standard of “beyond a reasonable doubt” has been met.
Another example of deductive vs. inductive reasoning is with “courts approving digital forensic tools”. First courts aren’t in the business of approving digital forensics tools. They may allow a person to testify about the use and conclusions drawn using the tools. This is fundamentally different from saying “tool XYZ is approved by this court”. The reasoning for allowing an examiner to testify using the results obtained from a tool typically involves a trusted third party. Essentially one (or more) third parties comes to a conclusion about the correctness of a tool. So the decision about allowing the original examiner to testify about the results found using the tool depends on what a third party thinks. This leads to the question: Just because a third party thinks so, does it mean it’s guaranteed to be true? Perhaps yes, perhaps no. [Note: I'm not commenting about any specific digital forensics tool, this could apply to any situation involving any type of tool or even process. This is one type of review used when considering whether or not to allow a scientific tool/process/technique into court.]
One concept that pervades digital forensics, reverse engineering, exploit analysis, even computing theory is that in order to fully understand information, you need to know the context the information is used in.
For example, categorize the following four pieces of information as either code or data:
1) push 0×6F6C6C65
2) “hello” (without the quotes)
3) 448378203247
4) 110100001100101011011000110110001101111
Some common answers might be:
1) Code (x86 instruction)
2) Data (string)
3) Data (integer)
4) Code or Data (unknown)
Really, all four are encoded internally (at least on an intel architecture) the same way, so they’re all code and they’re all data. Inside the metal box, they all have the same binary representation. The key is to know the context in which they’re used. If you thought #1 was code, this is probably based on past experience (e.g. having seen x86 assembly before). If the four ascii bytes ‘h’ ‘e’ ‘l’ ‘l’ ‘o’ were in a code segment, then it is possible that they were instructions, however it is also that they were data. This is because code and data can be interspersed even in a code segment (as is often done by compilers.)
Note: Feel free to skip the following paragraph if you’re not really interested in the theory behind why this is possible. The application of information context is in the rest of the post.
The reason code and data can be interspersed is often attributed to the Von Neumann architecture, which stores both code and data in a common memory area. Other computing architectures, such as the Harvard architecture have seperate memory storage areas for code and data. However, this is an implementation issue, as information context (or lack thereof) can also be seen in Turing machines. In a Universal Turing Machine (UTM), you can’t distinguish between code and data if you encode both the instructions to the UTM and the data to the UTM with the same set (or subset) of tape symbols. Both the instructions for the UTM and the data for the UTM sit on the tape, and if they’re encoded with the same set (or subset) of tape symbols, then just by looking at any given set of symbols, there isn’t enough information about how the symbols are used to determine if they’re instructions (e.g. move the tape head) or data. This type of UTM would be more along the lines of a Von Neumann machine. A UTM which was hard-coded (via the transition function) to use different symbols for instructions and data would be more along the lines of a Harvard machine.
One area where information context greatly determines understanding of code and data is in reverse engineering, specifically executable packers/compressors/encryption/etc. (Note: executable packers/compressors/encryption/etc. are really examples of self-modifying code, so this concept extends to self-modifying code as well). Here’s an abstract view of how common block-based executable encryption works (e.g. ASPack, etc.):
| Original executable | — Packer —> | Encrypted data |
The encrypted data is then combined with a small decryption stub resulting in an encrypted executable that looks something like:
| Decryption stub | Encrypted data |
When the encrypted executable is run, the decryption stub decrypts the encrypted data, yielding something that can look like:
| Decryption stub | Encrypted data | Original executable |
(Note: this is an abstract view, there are of course implementation details such as import tables, etc. It’s also possible to have the encrypted data decrypted in place).
The encrypted data is really code, just in a different representation. The same concept applies when you zip / gzip / bzip / etc. an executable from disk.
Another example where the duality between code and data comes into play is with exploits. Take for example SEH overwrites. An SEH overwrite is a mechanism for gaining control of execution (typically during a stack based buffer overflow) without using the return pointer. SEH stands for Structured Exception Handling, an error/exception handling mechanism used on the Windows operating system. One of the structures used to implement SEH sits on the stack, and can be overwritten during a stack-based buffer overflow. The structure consists of two pointers, and looks something like this:
| Pointer to previous SEH structure | Pointer to handler code |
Now in theory, a pointer, regardless of what it points to, is considered data. The value of a pointer is the address of something in memory, hence data. During an exploit that gains control by overwriting the SEH structure, the pointer to the previous SEH structure is typically overwritten with a jump instruction (often a jump to shellcode.) The pointer to handler code is typically overwritten with the address of a set of pop+pop+ret instructions. The SEH structure now looks like:
| Jump (to shellcode) | Pointer to pop+pop+ret |
The next thing that happens is to trigger an exception so that the pop+pop+ret executes. Due to the way the stack is set up when the exection handling code (now pop+pop+ret) is called, the ret transfers control to the jump (to shellcode). The code/data duality comes into play since this was originally a pointer (to the previous SEH structure) but is now code (a jump). In the context of the operating system, it treats this as data, but in the context of a pop+pop+ret it is treated as code.
Information context goes beyond just code/data duality. Take for example string searches (a.k.a. keyword searches) which are commonly used in digital forensic examinations to generate new leads to investigate. Assume a suspect is accused of stealing classified documents. Searching a suspect’s media (hard disk, usb drive, digital camera, etc.) for the string “Classified” (amongst other things) could seem prudent. However a hit on the word “Classified” does not necessarily suggest guilt, but it does warrant further investigation. For instance the hit for “Classified” could come from a classified document, or the hit could come from a cached HTML page for “Classified Ads”. Again the key is to understand the context in which the hit comes from.
To summarize this post in a single sentence: Information context can be vital in understanding/analyzing what you’re looking at.
It’s been quite some time (over a month) since I made a post (to here or the forensically sound yahoo group). I’ve had a whirlwind of client work, including teaching at a number of SANS conferences. I did get a bit of press coverage while at the San Jose SANS conference. The press came to me seeking information about Schwarzenegger’s ethnic comments. Let me state that I have absolutely NO knowledge about the issue outside of what has been presented in the news. I have not been contacted by anyone other than NBC11 about this.
A reporter from NBC11 showed up at the end of one of the days of the conference, and asked me some questions about what is and is not possible. The “interview” made an 8 second blurb onto the nightly news, and here is a link to a web write-up of the “interview”. To clarify the comments made by me, they were pieced together from multiple different sentences. I did not see anything on the govenor’s website that appeared to be related to the ethnic comments. I did not perform a thorough search.
On a slightly different note, I registered the domain forensiccomputing.us and pointed it at this blog. 
So after the whirl of feedback I’ve received, we’ve moved discussions of this thread from Richard Bejtlich’s blog to a Yahoo! group. The url for the group is: http://groups.yahoo.com/group/forensically_sound/
We now return this blog to it’s regularly scheduled programming…
I was reading Craig Ball’s (excellent) presentations on computer forensics for lawyers at (http://www.craigball.com/articles.html). One of the articles mentions a definition for forensically sound duplicate as:
“A ‘forensically-sound’ duplicate of a drive is, first and foremost, one created by a method which does not, in any way, alter any data on the drive being duplicated. Second, a forensically-sound duplicate must contain a copy of every bit, byte and sector of the source drive, including unallocated ‘empty’ space and slack space, precisely as such data appears on the source drive relative to the other data on the drive. Finally, a forensically-sound duplicate will not contain any data (except known filler characters) other than which was copied from the source drive.”
There are 3 parts to this definition:
This definition seems to fit when performing the traditional disk-to-disk imaging. That is, imaging a hard disk from a non-live system, and writing the image directly to another disk (not a file on the disk, but directly to the disk.)
Picking this definition apart, the first thing I noticed (and subsequently emailed Craig about) was the fact that the first part of the definition is often an ideal. Take for instance imaging RAM from a live system. The act of imaging a live system changes the RAM and consequently the data. The exception would be to use a hardware device that dumps RAM (see “A Hardware-Based Memory Acquisition Procedure for Digital Investigations” by Brian Carrier.)
During the email discussions, Craig pointed out an important distinction between data alteraration inherent in the acquisition process (e.g. running a program to image RAM requires the imaging program to be loaded into RAM, thereby modifying the evidence) and data alteration in an explicit manner (e.g. wipe the source evidence as it is being imaged.) Remeber, one of the fundamental components of digital forensics is the preservation of digital evidence.
A forensically sound duplicate should be acquired in such a manner that the acquisition process minimizes the data alterations inherent to data acquisition, and not explicitly alter the source evidence. Another way of wording this could be “an accurate representation of the source evidence”. This wording is intentionally broad, allowing one to defend/explain how the acquisition was accurate.
The second part of the definition states that the duplicate should contain every bit, byte, and sector of the source evidence. Similar to the first part of the definition, this is also an ideal. If imaging a hard disk or other physical media, then this part of the definition normally works well. Consider the scenario when a system with multiple terabytes of disk storage contains an executable file with malicious code. If the size of the disk (or other technological restriction) prevents imaging every bit/byte/sector of the disk, then how should the contents of the file be analyzed if simply copying the contents of the file does not make it “forensically sound”? What about network based evidence? According to the folks at the DFRWS 2001 conference (see the “Research Road Map pdf“) there are 3 “types” of digital forensic analysis that can be applied:
- Media analysis (your traditional file system style analysis)
- Code analysis (which can be further abstracted to content analysis)
- Network analysis (analyzing network data)
Since more and more of the latter two types of evidence are starting to come into play (e.g. the recent UBS trial with Keith Jones analyzing a logic bomb), a working definiton of “forensically sound duplicate” shouldn’t be restricted to just “media analysis”. Perhaps this can be worded as “a complete representation of the source evidence”. Again, intentionally broad so as to leave room for explanation of circumstances.
The third part of the definition states that the duplicate will not contain any additional data (with the exception of filler characters) other than what was copied from the source medium. This part of the definition rules out “logical evidence containers”, essentially any type of evidence file format that includes any type of metadata (e.g. pretty much anything “non dd”.) Also compressing the image of evidence on-the-fly (e.g. dd piped to gzip piped to netcat) would break this. Really, if the acquisition process introduces data not contained in the source evidence, the newly introduced data should be distinguishable from the duplication of the source evidence.
Now beyond the 3 parts that Craig mentions, there are a few other things to examine. First of all is what components of digital forensics should a working definition of “forensically sound” cover? Ideally just the acquisition process. The analysis component of forensics, while driven by what was and was not acquired, should not be hindered by the definition of “forensically sound”.
Another fact to consider is that a forensic exam should be neutral, and not “favor” one side or the other. This is for several reasons:
- Digital forensic science is a scientific discipline. Science is ideally as neutral as possible (introducing as little bias as possible). Favoring one side or the other introduces bias.
- Often times the analysis (and related conclusions) are used to support an argument for or against some theory. Not examining relevant information that could either prove or disprove a theory (e.g. inculpatory and exculpatory evidence) can lead to incorrect decisions.
So, the question as to what data should and shouldn’t be included in a forensically sound duplicate is hard to define. Perhaps “all data that is relevant and reasonably believed to be relevant.” The latter part could come into play when examining network traffic (especially on a large network). For instance, when monitoring a suspect on the network (sniffing traffic) and I create a filter to only log/extract traffic to and from a system the suspect is on, I am potentially missing other traffic on the network (sometimes this can even be legally required as sniffing network traffic is considered in many places a wiretap). A definition of “forensically sound duplicate” shouldn’t prevent this type of acquisition.
So, working with some of what we have, here is perhaps a (base if nothing else) working defintion for “forensically sound”:
“A forensically sound duplicate is a complete and accurate representation
of the source evidence. A forensically sound duplicate is obtained in a
manner that may inherently (due to the acquistion tools, techniques, and
process) alter the source evidence, but does not explicitly alter the
source evidence. If data not directly contained in the source evidence is
included in the duplicate, then the introduced data must be
distinguishable from the representation of the source evidence. The use
of the term complete refers to the components of the source evidence that
are both relevant, and reasonably believed to be relevant.”
At this point I’m interested in hearing comments/criticisms/etc. so as to improve this defintion. If you aren’t comfortable posting in a public forum, you can email me instead and I’ll anonymize the contents
Up until now, this thread of posts has been rather theoretical, talking about Turing machines, etc. the only time there was some source code was for showing a program that can print out a description of itself (its source code).
Well, one problem with the self-replication method for getting a copy of a program’s description is that the program needs to contain a partial copy (and it computes the rest). This can cause some nasty code bloat. The method many viruses use is to copy themselves from another spot in memory.
For instance, if you have an executable file being run in memory (the host), and a portion of the executable code is a “virus” (a.k.a viral code), then by virtue of the fact that the host program is running in memory, a copy of the virus code is also in memory. All a virus needs to do is locate the start of itself in memory and copy it out. No need for the recursion theorem, no need to carry a partial copy of itself.
Some simple methods for finding where the virus is in memory are:
To accomplish the first method can require some careful forethought. In essence, the virus has to find a location in memory that is normally not taken by some portion of code or data. When the “virus” part of the executable code runs, it can copy itself out of memory since it knows where it starts (and assuming it also knows the size)
The second method requires that the virus (rather the virus’s author) understand a bit about the loading process that the executable file undergoes when it is loaded (assuming the virus is infecting a file on disk rather than a process running in memory). The virus can then “hard-code” the address of the viral code in the newly infected host. When the newly infected host file gets executed (e.g. by the user) and control gets transferred to the virus portion of the host, the virus knows where it is in memory since it was recorded by the previous incarnation.
The third method normally requires a bit of hackery. When the virus portion of the host file gets control of execution it needs to perform some sort of set of instructions to figure out where it is. The classic method of doing this in Intel x86 assembly is:
0×8046453: CALL 0×8046458
0×8046458: POP EAX
The first line calls a function which starts at the second line. The call instruction first pushes the address of the next instruction (which would be 0×8046458) onto the stack, and then transfers control to the operand of the call (which is also 0×8045458). The second line pops the last value that was pushed onto the stack (the address in memory) and saves a copy in the EAX register.
The fourth method simply requires that the virus have a static signature, and that once control of execution gets transferred to the virus portion of the host file, the virus scan memory until it finds the signature. Of course there is the possibility for a false positive, but by carefully choosing the signature, this could be reduced.
There is another method that I haven’t described, and that is that the virus can obtain a copy of itself from a file on disk. This generally works for script based viruses, but also has the potential to work for other types of executable files. This was the method used by the biennale.py virus.
This ends this thread of posts (at least for a little while). The original reason for creating this thread was to explain a little bit about how viruses work. This is useful for computer forensic analysts/examiners examining viruses, since understanding the basics goes a long way when examining actual specimens. Of course there is much more than the simplification given in this series of posts, but hopefully this can provide some guidance.
In this post I’ll cover the proof of the Recusion theorem (see Self Replicating Software - Part 1 - The Recursion Theorem).
The proof for the Recursion theorem is a constructive proof, meaning that a Turing Machine (TM) that can reference its own description is constructed. This proof was taken from Michael Sipser’s “An Introduction to the Theory of Computation”.
Before we get into the proof of the Recursion Theorem, we’ll need a special TM. There is a computable function q which can print out the description of a TM that prints the input that was given to q.
So, if we have a machine P_w, that prints out w (where w is input to the machine), q(w) prints out the description of TM_w. The construction of such a machine is relatively simple. Lets call the machine that computes q(w) Q_w. Here is an informal description:
Q_w = "
Step 1: Create a machine P_w ="
Step 1.1: print w"
Step 2: Print <P_w>
Recall that <P_w> is notation for “The description of the Turing Machine P_w”.
Last time, we had a TM called TM_T that took two inputs, one being the description of a TM, the other input called w, and performed some computation with it. We also had another TM called TM_R which took one input, namely the same w passed to TM_T and performed the same computation as TM_T (on the description of a TM) but with it’s own description (<TM_R>) filled in. Since TM_R only takes one input, w, the description of TM_R is internal to TM_R.
The TM_R is constructed in a special manner, namely it has 3 components. Let’s call these TM_A, TM_B, and TM_T where TM_T is the same TM_T referenced before. TM_A is a special TM that generates a description of TM_B and TM_T. TM_B computes the description of TM_A. The tricky part is to avoid creating a cyclic reference. In essence, you can’t have TM_A print out <TM_B><TM_T> and then have TM_B print out <TM_A> since they reference each other directly. The trick is to have TM_B calculate <TM_A> by using the output from TM_A.
Think about this abstractly for a moment, if TM_A were to print some string w, then <TM_A> is simply q(w) (a.k.a. the description of a machine that prints w). In case of the recursion theorem, TM_A is the machine that prints out <TM_B><TM_T> and TM_B prints the description of a machine that prints out <TM_B><TM_T>
So, the proof goes as follows:
TM_R(w) = "
TM_A which is P_<TM_B><TM_T>
TM_B which is Q_w
TM_T which is specified ahead of time
Step 1: Run TM_A
Step 2: Run TM_B on the output of TM_A
Step 3: Combine the output of TM_A with the output of TM_B and w
Step 4: Pass control to TM_T
"
Think about this, TM_A is a machine that prints out <TM_B><TM_T>. <TM_B> computes the description of a machine that prints out <TM_B><TM_T>. Note the following:
TM_A = P_<TM_B><TM_T>
<TM_A> = <P_<TM_B><TM_T>>
<P_<TM_B><TM_T>> = Q(<TM_B><TM_T>)
TM_B = Q(w) where w is <TM_B><TM_T>
If TM_T prints the description, then TM_T is called a quine. For TM_T to be a virus, it would “print” the description to a file (somewhere on the tape).
We’ve covered a fair amount of theory between this post and the last post so let’s put it into some concrete code. In this example, TM_T will just print the description of the machine. This type of program is known as a quine or selfrep.
[lost@pagan code]$ grep -n “.*” quine.py
1:#!/usr/bin/python
2:
3:def TM_T(M):
4: print M;
5:
6:def TM_B(w):
7: computedA = ‘# Below is TM_A’ + chr(0xA) + ’s = ‘ + ‘”‘ + ‘”"‘ + w + ‘”‘ + ‘”";’ + chr(0xA) + ‘TM_B(s);’;
8: TM_T(w + computedA);
9:
10:# Below is TM_A
11:s = “”"#!/usr/bin/python
12:
13:def TM_T(M):
14: print M;
15:
16:def TM_B(w):
17: computedA = ‘# Below is TM_A’ + chr(0xA) + ’s = ‘ + ‘”‘ + ‘”"‘ + w + ‘”‘ + ‘”";’ + chr(0xA) + ‘TM_B(s);’;
18: TM_T(w + computedA);
19:
20:”"”;
21:TM_B(s);
[lost@pagan code]$ clear
[lost@pagan code]$ grep -n “.*” quine.py
1:#!/usr/bin/python
2:
3:def TM_T(M):
4: print M;
5:
6:def TM_B(w):
7: computedA = ‘# Below is TM_A’ + chr(0xA) + ’s = ‘ + ‘”‘ + ‘”"‘ + w + ‘”‘ + ‘”";’ + chr(0xA) + ‘TM_B(s);’;
8: TM_T(w + computedA);
9:
10:# Below is TM_A
11:s = “”"#!/usr/bin/python
12:
13:def TM_T(M):
14: print M;
15:
16:def TM_B(w):
17: computedA = ‘# Below is TM_A’ + chr(0xA) + ’s = ‘ + ‘”‘ + ‘”"‘ + w + ‘”‘ + ‘”";’ + chr(0xA) + ‘TM_B(s);’;
18: TM_T(w + computedA);
19:
20:”"”;
21:TM_B(s);
[lost@pagan code]$ ./quine.py | md5sum; md5sum quine.py
dd9958745db4735ceab8101cae0a15a8 -
dd9958745db4735ceab8101cae0a15a8 quine.py
(Note the md5sum of the output and the md5sum of the input are the same)
Let’s analyze this piece by piece. In this program, TM_A is represented by lines 11 - 21. TM_A is the description of TM_B and TM_T. Notice that TM_A is a copy of (the descriptions of) TM_B and TM_T and stuck in triple quotes (one method in Python for representing strings).
TM_B is on lines 6-10 (including the comment “# Below is TM_A”). Recall that TM_B computes the description of TM_A using the output from TM_A. The input to TM_B is the output of TM_A, which was the description of TM_B and TM_T. Finally, the output from TM_B is transferred to TM_T which prints the contents.
Here is the logic flow:
Lines 11-20 calculate P_<TM_B><TM_T>
Line 21 takes the output (s) and passes it to TM_B
Line 7 computes the description of TM_A (computedA) from the output of TM_A (which was passed to TM_B)
Line 8 combines the computed description of TM_A with the output of TM_A and passes the whole string to TM_T.
Line 4 prints the description of the machine
In the case of a virus, instead of printing the description to the screen, a virus would print the description to another python file.
What we’ve done is prove (from a theoretical point of view) why viruses can exist. The fact viruses exist already tells us this, but we’ve now proven from an abstract view that they do exist. We’ve also given a basic algorithm for creating viruses, and shown how to implement something simple in Python.
In the next post we’ll cover another method (perhaps more commonly used) a virus can use to get it’s own description (which doesn’t depend on the recursion theorem).
This is the first in a multi part post about computing theory and self replicating software. This post assumes you have knowledge and understanding of a Turing Machine (abbreviated TM). If you aren’t familiar with Turing Machines (TMs) then you may want to take a look at the Wikipedia entry on the topic at http://en.wikipedia.org/wiki/Turing_machine before continuing. Much of the material for this post comes from Michael Sipser’s “An Introduction to the Theory of Computation”.
Let’s assume there is a computable function t which takes two inputs and yields one output. This function can be stated as:
t: E* x E* -> E*
Call the TM that implements this function TM_T. Now if one of the inputs that TM_T takes is the description of a TM (perhaps a description of TM_T or the description of another TM) we can call TM_T a “Meta TM”, meaning it operates on TMs (more accurately, descriptions of TMs). TM_T could do a number of things with the description, such as emulate it (making TM_T a universal TM), or print the description to the TM’s tape (making TM_T a “quine”). For the purpose of the recursion theorem, it’s irrelevant what TM_T does with the description. So TM_T can be written as taking two inputs:
TM_T(<TM>, w)
Where <TM> is a description of a TM. The other argument (w) could be input to the TM described by the <TM> argument.
Now, assume there is another computable function r which takes one parameter, w, the same w passed as the second argument to function t. Function r can be stated as:
r: E* -> E*
Call the TM that implements this function TM_R. So TM_R can be written as taking one input:
TM_R(w)
The TM_R is described by <TM_R>.
The recursion theorem states (in terms of functions r and t):
r(w) = t(<TM_R>, w)
alternatively
TM_R(w) = TM_T(<TM_R>, w)
This means that the ouput from TM_T given a description of TM_R and input w yields the same output as TM_R with input w. Think about the implications of this for a moment. If TM_T prints the description of the TM passed to it (which in this case is the description of TM_R), then TM_R can do the same thing without having the description passed in explicitly, instead TM_R can calculate <TM_R>. In essence TM_R could print out a description of itself, without having the description given to it.
I’ll post the proof and examples in Python in later entries. The recursion theorem can allow a virus to obtain a description of itself and “print” the description into a file. Although, there are other methods that virii can use to obtain descriptions of themselves, which will also be covered in later posts.
Was doing some research on the structure of the Windows Recycle Bin, and found an interesting article over at Microsoft. It talks about the naming structure of the files in the Recycle Bin directories. In essence, the structure is as follows:
D<drive letter from original path><order #>.<original extension>
The field is a number signifying when the order the file was deleted since the recycle bin was last emptied.
For example, lets say I empty the recycle bin and then delete the following files (in the order shown):
c:\somefile.txt
e:\document.doc
d:\picture.jpg
f:\suspect_file.txt
Then, in the recycle bin directory for my user, I would find the following file names:
Dc1.txt
De2.doc
Dd3.jpg
Df4.txt
This is probably already well known, thought it would be interesting to share.
