The Nice Fuzzy Hashing Debate

Within the first submit on this sequence, we launched the usage of hashing methods to detect related capabilities in reverse engineering situations. We described PIC hashing, the hashing approach we use in SEI Pharos, in addition to some terminology and metrics to judge how effectively a hashing approach is working. We left off final time after exhibiting that PIC hashing performs poorly in some instances, and puzzled aloud whether it is potential to do higher.

On this submit, we are going to attempt to reply that query by introducing and experimenting with a really completely different kind of hashing known as fuzzy hashing. Like common hashing, there’s a hash perform that reads a sequence of bytes and produces a hash. In contrast to common hashing, although, you do not evaluate fuzzy hashes with equality. As a substitute, there’s a similarity perform that takes two fuzzy hashes as enter and returns a quantity between 0 and 1, the place 0 means utterly dissimilar and 1 means utterly related.

My colleague, Cory Cohen, and I debated whether or not there may be utility in making use of fuzzy hashes to instruction bytes, and our debate motivated this weblog submit. I believed there could be a profit, however Cory felt there wouldn’t. Therefore, these experiments. For this weblog submit, I will be utilizing the Lempel-Ziv Jaccard Distance fuzzy hash (LZJD) as a result of it is quick, whereas most fuzzy hash algorithms are sluggish. A quick fuzzy hashing algorithm opens up the potential of utilizing fuzzy hashes to seek for related capabilities in a big database and different attention-grabbing potentialities.

As a baseline I will even be utilizing Levenshtein distance, which is a measure of what number of adjustments it is advisable make to at least one string to remodel it to a different. For instance, the Levenshtein distance between “cat” and “bat” is 1, since you solely want to alter the primary letter. Levenshtein distance permits us to outline an optimum notion of similarity on the instruction byte stage. The tradeoff is that it is actually sluggish, so it is solely actually helpful as a baseline in our experiments.

Experiments in Accuracy of PIC Hashing and Fuzzy Hashing

To check the accuracy of PIC hashing and fuzzy hashing below numerous situations, I outlined a couple of experiments. Every experiment takes an analogous (or similar) piece of supply code and compiles it, typically with completely different compilers or flags.

Experiment 1: openssl model 1.1.1w

On this experiment, I compiled openssl model 1.1.1w in a couple of other ways. In every case, I examined the ensuing openssl executable.

Experiment 1a: openssl1.1.1w Compiled With Totally different Compilers

On this first experiment, I compiled openssl 1.1.1w with gcc -O3 -g and clang -O3 -g and in contrast the outcomes. We’ll begin with the confusion matrix for PIC hashing:

As we noticed earlier, this ends in a recall of 0.07, a precision of 0.45, and a F1 rating of 0.12. To summarize: fairly dangerous.

How do LZJD and Levenshtein distance do? Properly, that is a bit more durable to quantify, as a result of we now have to choose a similarity threshold at which we take into account the perform to be “the identical.” For instance, at a threshold of 0.8, we might take into account a pair of capabilities to be the identical if that they had a similarity rating of 0.8 or larger. To speak this data, we may output a confusion matrix for every potential threshold. As a substitute of doing this, I will plot the outcomes for a variety of thresholds proven in Determine 1 beneath:

The pink triangle represents the precision and recall of PIC hashing: 0.45 and 0.07 respectively, similar to we calculated above. The strong line represents the efficiency of LZJD, and the dashed line represents the efficiency of Levenshtein distance (LEV). The colour tells us what threshold is getting used for LZJD and LEV. On this graph, the best end result could be on the high proper (100% recall and precision). So, for LZJD and LEV to have a bonus, it needs to be above or to the appropriate of PIC hashing. However, we will see that each LZJD and LEV go sharply to the left earlier than transferring up, which signifies {that a} substantial lower in precision is required to enhance recall.

Determine 2 illustrates what I name the violin plot. Chances are you’ll need to click on on it to zoom in. There are three panels: The leftmost is for LEV, the center is for PIC hashing, and the rightmost is for LZJD. On every panel, there’s a True column, which exhibits the distribution of similarity scores for equal pairs of capabilities. There’s additionally a False column, which exhibits the distribution scores for nonequivalent pairs of capabilities. Since PIC hashing doesn’t present a similarity rating, we take into account each pair to be both equal (1.0) or not (0.0). A horizontal dashed line is plotted to indicate the brink that has the best F1 rating (i.e., a great mixture of each precision and recall). Inexperienced factors point out perform pairs which are appropriately predicted as equal or not, whereas pink factors point out errors.

This visualization exhibits how effectively every similarity metric differentiates the similarity distributions of equal and nonequivalent perform pairs. Clearly, the hallmark of a great similarity metric is that the distribution of equal capabilities needs to be larger than nonequivalent capabilities. Ideally, the similarity metric ought to produce distributions that don’t overlap in any respect, so we may draw a line between them. In apply, the distributions often intersect, and so as an alternative we’re compelled to make a tradeoff between precision and recall, as might be seen in Determine 1.

General, we will see from the violin plot that LEV and LZJD have a barely larger F1 rating (reported on the backside of the violin plot), however none of those methods are doing an incredible job. This suggests that gcc and clang produce code that’s fairly completely different syntactically.

Experiment 1b: openssl 1.1.1w Compiled With Totally different Optimization Ranges

The subsequent comparability I did was to compile openssl 1.1.1w with gcc -g and optimization ranges -O0, -O1, -O2, -O3.

Evaluating Optimization Ranges -O0 and -O3

Let’s begin with one of many extremes, evaluating -O0 and -O3:

The very first thing you could be questioning about on this graph is, The place is PIC hashing? Properly, when you look carefully, it is there at (0, 0). The violin plot provides us a bit of extra details about what’s going on.

Right here we will see that PIC hashing made no constructive predictions. In different phrases, not one of the PIC hashes from the -O0 binary matched any of the PIC hashes from the -O3 binary. I included this experiment as a result of I believed it might be very difficult for PIC hashing, and I used to be proper. However, after some dialogue with Cory, we realized one thing fishy was happening. To realize a precision of 0.0, PIC hashing cannot discover any capabilities equal. That features trivially easy capabilities. In case your perform is only a ret there’s not a lot optimization to do.

Finally, I guessed that the -O0 binary didn’t use the -fomit-frame-pointer choice, whereas all different optimization ranges do. This issues as a result of this feature adjustments the prologue and epilogue of each perform, which is why PIC hashing does so poorly right here.

LEV and LZJD do barely higher once more, attaining low (however nonzero) F1 scores. However to be honest, not one of the methods do very effectively right here. It is a troublesome downside.

Evaluating Optimization Ranges -O2 and -O3

On the a lot simpler excessive, let’s take a look at -O2 and -O3.

PIC hashing does fairly effectively right here, attaining a recall of 0.79 and a precision of 0.78. LEV and LZJD do about the identical. Nonetheless, the precision vs. recall graph (Determine 11) for LEV exhibits a way more interesting tradeoff line. LZJD’s tradeoff line is just not almost as interesting, because it’s extra horizontal.

You can begin to see extra of a distinction between the distributions within the violin plots right here within the LEV and LZJD panels. I will name this one a three-way “tie.”

Evaluating Optimization Ranges -O1 and -O2

I’d additionally anticipate -O1 and -O2 to be pretty related, however not as related as -O2 and -O3. Let’s examine:

The precision vs. recall graph (Determine 7) is sort of attention-grabbing. PIC hashing begins at a precision of 0.54 and a recall of 0.043. LEV shoots straight up, indicating that by reducing the brink it’s potential to extend recall considerably with out dropping a lot precision. A very engaging tradeoff could be a precision of 0.43 and a recall of 0.51. That is the kind of tradeoff I hoped to see with fuzzy hashing.

Sadly, LZJD’s tradeoff line is once more not almost as interesting, because it curves within the incorrect course.

We’ll say it is a fairly clear win for LEV.

Evaluating Optimization Ranges -O1 and -O3

Lastly, let’s evaluate -O1 and -O3, that are completely different, however each have the -fomit-frame-pointer choice enabled by default.

These graphs look nearly similar to evaluating -O1 and -O2. I’d describe the distinction between -O2 and -O3 as minor. So, it is once more a win for LEV.

Experiment 2: Totally different openssl Variations

The ultimate experiment I did was to check numerous variations of openssl. Cory instructed this experiment as a result of he thought it was reflective of typical malware reverse engineering situations. The concept is that the malware creator launched Malware 1.0, which you reverse engineer. Later, the malware adjustments a couple of issues and releases Malware 1.1, and also you need to detect which capabilities didn’t change so as to keep away from reverse engineering them once more.

I in contrast a couple of completely different variations of openssl:

I compiled every model utilizing gcc -g -O2.

openssl 1.0 and 1.1 are completely different minor variations of openssl. As defined right here:

Letter releases, corresponding to 1.0.2a, solely comprise bug and safety fixes and no new options.

So, we’d anticipate that openssl 1.0.2u is pretty completely different from any 1.1.1 model. And, we’d anticipate that in the identical minor model, 1.1.1 could be much like 1.1.1q, however it might be extra completely different than 1.1.1w.

Experiment 2a: openssl 1.0.2u vs 1.1.1w

As earlier than, let’s begin with essentially the most excessive comparability: 1.0.2u vs 1.1.1w.

Maybe not surprisingly, as a result of the 2 binaries are fairly completely different, all three methods battle. We’ll say it is a three method tie.

Experiment 2b: openssl 1.1.1 vs 1.1.1w

Now, let’s take a look at the unique 1.1.1 launch from September 2018 and evaluate it to the 1.1.1w bugfix launch from September 2023. Though loads of time has handed between the releases, the one variations needs to be bug and safety fixes.

All three methods do a lot better on this experiment, presumably as a result of there are far fewer adjustments. PIC hashing achieves a precision of 0.75 and a recall of 0.71. LEV and LZJD go nearly straight up, indicating an enchancment in recall with minimal tradeoff in precision. At roughly the identical precision (0.75), LZJD achieves a recall of 0.82 and LEV improves it to 0.89. LEV is the clear winner, with LZJD additionally exhibiting a transparent benefit over PIC.

Experiment 2c: openssl 1.1.1q vs 1.1.1w

Let’s proceed taking a look at extra related releases. Now we’ll evaluate 1.1.1q from July 2022 to 1.1.1w from September 2023.

As might be seen within the precision vs. recall graph (Determine 15), PIC hashing begins at a formidable precision of 0.81 and a recall of 0.94. There merely is not loads of room for LZJD or LEV to make an enchancment. This ends in a three-way tie.

Experiment second: openssl 1.1.1v vs 1.1.1w

Lastly, we’ll take a look at 1.1.1v and 1.1.1w, which have been launched solely a month aside.

Unsurprisingly, PIC hashing does even higher right here, with a precision of 0.82 and a recall of 1.0 (after rounding). Once more, there’s mainly no room for LZJD or LEV to enhance. That is one other three method tie.

Conclusions: Thresholds in Apply

We noticed some situations wherein LEV and LZJD outperformed PIC hashing. Nonetheless, it is vital to understand that we’re conducting these experiments with floor reality, and we’re utilizing the bottom reality to pick out the optimum threshold. You possibly can see these thresholds listed on the backside of every violin plot. Sadly, when you look fastidiously, you will additionally discover that the optimum thresholds will not be all the time the identical. For instance, the optimum threshold for LZJD within the “openssl 1.0.2u vs 1.1.1w” experiment was 0.95, but it surely was 0.75 within the “openssl 1.1.1q vs 1.1.1w” experiment.

In the actual world, to make use of LZJD or LEV, it is advisable choose a threshold. In contrast to in these experiments, you would not choose the optimum one, since you would haven’t any method of figuring out in case your threshold was working effectively or not. When you select a poor threshold, you may get considerably worse outcomes than PIC hashing.

PIC Hashing is Fairly Good

I feel we realized that PIC hashing is fairly good. It is not good, but it surely typically supplies wonderful precision. In principle, LZJD and LEV can carry out higher by way of recall, which is interesting. In apply, nevertheless, it might not be clear that they might as a result of you wouldn’t know which threshold to make use of. Additionally, though we did not discuss a lot about computational efficiency, PIC hashing could be very quick. Though LZJD is a lot quicker than LEV, it is nonetheless not almost as quick as PIC.

Think about you’ve got a database of 1,000,000 malware perform samples and you’ve got a perform that you simply need to search for within the database. For PIC hashing, that is simply an ordinary database lookup, which might profit from indexing and different precomputation methods. For fuzzy hash approaches, we would wish to invoke the similarity perform 1,000,000 instances every time we wished to do a database lookup.

There is a Restrict to Syntactic Similarity

Do not forget that we included LEV to characterize the optimum similarity based mostly on the edit distance of instruction bytes. LEV didn’t considerably outperform PIC , which is sort of telling, and suggests that there’s a basic restrict to how effectively syntactic similarity based mostly on instruction bytes can carry out. Surprisingly, PIC hashing seems to be near that restrict. We noticed a hanging instance of this restrict when the body pointer was by accident omitted and, extra typically, all syntactic methods battle when the variations turn into too nice.

It’s unclear whether or not any variants, like computing similarities over meeting code as an alternative of executable code bytes, would carry out any higher.

The place Do We Go From Right here?

There are after all different methods for evaluating similarity, corresponding to incorporating semantic data. Many researchers have studied this. The final draw back to semantic methods is that they’re considerably costlier than syntactic methods. However, when you’re keen to pay the upper computational worth, you will get higher outcomes.

Not too long ago, a serious new function known as BSim was added to Ghidra. BSim can discover structurally related capabilities in probably giant collections of binaries or object recordsdata. BSim is predicated on Ghidra’s decompiler and may discover matches throughout compilers used, architectures, and/or small adjustments to supply code.

One other attention-grabbing query is whether or not we will use neural studying to assist compute similarity. For instance, we’d have the ability to practice a mannequin to grasp that omitting the body pointer doesn’t change the that means of a perform, and so should not be counted as a distinction.