The Nice Fuzzy Hashing Debate

Within the first put up on this collection, we launched using hashing strategies to detect comparable capabilities in reverse engineering situations. We described PIC hashing, the hashing method we use in SEI Pharos, in addition to some terminology and metrics to judge how effectively a hashing method is working. We left off final time after displaying that PIC hashing performs poorly in some instances, and puzzled aloud whether it is potential to do higher.

On this put up, we are going to attempt to reply that query by introducing and experimenting with a really totally different sort of hashing referred to as fuzzy hashing. Like common hashing, there’s a hash perform that reads a sequence of bytes and produces a hash. Not like common hashing, although, you do not examine fuzzy hashes with equality. As an alternative, 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 comparable.

My colleague, Cory Cohen, and I debated whether or not there’s utility in making use of fuzzy hashes to instruction bytes, and our debate motivated this weblog put up. I believed there could be a profit, however Cory felt there wouldn’t. Therefore, these experiments. For this weblog put up, 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 for utilizing fuzzy hashes to seek for comparable capabilities in a big database and different fascinating prospects.

As a baseline I will even be utilizing Levenshtein distance, which is a measure of what number of adjustments you might want to make to 1 string to remodel it to a different. For instance, the Levenshtein distance between “cat” and “bat” is 1, since you solely want to vary the primary letter. Levenshtein distance permits us to outline an optimum notion of similarity on the instruction byte degree. 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 underneath numerous situations, I outlined a number of experiments. Every experiment takes an identical (or equivalent) piece of supply code and compiles it, typically with totally different compilers or flags.

Experiment 1: openssl model 1.1.1w

On this experiment, I compiled openssl model 1.1.1w in a number 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:

Hashing says identical

Hashing says totally different

Floor fact says identical



Floor fact says totally different



As we noticed earlier, this leads to a recall of 0.07, a precision of 0.45, and a F1 rating of 0.12. To summarize: fairly unhealthy.

How do LZJD and Levenshtein distance do? Nicely, that is a bit tougher to quantify, as a result of we’ve to choose a similarity threshold at which we think about the perform to be “the identical.” For instance, at a threshold of 0.8, we might think about a pair of capabilities to be the identical if they’d a similarity rating of 0.8 or larger. To speak this info, we may output a confusion matrix for every potential threshold. As an alternative of doing this, I will plot the outcomes for a spread of thresholds proven in Determine 1 beneath:


Determine 1: Precision Versus Recall Plot for “openssl GCC vs. Clang”

The purple 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 outcome could be on the prime proper (100% recall and precision). So, for LZJD and LEV to have a bonus, it needs to be above or to the proper 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 wish 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 reveals the distribution of similarity scores for equal pairs of capabilities. There may be additionally a False column, which reveals the distribution scores for nonequivalent pairs of capabilities. Since PIC hashing doesn’t present a similarity rating, we think about each pair to be both equal (1.0) or not (0.0). A horizontal dashed line is plotted to indicate the edge that has the best F1 rating (i.e., a great mixture of each precision and recall). Inexperienced factors point out perform pairs which might be appropriately predicted as equal or not, whereas purple factors point out errors.


Determine 2: Violin Plot for “openssl gcc vs clang”. Click on to zoom in.

This visualization reveals 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 follow, the distributions normally intersect, and so as a substitute we’re compelled to make a tradeoff between precision and recall, as could be seen in Determine 1.

Total, 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 strategies are doing an awesome job. This means that gcc and clang produce code that’s fairly totally 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:


Determine 3: Precision vs. Recall Plot for “openssl -O0 vs -O3”

The very first thing you is perhaps questioning about on this graph is, The place is PIC hashing? Nicely, should you look intently, it is there at (0, 0). The violin plot offers us slightly extra details about what’s going on.


Determine 4: Violin Plot for “openssl -O0 vs -O3”. Click on to zoom in.

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 could be very difficult for PIC hashing, and I used to be proper. However, after some dialogue with Cory, we realized one thing fishy was occurring. To attain 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.

Ultimately, 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, reaching low (however nonzero) F1 scores. However to be truthful, not one of the strategies do very effectively right here. It is a tough drawback.

Evaluating Optimization Ranges -O2 and -O3

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


Determine 5: Precision vs. Recall Plot for “openssl -O2 vs -O3”


Determine 6: Violin Plot for “openssl -O1 vs -O2”. Click on to zoom in.

PIC hashing does fairly effectively right here, reaching a recall of 0.79 and a precision of 0.78. LEV and LZJD do about the identical. Nevertheless, the precision vs. recall graph (Determine 11) for LEV reveals a way more interesting tradeoff line. LZJD’s tradeoff line will not be 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 comparable, however not as comparable as -O2 and -O3. Let’s have a look at:


Determine 7: Precision vs. Recall Plot for “openssl -O1 vs -O2”


Determine 8: Violin Plot for “openssl -O1 vs -O2”. Click on to zoom in.

The precision vs. recall graph (Determine 7) is sort of fascinating. PIC hashing begins at a precision of 0.54 and a recall of 0.043. LEV shoots straight up, indicating that by reducing the edge it’s potential to extend recall considerably with out dropping a lot precision. A very enticing tradeoff is perhaps 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 fallacious course.

We’ll say this can be a fairly clear win for LEV.

Evaluating Optimization Ranges -O1 and -O3

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


Determine 9: Precision vs. Recall Plot for “openssl -O1 vs -O3”


Determine 10: Violin Plot for “openssl -O1 vs -O3”. Click on to zoom in.

These graphs look virtually equivalent 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 advised this experiment as a result of he thought it was reflective of typical malware reverse engineering situations. The thought is that the malware creator launched Malware 1.0, which you reverse engineer. Later, the malware adjustments a number of issues and releases Malware 1.1, and also you wish to detect which capabilities didn’t change so as to keep away from reverse engineering them once more.

I in contrast a number of totally different variations of openssl:


I compiled every model utilizing gcc -g -O2.

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

Letter releases, akin to 1.0.2a, solely include bug and safety fixes and no new options.

So, we’d anticipate that openssl 1.0.2u is pretty totally 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 could be extra totally 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.


Determine 11: Precision vs. Recall Plot for “openssl 1.0.2u vs 1.1.1w”


Determine 12: Violin Plot for “openssl 1.0.2u vs 1.1.1w”. Click on to zoom in.

Maybe not surprisingly, as a result of the 2 binaries are fairly totally different, all three strategies battle. We’ll say this can be a three manner tie.

Experiment 2b: openssl 1.1.1 vs 1.1.1w

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


Determine 13: Precision vs. Recall Plot for “openssl 1.1.1 vs 1.1.1w”


Determine 14: Violin Plot for “openssl 1.1.1 vs 1.1.1w”. Click on to zoom in.

All three strategies do significantly 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 virtually 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 displaying a transparent benefit over PIC.

Experiment 2c: openssl 1.1.1q vs 1.1.1w

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


Determine 15: Precision vs. Recall Plot for “openssl 1.1.1q vs 1.1.1w”


Determine 16: Violin Plot for “openssl 1.1.1q vs 1.1.1w”. Click on to zoom in.

As could 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 a whole lot of room for LZJD or LEV to make an enchancment. This leads to a three-way tie.

Experiment 2nd: openssl 1.1.1v vs 1.1.1w

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


Determine 17: Precision vs. Recall Plot for “openssl 1.1.1v vs 1.1.1w”


Determine 18: Violin Plot for “openssl 1.1.1v vs 1.1.1w”. Click on to zoom in.

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 manner tie.

Conclusions: Thresholds in Apply

We noticed some situations through which LEV and LZJD outperformed PIC hashing. Nevertheless, it is necessary to appreciate that we’re conducting these experiments with floor fact, and we’re utilizing the bottom fact to pick out the optimum threshold. You’ll be able to see these thresholds listed on the backside of every violin plot. Sadly, should you look fastidiously, you will additionally discover that the optimum thresholds aren’t 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, nevertheless it 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, you might want to choose a threshold. Not like in these experiments, you may not choose the optimum one, since you would don’t have any manner of understanding in case your threshold was working effectively or not. For those who select a poor threshold, you may get considerably worse outcomes than PIC hashing.

PIC Hashing is Fairly Good

I feel we discovered that PIC hashing is fairly good. It isn’t excellent, nevertheless it usually supplies wonderful precision. In idea, LZJD and LEV can carry out higher by way of recall, which is interesting. In follow, nevertheless, it could not be clear that they’d as a result of you wouldn’t know which threshold to make use of. Additionally, though we did not speak a lot about computational efficiency, PIC hashing may be very quick. Though LZJD is a lot quicker than LEV, it is nonetheless not almost as quick as PIC.

Think about you’ve gotten a database of 1,000,000 malware perform samples and you’ve got a perform that you simply wish to search for within the database. For PIC hashing, that is simply an ordinary database lookup, which might profit from indexing and different precomputation strategies. 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 symbolize 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 elementary 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 placing instance of this restrict when the body pointer was by chance omitted and, extra usually, all syntactic strategies battle when the variations turn into too nice.

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

The place Do We Go From Right here?

There are in fact different methods for evaluating similarity, akin to incorporating semantic info. Many researchers have studied this. The final draw back to semantic strategies is that they’re considerably dearer than syntactic strategies. However, should you’re keen to pay the upper computational worth, you will get higher outcomes.

Just lately, a significant new characteristic referred to as BSim was added to Ghidra. BSim can discover structurally comparable capabilities in probably massive collections of binaries or object information. BSim relies on Ghidra’s decompiler and might discover matches throughout compilers used, architectures, and/or small adjustments to supply code.

One other fascinating query is whether or not we will use neural studying to assist compute similarity. For instance, we would be capable 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.

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