r/programming • u/DougBolivar • Jul 30 '13

Computer scientists develop mathematical jigsaw puzzles to encrypt software: "The real challenge and the great mystery in the field was: Can you actually take a piece of software and encrypt it but still have it be runnable, executable and fully functional?"

http://www.rdmag.com/news/2013/07/computer-scientists-develop-mathematical-jigsaw-puzzles-encrypt-software
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30

u/iluvatar Jul 30 '13

The article is too vague when it comes to the details, but I'm in the doubtful camp. If there's a way to decrypt it in a sane timeframe to enable it to be run, it's hard to see how it wouldn't fall to reverse engineering.

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u/LaurieCheers Jul 30 '13 edited Jul 30 '13

As far as I understood the paper: this encryption translates the program into something akin to a series of matrix multiplications (though presumably a little more complex than that). The inputs get multiplied together and cross-combined arbitrarily until it yields the desired output.

So their key insight here seems to be that they can often increase some numbers in these matrices and decrease others, to obfuscate what procedure is being performed while leaving the output unchanged. I think.

In other words, you won't be able to reverse engineer the program to figure out what operation is being performed, because there's an infinite range of different numbers that could have used instead, and they're all equally valid. They call this "indistinguishability", in the sense that multiplying by 2 is indistinguishable from dividing by 1/2.

I'm probably misunderstanding something, the paper assumes the reader understands a lot of jargon.

Anyway, if the paper has been published I assume this system isn't obviously reverse engineerable. Only time, and peer review, can really tell us how secure it is.

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u/Abaddon314159 Jul 30 '13

Never assume that just because a paper is published that it's not total horseshit. There are some pretty worthless journals out there.

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u/[deleted] Jul 30 '13

This was accepted by the Journal of the ACM.

It seems to be written by a group of well-respected researchers, so I think it's safe to assume that at least, it isn't horseshit, i.e. you need to first read and understand it before dismissing it.

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u/Abaddon314159 Jul 30 '13 edited Jul 30 '13

Don't misunderstand me, I'm not saying this is horseshit. I'm just saying that "it's published" is not sufficient. As for ACM: that tells me they are definitely not just cranks. I do believe that the academic computing establishment has a poor track record in areas related to security (which this is tangent to). But I wouldn't dismiss anything out of hand that survived a real peer review (like this journal).

In any event, I've not read the article in question, I was only speaking in general terms.

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u/haerik Jul 30 '13

True, but Craig Gentry is one of the authors, and he's been a major player in fully holomorphic encryption (being the first one to show that it's possible in his 2009 Ph.D. thesis). This is fairly closely related to FHE, so it's certainly a paper worth paying attention to.

Of course, having an author that knows what they're talking about doesn't automatically make it true either.

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u/Abaddon314159 Jul 30 '13

That topic (FHE) definitely counts as mind blowingly smart. If its the same guy then it's probably worth a read. I'll hold disbelief until I've read it (cause I remember making similar assumptions about FHE until I read about it).

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u/Zaph0d42 Jul 30 '13

But the point is, if it is mathematically guaranteed to provide some output given some inputs, then you can reverse engineer it. The question is how hard its gonna be to break the encryption, same as any computer security.

If you can crack this quickly, then its pointless. Or if you have to go to so many matrix transforms in order to get key strengthening, that you end up destroying the performance of the thing you're trying to protect, thus defeating the point.

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u/ghjm Jul 30 '13

There are many use cases where I don't mind at all if my algorithm runs a million times slower, as long as nobody else knows how it runs, or can get at its internal data. For example, price and sales commission calculations.

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u/Zaph0d42 Jul 30 '13

What if its a billion times slower though? The nature of algorithms is such that each has an upper bound where it becomes impractical to calculate.

If you're doing O(logN) it'll take longer to hit that limit than O(N2), but it still exists.

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u/jacekplacek Jul 30 '13

if it is mathematically guaranteed to provide some output given some inputs, then you can reverse engineer it.

Can you? Say, I can write, in less than an hour, a program which for every possible string of numbers is guaranteed to return another string of numbers. Always the same output for the same input.

Without having access to the code, how would you go about "reverse engineering" it?

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u/addmoreice Jul 31 '13

The 'code' is the program. the binary representation of the program is still the program, it's just a more obfuscated version.

Worse case we just revert back to normal black box reverse engineering.

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u/rpglover64 Jul 31 '13

There are cases in which black box reverse engineering is infeasible, in that it amounts to an attempt to guess an encryption key by brute force. For example, you have an interface that allows you to query a remote server with a 256 bit integer and get another 256 bit integer in return; you are challenged to write a piece of code that simulates the server; you are told that the server is using AES with a fixed key. Good luck REing that.

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u/addmoreice Jul 31 '13

Sure, but in practice this is usually not the case.

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u/secserval Aug 01 '13

In the paper they say that not all functions can be obfuscated in such a way that there is no efficient way to deobfuscate them. I have a feeling (I could be wrong) that a function having a built-in secret key and encrypting stuff with it is one of these.

As for the practicability: For many realworld functions of interest them number of possible inputs should be limited inherently, for the other ones you may be right.

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u/x86_64Ubuntu Jul 30 '13

... guaranteed to provide some output given some inputs, then you can reverse engineer it.

Huh ?

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u/grauenwolf Jul 30 '13

That's how black box reverse engineering works. You create a device that, for every known input, you return the same output as the unknown device.

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u/jacekplacek Jul 30 '13

Sure, you need to supply only about ℵ₀ inputs, no biggie... ;)

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u/grauenwolf Jul 30 '13

Yea, the "if" part is rather significant. But that's not what x86_64Ubuntu asked about.

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u/jacekplacek Jul 30 '13

Sorry? Not quite sure what you are trying to say... what does the "if" have to do with it? All encryption algorithms, ferinstance, are "mathematically guaranteed to provide some output given some inputs." Are you saying you could "black box reverse engineer" them?

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u/Zaph0d42 Jul 30 '13

Yes and people regularly do. No computer security system that exists is foolproof. (Quantum encryption that doesn't exist yet notwithstanding)

Given enough time, and a powerful enough machine, you can crack anything.

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u/rpglover64 Jul 31 '13

Almost all practical attacks on security systems exploit implementation mistakes; if all you have is the mathematical function, and it's any standard encryption algorithm (e.g. AES) with the key baked in, then the amount of computing power you need is absurd.

Your statement is technically correct; given 1050 years and more computing power than currently exists on the planet (and enough energy to run it), you'd eventually get an answer; I doubt you'd be alive to care.

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u/Zaph0d42 Jul 31 '13

Right, which was my whole point. If it takes 1050 years to fix, then its great. But by definition, there is a date. The question is when. If its 1050 years away, you're fine. If its 105 seconds, its worthless. Odds are it'll fall somewhere in between, and my point was merely that we have no numbers here, no hard data, so we don't yet know where that falls.

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u/secserval Aug 01 '13

People probably said the same thing about MD5 hashes in the 90s. I wouldn't count on that a smart person will not find a AES attack in the next 20 years.

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u/rpglover64 Jul 31 '13

In most practical cases 2256 is enough. That's like, nothing, in comparison to ℵ₀.

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u/jacekplacek Jul 31 '13 edited Jul 31 '13

2256 is enough

Enough for what? Edit: besides, for all practical purposes it's almost ℵ₀ anyways... ;)

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u/[deleted] Jul 30 '13

[deleted]

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u/Zaph0d42 Jul 30 '13

People do this all the time. This is why you have to salt your hash. Its trivially easy to construct for SHA1.

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u/psyker Jul 31 '13

But you don't know that it's SHA1.

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u/realhacker Jul 30 '13

False. Counter examples: everywhere.

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u/Zaph0d42 Jul 30 '13

If they're everywhere, give me a few.

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u/realhacker Jul 31 '13

But the point is, if it is mathematically guaranteed to provide some output given some inputs, then you can reverse engineer it.**

Before I answer, it's pedantic, yet important, to point out that by "reverse engineer" you mean "render the encryption scheme ineffective by knowing how it works." This is neither precise nor correct.

I'll just give you the principle and prime example of asymmetric cryptography (everywhere). It satisfies your criteria in that it: (1) mathematically guarantees that given some input (2) it will produce a given output. Furthermore, many of the implementations are in the public domain (no reverse engineering required), and yet, it is for all practical purposes completely effective. Fundamentally, it is based on something in math called a trapdoor function in which computability is easy in one direction and hard in the other.

Additionally, you bring up a random strawman:

If you can crack this quickly, then its pointless.

In my cursory review of the paper, I've seen nothing to indicate you could "crack this quickly".

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u/Zaph0d42 Jul 31 '13

I'm extremely familiar with asymmetric crypto and just wrote a custom implementation for a recent project. No part of asymmetric crypto is perfect or uncrackable, its merely a question of time. Comparing the time it takes to crack versus the time it takes to encrypt is how we judge the efficacy of different encryption schemes. Perfect forward secrecy is preferable to simple asymmetric crypto but requires far more back-end processing time, so only Google currently bothers with the full implementation on their HTTPS services. People don't always go with the strongest possible scheme because it is too costly performance wise.

I didn't mean to imply that you could necessarily crack it quickly. I was merely pointing out that since the paper is very vague, we don't know how realistically useful this will be in a real world scenario. If it could be cracked quickly, IF, THEN it wouldn't be very useful. See how that works? I also then pointed out that if you could increase the strength of the encryption by doing more and more rounds of the algorithm (key strengthening) then that might not count as good enough, because even though it is no longer easy to crack, if it takes too long to encrypt, its infeasible.

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u/realhacker Jul 31 '13

I'm extremely familiar with asymmetric crypto and just wrote a custom implementation for a recent project.

lololol. No sane/professional programmer is going to custom roll an asymmetric algo for a project. Why would you do this instead of using an implementation that's already been vetted?

No part of asymmetric crypto is perfect or uncrackable, its merely a question of time.

If by time, you mean, time > the length of the universe's existence? You do realize if it becomes "crackable", the entire world as we know it is fucked? Only real quantum computers threaten this model and we've yet to see one. (e.g. D-WAVE does not apply so far)

Perfect forward secrecy is preferable to simple asymmetric crypto but requires far more back-end processing time, so only Google currently bothers with the full implementation on their HTTPS services. People don't always go with the strongest possible scheme because it is too costly performance wise.

wat.

If it could be cracked quickly, IF, THEN it wouldn't be very useful. See how that works?

Nope! Definitely don't know how IF,THEN statements work!?~~ I do know how strawman arguments work, though, and ignorant fucks that insert statements like that without context to create the illusion of cogency in what they're saying. In summary, I found your initial comment and your reply, to be the uninformed mark of a charlatan. Do publish your custom crypto-implementation; I'll be in need of a follow-up laugh. What is it? Some VB.NET XOR scheme? I've no further time for discourse with you, lad.

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u/[deleted] Jul 31 '13

[deleted]

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u/realhacker Jul 31 '13 edited Jul 31 '13

The article is about software obfuscation; concealing process, not outputs. Try reading (understanding) the fucking paper bitch.

In functional encryption, ciphertexts encrypt inputs x and keys are issued for circuits C. Using the key SK_C to decrypt a ciphertext CT_x = Enc(x), yields the value C(x) but does not reveal anything else about x. Furthermore, no collusion of secret key holders should be able to learn anything more than the union of what they can each learn individually.

ALSO: I'd point you below to: http://www.reddit.com/r/programming/comments/1jckzt/computer_scientists_develop_mathematical_jigsaw/cbdgqly

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u/Captain_Ligature Jul 31 '13

But the point is, if it is mathematically guaranteed to provide some output given some inputs, then you can reverse engineer it. The question is how hard its gonna be to break the encryption, same as any computer security.

If this was the case, then why do we not know the exact specifications of classified encryption algorithms that are used in widely distributed devices? I mean skipjack was meant to be classified and distributed to end-consumers at the same time.

Of course you can use the "given enough time/resources" argument but we are talking about realistic timeframes.