Security is Mathematics
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Security is Mathematics
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Re: Security is Mathematics
#2This article is correct, except it omits one important point... writing programs is harder than writing a proof. Especially security code. With sufficiently complex proofs it is often hard to find holes in the proof, but with security code (and code in general) there are ways to attack it, that just isn't doable with standard math proofs. There's no notion of "fuzzing" with proofs.
But in any case, the gist of the article is correct -- the rigor used in math proofs is the MIN bar for security code.
Re: Security is Mathematics
#3I am not sure that I buy this. There are plenty of people who have internalized a painstaking and rigorous approach to problem solving, often from a young age. While many of these are also those who would excel in a mathematical environment, a mathematical education fails to capture any of the specific details of security.
Re: Security is Mathematics
#4This article is correct, except it omits one important point... writing programs is harder than writing a proof. Especially security code. With sufficiently complex proofs it is often hard to find holes in the proof, but with security code (and code in general) there are ways to attack it, that just isn't doable with standard math proofs. There's no notion of "fuzzing" with proofs. But in any case, the gist of the ar…
>writing programs is harder than writing a proof
Which programs and which proofs?
Re: Security is Mathematics
#5I am not sure that I buy this. There are plenty of people who have internalized a painstaking and rigorous approach to problem solving, often from a young age. While many of these are also those who would excel in a mathematical environment, a mathematical education fails to capture any of the specific details of security.
I don't think he is trying to say mathematics is sufficient to be good at security, just that training in mathematics develops the right mindset for security.
I have a degree in math and can see how my attitude changed as I progressed. When taking my first analysis class I was sure it is no coincidence the word begins with anal. It took a while for me to develop habits of skepticism about things that seem obvious at first glance. That's the attitude I think he is describing.
Re: Security is Mathematics
#6This article is correct, except it omits one important point... writing programs is harder than writing a proof. Especially security code. With sufficiently complex proofs it is often hard to find holes in the proof, but with security code (and code in general) there are ways to attack it, that just isn't doable with standard math proofs. There's no notion of "fuzzing" with proofs. But in any case, the gist of the ar…
My take is that mathematics provides rigorously defined, leak-proof primitives and operations. Most of the difficulty involved in porting a piece of math to a program is in plugging the leaks in the abstractions provided by efficient machines. For example, infinite-precision real arithmetic (with no overflows, loss of entropy due to FP rounding mode, etc.) is assumed in mathematics, but is devilishly hard to get right (and fast) on fixed-width machines. Obtaining a passphrase from the user in order to hash it is assumed in the algorithm for the hash function, but in reality doing so without compromising the rest of your system can be much harder than coding the hash function correctly.
Things like side channel (e.g., timing) attacks add an orthogonal dimension of complexity to secure complexity that simply doesn't exist (or is rightly elided) in the related math.
Proofs only operate in the domain of the pure and infinite. The glue logic to interface that with the real world is what makes it tricky to write secure code, especially when errors in any part of any program can compromise an entire system (better hardware-enforced isolation between pieces of code is possible today, and indeed used, but isn't pervasive yet because performance is still king, IMO.
Re: Security is Mathematics
#7This article is correct, except it omits one important point... writing programs is harder than writing a proof. Especially security code. With sufficiently complex proofs it is often hard to find holes in the proof, but with security code (and code in general) there are ways to attack it, that just isn't doable with standard math proofs. There's no notion of "fuzzing" with proofs. But in any case, the gist of the ar…
>writing programs is harder than writing a proof Which programs and which proofs?
Any program function can be cast as a theorem (although vice-verse is difficult). Proving this theorem is easier than writing the corresponding program function.
And by easier, I mean that the proof is easier to pass off as a correct proof than the program is to pass as a correct program. Of course, writing an actually correct proof is just as difficult as writing an actually correct program -- for the most part. Of course sometimes, due to real world constraints in programs (like dealing with fault tolerance or races for perf) correctness in programs can become magnitudes more difficult.
Re: Security is Mathematics
#8Computer security is a social science, so degrees in ethnography, epistemology, or organizational behavior are a lot more relevant than mathematics. Agreed that math teaches you rigorous thinking and questioning assumptions, but outside of the narrow areas of cryptography and systems analysis the specific skills you learn aren't that important for security work.
Re: Security is Mathematics
#9I am not sure that I buy this. There are plenty of people who have internalized a painstaking and rigorous approach to problem solving, often from a young age. While many of these are also those who would excel in a mathematical environment, a mathematical education fails to capture any of the specific details of security.
I don't think he is trying to say mathematics is sufficient to be good at security, just that training in mathematics develops the right mindset for security. I have a degree in math and can see how my attitude changed as I progressed. When taking my first analysis class I was sure it is no coincidence the word begins with anal. It took a while for me to develop habits of skepticism about things that seem obvious at…
When taking my first analysis class I was sure it is no coincidence the word begins with anal.
I'm going to steal that line, if you don't mind. :-)
It took a while for me to develop habits of skepticism about things that seem obvious at first glance. That's the attitude I think he is describing.
Yes. The attitude of "I don't care if this looks right; am I absolutely certain that it is right, in all possible universes consistent with my axioms".
Re: Security is Mathematics
#10Computer security is a social science, so degrees in ethnography, epistemology, or organizational behavior are a lot more relevant than mathematics. Agreed that math teaches you rigorous thinking and questioning assumptions, but outside of the narrow areas of cryptography and systems analysis the specific skills you learn aren't that important for security work.
Right. I don't think thorough economic analyses come into play nearly enough when people think about security.