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Rogaway wrote an companion essay for his invited talk that is rather accessible: http://web.cs.ucdavis.edu/~rogaway/papers/moral-fn.pdf

If all it does is prevent length extension attacks, then there are much simpler and less risky ways to do that (i.e., MD variants). Also, your explanation of the sponge structure o…

He is mistaken. What he meant is that there exists a finite field with exactly 256 elements, so you can "make" {0, ..., 255} into a finite field (in the sense that you can make any…

Cryptographic hash functions, by contrast, are not well understood at all. They are "magic" in many ways, and aren't modeled after anything. Many more "bad things" happen in this s…

You might want to read the cartoon again to see why this is useless, counterproductive advice.

The suggested solution (modular squaring) already reduces to factoring. http://en.wikipedia.org/wiki/One-way_function#Modular_squari... (And we'd use a cryptographic hash function …

Re: the crypto questions. Not only are these just trying establish if you're in the club or not, but judging from his answers on the DH vs RSA questions (which are not-well formed …

It's the most counter-intuitive thing in the world that rand() rand() is less secure than rand(); shouldn't it be twice as unpredictable?* Under some reasonable assumptions, rand()…

This is because Shannon entropy is basically useless when it comes to proving anything about randomized algorithms or cryptography.

During my first semester in college I took a course that used these notes. It was perhaps the most valuable course I took in college, as I subsequently became a researcher in theor…

This is absolutely not true. The wikipedia page for the max flow problem lists several (slower) poly-time algorithms for solving exact max flow. Most theory-101 classes cover at le…

Sadly, "finite time" is not what we need - they are looking for approximations that will be much rougher than the imprecision of finite numerical precision, and they want the appro…

Matt, I understand that you are writing primarily to your graduate students, but I also have to object to your first two points in general. I am a counterexample, as I took 12+ unn…

It seems like a bit much to hope to understand and verify the proof without a huge investment of time and effort. The problem is exponentially compounded if you don't already do re…

Ah, that is not how those "barriers" work. Roughly, the relativization barrier goes like this: Say you have a proof that P!=NP. Does it also prove that P^A != NP^A for any oracle A…

"only certain proof strategies" is technically correct, but its closer to "essentially every proof strategy we can conceive of". And besides, the question is over the entire proof …

The Hacker News community has a strange and sad relationship with actual math, that is, math as mathematicians define it. Math formalizable in ZFC and not arguments of A/B test eff…

>You don't know how much money is in either envelope, but it needn't have been selected randomly. This is exactly wrong, at least in the mathematical formalization of this problem …

You might find the blog post linked below encouraging. It was written by a professor at UIUC. http://3dpancakes.typepad.com/ernie/2005/03/re_phd_with_low.... My advice is think abo…