A new approach to provable security
The idea of "Practice-Oriented Provable-Security" as pioneered by Mihir Bellare and Phil Rogaway is probably one of the most important innovations in modern cryptography. It almost single-handedly moved cryptography from being a "black art," like it was in the pre-dot-com era, to the rigorous science that it is today. Unfortunately, because it requires more math than most people are willing to learn, most people will probably never understand the types of proofs that we see in cryptography papers today.
Fortunately, there are several alternatives to POPS, many of which are much easier to understand than POPS, and Uncyclopedia (probably as close as we can come to an Internet version of National Lampoon and which probably isn't suitable for viewing at work, which is why there's no link to it here) has conveniently collected many of these. One of my favorites is "Proof by TeX:"
The proof is typeset using TeX or LaTeX, preferably using one of the AMS or ACM stylesheets. When laid out so professionally, it can't possibly have any flaws.
The one that's most commonly seen, and the one that's found many uses outside the field of cryptography, however, may actually be a variant of "Proof by Irrelevant References":
A proof that is backed up by citations that may or may not contain a proof of the assertion. This includes references to documents that don't exist. (Cf. Schott, Wiggenmeyer & Pratt, Annals of Veterninary Medicine and Modern Domestic Plumbing, vol. 164, Jul 1983.)
That's sort of what you see in lots of vendor presentations that make some outlandish claim and then follow it with a vague citation to some industry analyst firm. I almost always assume that those types of claims are totally fictitious because if there was a more accurate reference then they'd give it, but I suspect that most people are a bit more trusting.