I've been putting some thought in some deeper solutions, and while I don't have a solution I do think I have some inkling as tho were the problems come from.
The real problems with security are obviously not inherently tied to computers. In very _very_ abstract terms I think security is very closely tied to decision making systems, not in the sense of talking with others in boardrooms (although this constitutes a decision making system), but the decisions you make unconsciously to achieve some goal. The type of decision making I'm getting at now is very well explained by Eliezer over at less wrong[0]. The act of 'breaching' security is of course altering someone else's decision(to suit your needs) with false/fake inputs that your target fails to verify correctly
To be secure in the decisions you make you must verify all the inputs into your personal decision algorithm. For humans this system is more often right than for computers.
We have eyes: we can see who we're talking to, computers only have a vague 'trust' 'these numbers ensure that who you're talking to really is who he says he is'. A very fragile system that can be broken if enough resources are available to the adversary.
Now I'm not saying that the 'trust' systems of humans and computers differ fundamentally as both rely on external inspection (eg. I can't read you mind I'm still only basing my trust in you on what my senses tell me), but I do say that the 'trust' of computers has a much lower standard as opposed to that of a human.
We can better verify if what others are saying is true, in any context. Human understanding, under most circumstances, is such that it allows us to test things that others are saying on a huge amount of experience and knowledge, either that of our own or that of other humans.
Computers, on the other hand, only understand the protocols we've written for them. And those are only as good as the risk predictions of the programmer(s) that wrote the protocol. They are very limited and very fragile in the sense that they age and weaken as they get older. What if a break-through in prime-factorization is to take place at this very moment? In one swoop we'd lose a major part of the security infrastructure on the Internet. There is no reason to believe that prime-factorization can't be solved efficiently and quickly, someday. A human faced in this situation understands that his/her security protocol no longer suffices, he/she would change said protocol.
Of course, in the hypothetical scenario of prime-factorization break-through we'd just patch the systems, right? Yes, but then we're back at playing whack-a-mole again.
Last but not least, there are no huge/vast differences of intelligence between two people talking, where one is trying to manipulate the other. Sure Einstein vs the Village idiot could be considered a 'vast' difference in intelligence. But next to the differences in what constitutes intelligence for computers it is almost negligent. A smart phone with a punny dual-core processor must somehow be resistant against billion-dollar super computers, hell your simcard who's clock-speed can be measured in megahertz must be resistant against these super computers. It's just not doable, such a difference in capabilities just does not exist between two people.
Of course when you start mixing people and computers, your security is only as good as the weakest link (the computer). You would not fall for a 'phising' talk if you were face-to-face with the hacker (who is at this point not inside your network yet). The scenario is akin to the hacker, who's outside your door, asking you to give him the key. You wouldn't fall for this. But in your email program things are different, you can't see a face. Can't hear the inflections in the hacker's voice, he isn't even asking for the key he's only asking for you to click a link...
The solution, in a very general way, would be to design systems such that they are more 'intelligent'. Some sort of AI security. Don't just make the protocols more complex by adding more rules/functionality to it, instead program the computer in such a way that it can be 'inventive' in verifying it's inputs. Obviously such a system does not exist (yet?), and it's only wishful thinking that it can exist anytime soon (no infrastructure or backwards-compatibility), software not there yet, hardware might be but not sure). So for the time being we're stuck playing whack-a-mole.
[0] http://lesswrong.com/lw/v9/aiming_at_the_target/ - Aiming at the target.