The benefits of provable security

When I was in graduate school, I had a teaching assistantship that paid my tuition and fees and gave me a few thousand dollars to live on. In return, I had to teach a few undergraduate math classes. To prepare us for this, we had to sit through a class that gave us an overview of how to teach math classes. I don’t think that the class lasted that long. I’m fairly sure that it was more than one hour but less than two hours. After this, we were set loose on the unsuspecting undergraduates.

In this class, we were told that studies have estimated that many people don’t have the cognitive ability to understand much past high-school algebra. This means that if you’re teaching a math class, there will probably be people in your classes who are smart and hard-working, but they won’t be able to understand the more advanced math and there’s not much they can do about it.

At the time, I believed it. Now, I’m not so sure that this is actually true. Today, I’m more inclined to believe that understanding complicated things is just a question of having enough interest to spend the time and effort needed to understand the complicated things. Math is just one example of something that’s complicated, and it’s far from being the only example.

Not many people understand the math behind public-key cryptographic algorithms. The math behind the pairing-based algorithms that Voltage uses is particularly difficult, and most people don’t get around to understanding it. Most of them don’t need to, of course. For most people, knowing that there are formal proofs that Voltage’s IBE is secure is good enough, and they don’t want to understand the details of exactly why this is true. This is as it should be.

All businesses have more important things to worry about than the details of exactly why their secure e-mail is actually secure. If my theory about interest being mistaken for aptitude is right, most people could actually understand the math behind public-key cryptography if they had enough interest in the subject. On the other hand, most people just don’t have enough interest to get them to take the time to understand the technology. They have things that are more important to them, and those are the things that they spend their time thinking about. If someone who understands these details showed that it’s secure, that’s good enough for them. Maybe that’s the real benefit from provable security.

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