What is Identity-Based Encryption (IBE) and why is it "better"? Most CS/Math undergrads run into the well-known RSA cryptosystem at some point.  But about 10 years ago Boneh and Franklin introduced a practical Identity-Based Encryption system (IBE) that has excited much of the research community and produced a huge flood of follow-up work.

What is IBE exactly and in what way does it improve over conventional public-key systems like RSA?
Conventional public-key cryptosystems require key distribution: in order to encrypt a message destined to Bob, you must know Bob's public key with enough certainty (an attacker could try to substitute his own key there). Various systems have been designed for that, e.g. certificates. In practice, key distribution proves complex.

With IBE, the name (email address) of Bob is his public key, so it is already distributed. To understand it, imagine the following model: there is a trusted central service, to which you send the email; the central service forwards it to Bob, and all communications are encrypted. This is how encrypted communications worked before the invention of RSA, so it is an old model. It has two drawbacks:


the central service must be trusted (it has the power to read all emails);
the central service must have oversized optic fibers and thousands of processors because every message goes through it.


IBE uses high-level mathematics to remove the second issue. With IBE, the "central service" must exist, but it needs not be "online"; its real-time action is replaced with a mathematical pairing.

Another, more mathematical way to say it, is that with IBE, a central authority has a key pair. The central authority can compute the private key corresponding to a given "public key", where public keys can be just any sequence of bits, e.g. email addresses. You cannot do that with RSA: RSA public keys have a strong internal mathematical structure. With IBE users key pairs, not so. The counterpart of that property is that the central authority public key must be involved in the encryption and decryption processes. In a full-fledged IBE system, users obtain their own private key from the central authority; afterwards, no need to talk to the central authority.

Voltage Security sells IBE-based products (Dan Boneh is one of the founders of that company). The practical point of IBE is to "avoid" certificates. See Voltages pages to get some descriptions of IBE; also, the Boneh-Franklin article is a good source of information. Details on the actual computation of Weil and Tate pairings are intricate; Ben Lynn's thesis is a good starting point.