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Monday, 26 October 2009

Good and bad notation

In the P1363.3 Standard for Identity-based Public Key Cryptography using Pairings, there's one particular bit of notation that seems to confuse and annoy people. That's the use of "ID" to indicate the string that represents a users identity. Every other variable in the document is represented by a single letter, and the fact that this particular variable is represented by two letters seems to be the source of the trouble. I hope that this particular bit of notation doesn't cause people too much trouble, although it certainly seems to have the potential for doing that: a good notation is its own heaven, a bad notation is its own h**l.

Quantum mechanics is an example of a field that seems to defined by its bad notation. Quantum mechanics, at least the material that I learned, is really nothing more than looking at how certain linear operators on Hilbert spaces behave. In other words, it's essentially just linear algebra, but with a notation that does its best to obscure that fact.

The notation that we used in a class on quantum electrodynamics that I had in graduate school is probably why I decided to not study physics any more and to stick to things that used a notation that I could understand. I probably made the right choice. If I had stuck with physics, I'd have spent a significant part of the rest of my life converting between the bra-ket notation and something that actually made sense to me. 

With any luck, the notation in the P1363.3 standard isn't bad enough to make someone decide to give up cryptography.

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