In the mid-1990s, Peter Shor, at AT&T Bell Labs and then one of its heirs, AT&T Labs, devised the first algorithms that one day could exploit the intrinsic parallelism of quantum computing. In particular, Shor, now at the Massachusetts Institute of Technology (MIT), showed that quantum techniques could be exponentially faster than any classical computer at finding the factors of a very large number, a task whose difficulty is key to the security of widely used public-key cryptography techniques....