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Cryptography is hardly a new field of endeavor. “Modern cryptography” was conceived twice—in Baghdad 1,200 years ago and in Italy 500 years ago—and born a bit over 100 years ago during World War I. Once we got our teeth into cryptography in the 20th century, it seemed like an important but limited problem, one that might actually be solved. Sure enough, when the U.S. National Security Agency announced its “Suite B” of unclassified algorithms trusted for all levels of classified information, it seemed that the problem might in fact have been solved. Cryptography, however, refused to go away. Information Technology journals and conferences flourished, and new theories and systems continued to appear. More significantly, for our purposes, a threat that had been lurking for more than a decade came to be better and better recognized. In about 1990, the physicists’ promise of quantum computing began to be widely written about. The idea was to compute on what is called a superposition of states in which every variable involved takes every possible value at the same time, a description you would be forgiven for thinking would allow you to do anything in one clock tick. The reality of quantum computing is more complex, but it quickly began to appear that quantum computing, albeit decades off, might make dramatic improvements in a variety of computational problems. Think about designing a new molecule, whether for a drug or a new structural material. Assembling atoms and molecules into larger molecules isn’t an easy process. Imagine a three-dimensional jigsaw puzzle—yes, it may be important to assemble it in just the right order to be able to get the pieces to where you want them to go—in which the pieces are not rigid; they can take on a number of forms, perhaps changing form during the process of assembly. One of the first applications to be explored seemed more of a threat than a benefit. In 1994, Peter Shor, working at Bell Labs in Providence, New Jersey, developed a quantum-computing algorithm for finding cycles in transformations on finite sets. The obvious application of Shor’s algorithm was finding secret cycle lengths in the public-key cryptosystems—called Diffie-Hellman and RSA (Rivest, Shamir, and Adleman) after their inventors—used to secure internet communications. Quantum computing was not the first new technology of vast interest to cryptanalysts. Over the decades of its existence, NSA has funded a variety of secret computing projects, particularly intended for attacking cryptographic systems it was working to break. Quantum computing, however, was different. On one hand, by the time it came to the NSA’s attention, or at least by the time the NSA took it seriously, it was already being widely talked about and studied. There was a limit to how secret it could be kept. On the other hand, the problem was too big to be solved out of the cryptanalytic budget alone. As a result—whatever research was and is being done on quantum-computing-based cryptanalysis—NSA began to work publicly (at least, publicly for the NSA) on securing the cryptographic systems on which U.S. security depends from the quantumcomputing threat.