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Quantum computing is a novel way to build computers -- one that takes advantage of the quantum properties of particles to perform operations on data in a very different way than traditional computers. In some cases, the algorithm speedups are extraordinary.
Specifically, a quantum computer using something called Shor's algorithm can efficiently factor numbers, breaking RSA. A variant can break Diffie-Hellman and other discrete log–based cryptosystems, including those that use elliptic curves. This could potentially render all modern public-key algorithms insecure. Before you panic, note that the largest number to date that has been factored by a quantum computer is 143. (That computation also accidentally "factored much larger numbers such as 3599, 11663, and 56153, without the awareness of the authors of that work," which shows how weird this all is.) So while a practical quantum computer is still science fiction, it's not stupid science fiction.
(Note that this is completely different from quantum cryptography, which is a way of passing bits between two parties that relies on physical quantum properties for security. The only thing quantum computation and quantum cryptography have to do with each other is their first words. It is also completely different from the NSA's QUANTUM program, which is its code name for a packet-injection system that works directly in the Internet backbone.)
Practical quantum computation doesn't mean the end of cryptography. There are lesser-known public-key algorithms such as McEliece and lattice-based algorithms that, while less efficient than the ones we use, are currently secure against a quantum computer. And quantum computation only speeds up a brute-force keysearch by a factor of a square root, so any symmetric algorithm can be made secure against a quantum computer by doubling the key length.
We know from the Snowden documents that the NSA is conducting research on both quantum computation and quantum cryptography. It's not a lot of money, and few believe that the NSA has made any real advances in theoretical or applied physics in this area. My guess has been that we'll see a practical quantum computer within 30 to 40 years, but not much sooner than that.
This all means that now is the time to think about what living in a post-quantum world would be like. NIST is doing its part, having hosted a conference on the topic earlier this year. And the NSA announced that it is moving towards quantum-resistant algorithms.
Earlier this week, the NSA's Information Assurance Directorate updated its list of Suite B cryptographic algorithms. It explicitly talked about the threat of quantum computers:
IAD will initiate a transition to quantum resistant algorithms in the not too distant future. Based on experience in deploying Suite B, we have determined to start planning and communicating early about the upcoming transition to quantum resistant algorithms. Our ultimate goal is to provide cost effective security against a potential quantum computer. We are working with partners across the USG, vendors, and standards bodies to ensure there is a clear plan for getting a new suite of algorithms that are developed in an open and transparent manner that will form the foundation of our next Suite of cryptographic algorithms.
Until this new suite is developed and products are available implementing the quantum resistant suite, we will rely on current algorithms. For those partners and vendors that have not yet made the transition to Suite B elliptic curve algorithms, we recommend not making a significant expenditure to do so at this point but instead to prepare for the upcoming quantum resistant algorithm transition.
Suite B is a family of cryptographic algorithms approved by the NSA. It's all part of the NSA's Cryptographic Modernization Program. Traditionally, NSA algorithms were classified and could only be used in specially built hardware modules. Suite B algorithms are public, and can be used in anything. This is not to say that Suite B algorithms are second class, or breakable by the NSA. They're being used to protect US secrets: "Suite A will be used in applications where Suite B may not be appropriate. Both Suite A and Suite B can be used to protect foreign releasable information, US-Only information, and Sensitive Compartmented Information (SCI)."
The NSA is worried enough about advances in the technology to start transitioning away from algorithms that are vulnerable to a quantum computer. Does this mean that the agency is close to a working prototype in their own classified labs? Unlikely. Does this mean that they envision practical quantum computers sooner than my 30-to-40-year estimate? Certainly.
Unlike most personal and corporate applications, the NSA routinely deals with information it wants kept secret for decades. Even so, we should all follow the NSA's lead and transition our own systems to quantum-resistant algorithms over the next decade or so -- possibly even sooner.