The National Security Agency is advising US agencies and businesses to prepare for a time in the not-too-distant future when the cryptography protecting virtually all e-mail, medical and financial records, and online transactions is rendered obsolete by quantum computing.
Quantum computers have capabilities that can lay to ruin all of the public-key cryptographic systems currently in use. These capabilities, which aren't known to be present in the classical computers of today, include the ability to almost instantly find the prime factors of extremely large numbers, using a method called Shor's algorithm. Quantum computing is also believed to be capable of tackling other mathematical problems classical computers can't solve quickly, including computing discrete logarithm mod primes and discrete logs over elliptic curves.
The difficulty of factoring and computing discrete log primes and elliptic curve discrete logs play an essential role in cryptographers' confidence in RSA, elliptic curve cryptography, and other public-key crypto systems. When implemented correctly, most scientists and cryptographers believe that the crypto can't be defeated with today's computers before the end of the universe.
The end is nigh
At the moment, quantum computers are believed to be little more than a theoretical phenomenon. Consider, for instance, that the biggest number factored to date using Shor's algorithm is just 21. But a significant percentage of computer scientists say practical quantum computing is only a matter of time, and once that happens (anywhere in the next 10 to 50 years, most of them forecast), public-key crypto systems that form the bedrock of most modern data protection will be trivial to break. Such a doomsday scenario would jeopardize not only all transactions and records going forward, but it would also allow attackers to decrypt more than half a century's worth of old communications, assuming someone took the time to collect and store the encrypted data.