It appears the RSA encryption scheme has fallen as cryptographers have http://eprint.iacr.org/2010/006.pdf [PDF] 768-bit keys via the widely used public-key algorithm.
An international team of mathematicians, computer scientists and cryptographers broke the key though NFS, or number field sieve, which allowed them to deduce two prime numbers that when multiplied together generated a number with 768 bits.
The discovery, which took about two-and-a-half years and hundreds of general-purpose computers, means 768-bit RSA keys can no longer be counted on to encrypt or authenticate sensitive communications.
To quote: "The latest milestone to fall is 768-bit RSA; in a paper posted on a cryptography preprint server, academic researchers have now announced that they factored one of these keys in early December.
Most modern cryptography relies on single large numbers that are the product of two primes. If you know the numbers, it's relatively easy to encrypt and decrypt data; if you don't, finding the numbers by brute force is a big computational challenge.
The paper describes how the process was done with commodity hardware, albeit lots of it."
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