Researchers have decomposed a 768-bit number with 232 decimal places into its two prime factors and published a paper
with their results. The number is the string released as "RSA-768″
under the now defunct RSA Challenge. As a result, RSA encryption with
768-bit keys must, from now on, be considered cracked.
It took the team of researchers from Switzerland, Japan, Germany,
France, the US and the Netherlands about two and a half years to perform
the factorization. The first step of the calculation, polynomial
selection, required half a year on a cluster consisting of 80 PCs, while
the second and considerably more labor-intensive sieving step took
about two years on a cluster of several hundred computers. According to
the researchers, a single Copter processor with 2 G bytes of RAM
...
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