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Factorization of a 768-Bit RSA Modulus
dtmos writes "The 768-bit, 232-digit number RSA-768 has been factored. 'The number RSA-768 was taken from the now obsolete RSA Challenge list as a representative 768-bit RSA modulus. This result is a record for factoring general integers. Factoring a 1024-bit RSA modulus would be about a thousand times harder, and a 768-bit RSA modulus is several thousands times harder to factor than a 512-bit one. Because the first factorization of a 512-bit RSA modulus was reported only a decade ago it is not unreasonable to expect that 1024-bit RSA moduli can be factored well within the next decade by an academic effort such as ours . . . . Thus, it would be prudent to phase out usage of 1024-bit RSA within the next three to four years.'"
I hope this is a joke. If not, you are confusing the strength of symmetric key encryption and public key encryption. The latter requires larger key sizes because the public and private key pair are mathetmically related whereas in symmetric encryption, there is a single key, and it ought to be randomly generated, and have no mathematical relation to any other value.
The key sizes are given for RSA/DSA encryption. Elliptical curve crypto can use much smaller key sizes while maintaining equivalent security levels. Unfortunately, most ECC is patent encumbered.
It's been a while since I studied this so take this with a grain of salt. I believe RSA involves 2 random large primes, 'p' and 'q' which are multiplied together to form a bigger number, 'n'. There is a bunch of other math to generate two more values 'd' and 'e' from 'p' and 'q'. The public key is 'n' and 'e', the private key is 'n' and 'd'. The math works that you can't get 'd' from 'e'. Factorization means just that, finding the factors of a number. In this case you're given 'n' which you know has only 2 factors ('p' and 'q' are both prime) so if you can factor 'n' and get 'p' and 'q' you can recalculate 'd' yourself and you now have the private key.
And newly generated keys for PGP/GPG are suggested to be at least 4096 bits.
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