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Comment Re:Can someone explain this to me? (Score 1) 192 192

GPU's are far less useful for the general number field sieve, and any other algorithm is completely useless to factor interesting sized RSA keys. This is because sieving is a memory intensive process which doesn't lend itself well to GPU architectures. Something drastic, as it relates to factoring, means the emergence of a new algorithm.

Comment Re:Bad math... (Score 4, Informative) 192 192

Cryptographic strength, as applied to RSA keys, is measured by the time needed to factor the public modulus. The fastest way to do this is today is using the general number field sieve. The run time of the general number field sieve can be estimated as T(b) = exp(1.923 * ln(2^b)^(1/3) * (ln( ln(2^b)))^(2/3)), where b is the size of the input in bits. See Aoki's paper on a kilobit SNFS factorization for details. Chug through this estimate for b = 1024 and b = 768, and you'll find that the ratio is approximately 1000 (I got 1221.15). That's why 1024 bit RSA keys are approximately 1000 times stronger.

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