Nomen Nescio wrote:: > James Donald writes: > > If one builds extraordinarily massive hardware capable of > > dowing 53 billion simultaneous independent ECM > > factorizations, Bernstein's method wil take 2^71 steps. > > > > Assuming that the massively parallel hardware does fifty > > billion factorizations each microsecond, then it will take > > Bernstein's super duper hardware about one hundred million > > years to factor an RSA 1024 modulus. > > No, this is not quite right. The 2^71 is the cost in terms of elementary > operations (add, xor, etc.). This is based on 2^53 ECM factorizations > per machine times 2^18 operations per factorization. > > James' quoted time would be correct if the machine could do 50 billion > *operations* per microsecond (a clock rate of 50,000,000 gigahertz > (50 petahertz), compared to 1-2 gigahertz available today). This fast > machine would then take 100 million years to break a 1024 bit key.
Another way to say it is if you had 50 million times more processors than is reasonable (where 1000 is reasonable) and they ran 50 million times faster than is reasonable (where 1 GHz is reasonable) then the operation would take 50 million times longer than is reasonable (where 2 years is reasonable).
