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Board Development & Technical Discussion
Re: Researcher Claims to Crack RSA-2048 With Quantum Computer
by
j2002ba2
on 05/11/2023, 01:36:26 UTC
they might not factor 10^1000 size numbers but 2048 bit numbers are an entirely different animal and should be vulnerable to quantum computers at some point. very vulnerable. the only question is, when do companies like atom computing scale up past 1000 qbits to say 1 million qbits. i'd say in the next 10 years at worst.
they went from 100 qbits to 1000 in like 2 years.

You got it wrong. RSA-2048 is not vulnerable to QC even theoretically. Neither is RSA-128 - yes only 128 bits are beyond Shor's algorithm even in theory. Current QC hardware struggles with RSA-6 (six bits).

Finally someone did put the noise into quantum equations and this is the result:
We consider Shor's quantum factoring algorithm in the setting of noisy quantum gates. Under a generic model of random noise for (controlled) rotation gates, we prove that the algorithm does not factor integers of the form pq when the noise exceeds a vanishingly small level in terms of n - the number of bits of the integer to be factored, where p and q are from a well-defined set of primes of positive density. We further prove that with probability 1−o(1) over random prime pairs (p,q), Shor's factoring algorithm does not factor numbers of the form pq, with the same level of random noise present.