

Quantum computing is so powerful it takes two years to understand what happened - tankenmate
http://www.theregister.co.uk/2014/12/04/boffins_we_factored_143_no_you_factored_56153/

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gus_massa
More details in a friendly format: [http://phys.org/news/2014-11-largest-
factored-quantum-device...](http://phys.org/news/2014-11-largest-factored-
quantum-device.html)

From the research article:

> _In fact, it turns out that the product of any two numbers differing at only
> 2 bits will lead to the equations:_

> _p_a + q_a = x (19)_

> _p_b + q_b = y (20)_

> _p_b q_a + p_a q_b = z, (21)_

> _where the subscripts a and b correspond to the two bit-positions that
> differ, and the right-side variables {x, y, z} can each be 0 or 1 depending
> on the number being factored. However, unless we know in advance that the
> factors will differ at two bits, this reduction will not allow us to crack
> big RSA codes._

This is interesting, but it's a very special family of numbers. When the
numbers are more different they need more qbits.

------
tankenmate
TLDR; it appears that quantum computing can factor whole _classes_ of numbers
at once, not just single numbers. This may lead to even larger blacklists for
RSA keys or even cripple RSA altogether.

~~~
dalke
Your last sentence is conjecture, and not in the Register article or in the
paper. (FWIW, jonbaer submitted a HN link to the paper last week.)

The paper points that the reason why it works is because the factors are only
off by two bits, eg.

    
    
      3599 = 0b111011 * 0b111101
    

It also specifically addresses the RSA claim you made:

> However, unless we know in advance that the factors will differ at two bits,
> this reduction will not allow us to crack big RSA codes.

