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Comment by CodesInChaos | Hacker News Reader

Those quantum computers can't execute Shor's algorithm, which is required to attack RSA. AFAIK the best relevant factoring result is still 21=3*7 from 2012.

There are claims of bigger factored numbers, but they exploited special cases (e.g. factors differing by only two bits) and have no hope of being extended to attack cryptography.

https://crypto.stackexchange.com/questions/59795/largest-int...

A 2019 paper manged to factor 21 on a 16 qubit ibmqx5, but failed to go up to 35:

> the algorithm fails to factor N=35. This is due to the cumulative errors coming from the increasing number of two-qubits gates necessary to implement the more complex MEF needed for this case

https://arxiv.org/abs/1903.00768

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Jennifer and Peter Shor wrote a limerick that seems relevant:

   If computers that you build are quantum,
   Then spies of all factions will want 'em.
   Our codes will all fail,
   And they'll read our email,
   Till we've crypto that's quantum, and daunt 'em.

And Volker Strassen responded at a conference:

   To read our E-mail, how mean
   of the spies and their quantum machine;
   Be comforted though,
   they do not yet know
   how to factorize twelve or fifteen.

Source: http://www-math.mit.edu/~shor/notapoet.html

> Till we've crypto that's quantum, and daunt 'em.

Luckily there are asymmetric algorithms which are are secure against quantum computers, so we don't have to resort to quantum-key-exchanges.

"Secure against quantum" doesn't really mean much because too little is known to make that claim confidently. AFAIK the term generally refers to algorithms that don't rely on factoring being hard, but instead make some different hardness assumptions that we currently don't have classical or quantum algorithms for.

For practically all computationally secure crypto we use "secure" for "no known attacks faster than we'd like". QCs just extend the set of efficient algorithms.

Indeed, but there is a much longer history of people trying and failing to break the schemes, and we have come to understand the hardness assumptions in classical crypto as probably quite reasonable.

>There are claims of bigger factored numbers, but they exploited special cases

Also, my understanding is that almost all of these factorizations utilize a "compiled" version of Shor's algorithm. Meaning that you need to know the factors in advance. So it's essentially "confirming" rather than "finding" the factors.

AFAIK factoring 21 is "compiled" Shor, so even that result simplifies the problem a bit.

According the first link in my post, the numbers bigger than 21 were chosen to have specific mathematical properties and attacked with algorithms even less realistic that compiled Shor.

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