[Cryptography] Has quantum cryptanalysis actually achieved anything?

[Aram Perez]

> On Feb 20, 2025, at 2:19 PM, Jon Callas <jon at callas.org> wrote:
> 
> I have a follow-up and addendum to my missive of last night.
> 
> I went over to Google and typed in "factor 2323" -- a four-digit number that my left hand pulled out of its fingers. I've learned that there are enough factoring resources on the web that numbers under six digits or so just pop up. There was a time when I had a file on my laptop of all primes under a million, which meant I could do a primality test with grep. I have apparently stuck that file somewhere safe where I won't lose it. Or find it.
> 
> I got back an AI reply, and I'm putting it in text for you, but I saved screen shots. Should you just want to skip ahead, feel free:
> 
> ---- AI Reasoning Starts, skip ahead if you like ----
> 
> AI Overview
> 
> What you're solving for
> Finding the prime factorization of the number 2323.
> 
> What's given in the problem
> The number to factor: 2323
> 
> How to solve
> Find the prime factors of 2323 by trial division.
> 
> Step 1
> Find the smallest prime factor
> 
> Divide 2323 by the smallest prime number, 2.
> 2323 is not divisible by 2 because it is not even.
> 
> Divide 2323  by the next smallest prime number, 3.
> 2+3+2+3=10, which is not divisible by 3, so 2323 is not divisible by 3.
> 
> Divide 2323 by the next smallest prime number, 5.
> 2323 does not end in 0 or 5, so it is not divisible by 5.
> 
> Divide 2323 by the next smallest prime number, 7.
> 2323÷7≈331.86, so it is not divisible by 7.
> 
> Divide 2323 by the next smallest prime number, 11.
> 2323÷11≈211.18, so it is not divisible by 11.


I'm not a mathematician (nor do I play one on TV ;-), but I believe that technically many of the steps provide a wrong statements, see below. I would have thought that AI would be smarter than that but my bad.

2323 _IS_ divisible by 2, 3 5, 7, and 11, etc. The issue for factoring is that you are searching for numbers that produce integer numbers, not just rational numbers.

/Aram

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