[Cryptography] Has quantum cryptanalysis actually achieved anything?

[Jon Callas]

> On Apr 7, 2025, at 00:45, Stephan Neuhaus <neut at zhaw.ch> wrote:
> 
> On 2/20/25 08:57, Jon Callas wrote:
>> As a factoid, the special forms that 15 and 21 have is that they're 2^n-1 * 2^n+1 -- so a string of 1 bits times a high bit, a bunch of zero bits, and then the low bit.
> 
> Hi Jon
> 
> I've just noticed this: While 15 does indeed have this form (as (4-1)(4+1)), I can't make 21 work. It's 3x7, which would be (4-1)(8-1), but that doesn't conform to your idea of "string of 1 bits, a bunch of zero bits, plus a 1 bit". I can't even make it work by relaxing the requirements to "(2^n + 1) x (2^m - 1)". If you want to write 21 as (n - k)(n + k) for some integers n and k, then n = 5 and k = 2.
> 
> Did I misunderstand something here?

7 is obviously 2^3-1. 3 is special because it is both 2^1+1 and 2^2-1, so it works as either of those. 

Yeah, in the bit expression sense, it's also special because there are zero zero bits between the high and the low one, and that's peculiar.

	Jon