Date: Tue, 13 Jan 2026 18:19:20 +0100
> On 13 Jan 2026, at 17:55, David Brown <david.brown_at_[hidden]> wrote:
>
> Are you thinking about more general modular arithmetic, rather than specifically powers of 2? I don't see why you would need division at all for powers of 2, but obviously it's a different matter for arbitrary modulo numbers.
This is the general case. For example, this crypto puzzle uses an integer close to 2048 bits that can be solved by a sequence of squarings, solved in one case by running it for 3 years on a personal computer, and another in a couple of months on specially accelerated hardware.
https://en.wikipedia.org/wiki/LCS35
>
> Are you thinking about more general modular arithmetic, rather than specifically powers of 2? I don't see why you would need division at all for powers of 2, but obviously it's a different matter for arbitrary modulo numbers.
This is the general case. For example, this crypto puzzle uses an integer close to 2048 bits that can be solved by a sequence of squarings, solved in one case by running it for 3 years on a personal computer, and another in a couple of months on specially accelerated hardware.
https://en.wikipedia.org/wiki/LCS35
Received on 2026-01-13 17:19:34