this post was submitted on 25 Sep 2026
130 points (95.1% liked)

Technology

89005 readers
2656 users here now

This is a most excellent place for technology news and articles.

Our Rules

  1. Follow the lemmy.world rules.
  2. Only tech related news or articles.
  3. Be excellent to each other!
  4. Mod approved content bots can post up to 10 articles per day.
  5. Threads asking for personal tech support may be deleted.
  6. Politics threads may be removed.
  7. No memes allowed as posts, OK to post as comments.
  8. Only approved bots from the list below, this includes using AI responses and summaries. To ask if your bot can be added please contact a mod.
  9. Check for duplicates before posting, duplicates may be removed
  10. Accounts 7 days and younger will have their posts automatically removed.

Approved Bots

founded 3 years ago
MODERATORS
L3s@lemmy.world
enu@lemmy.world
technopagan@lemmy.world
L4s@lemmy.world
L3s@hackingne.ws
130
There's a new way to break RSA that's faster than anything we've seen before (arstechnica.com)
submitted 4 weeks ago by return2ozma@lemmy.world to c/technology@lemmy.world
54 comments fedilink hide all child comments
you are viewing a single comment's thread
view the rest of the comments
[–] LodeMike@lemmy.today 1 points 4 weeks ago (1 children)

Factoring is at most NP-complete because we have a polynomial time verification for it.

[–] a_non_monotonic_function@lemmy.world 0 points 4 weeks ago (1 children)

Factoring is not NP-complete because it is not a member of NP-hard.

You are correct that verifiability is in there, but you have to also be able to do the reduction.

There are plenty of problems out there where we lack polynomial time solutions, while the problem also lacks the expressiveness required to reduce back and forth.

[–] LodeMike@lemmy.today 1 points 4 weeks ago* (last edited 4 weeks ago) (1 children)

Factoring is not in any category because we don't have a proof for it. As it stands, the algorithms we have require exponential time in the worst case, but solutions can be verified in polynomial time, which is NP-complete. I said "at most" for a reason.

Also, every algorithm is verifiable. If there's no better way to do it then re-running the algorithm and that algorithm is exponential, then it's NP-Hard.

[–] a_non_monotonic_function@lemmy.world 1 points 4 weeks ago

Factoring is in a category. Everything computable exists somewhere. We know factoring to be in NP.

What I was disagreeing with was the "at least" and "at most" characterization of NP completeness. It is a set, not a boundary. The actual diagram of the complexity zoo is much more complicated than concentric circles.

And for verifiability, I was not referring to it as an existential sort of thing. I was simply saying that I agreed with you in that particular facet, but it isn't sufficient to describe NP completeness. You also need NP-hardness.