User talk:Jehochman
 | Welcome to Jehochman's Talk Page Please feel free to put your feet on the coffee table, and speak candidly. Or for more better relaxation, stretch yourself luxuriously on the chaise longue in Bishzilla's Victorian parlour and mumble incoherently. |
 | Jehochman is busy with graduate school and may not respond swiftly to queries. |
 | This user is aware of the designation of the following topics as contentious topics:
|
January 2023
Greetings of the New Year! Earlier last year you did a rewrite of the lead section for the article on 2022 Russian invasion of Ukraine which looked quite good and improved. The lead section has again become a little bulky and suffers from many overedits, possibly you could simplify and shorten it again when time allows. It would be nice if you could somehow include that Ukraine is not a member of NATO, and that Ukraine does not have a military alliance with any of the member states of NATO, which is already covered in the main body of the article. ErnestKrause (talk) 21:39, 20 January 2023 (UTC)
- I gave it a shot. I'll look again tomorrow. Jehochman Talk 04:12, 21 January 2023 (UTC)
- It looks like its holding up and good going. Separately, after looking at your User page, I've done several years of studying formal automata theory in real life and thought to ask if your research has to do the computational theory of encryption of some other aspect? ErnestKrause (talk) 17:37, 22 January 2023 (UTC)
At the moment I’m working on number theory. So, yes, that’s part of it. I’m bothered by the fact that there’s a fast quantum algorithm for factoring. Quantum computing normally can only provide a quadratic speed up (n -> sqrt(n) using Grover's algorithm). This is a hint that there’s possibly an undiscovered factoring algorithm out there. Jehochman Talk 21:17, 22 January 2023 (UTC)
- I'm assuming that you have some evidence that makes you optimistic that a fast algorithm can be found on conventional computing machines; do you have a target for what order of complexity you think might be possible on conventional machines for integer factoring? ErnestKrause (talk) 19:12, 23 January 2023 (UTC)
- I know that the general number field sieve is an ugly algorithm that is sub-exponential, supra-polynomial. My suspicion is that there's something better, perhaps O(n^6) where n = log(N), but that's pure conjecture. Jehochman Talk 21:46, 23 January 2023 (UTC)
- Sounds ok. My own thoughts would be to try to do some preliminary theorem-proof studies and then to try to target something sub-quartic or even sub-cubic, to address the sixth order polynomial complexity currently found in the general number field sieve. I'm assuming that you have a fast algorithm for computing remainders for the division of one integer by another when the integers are over 200 or 300 digits long, and that you might be able to implement and test the theorem-proofs once I've set them up. My research is done mostly at Columbia which might make it easier to communicate results if this sounds like it might be interesting. ErnestKrause (talk) 17:13, 24 January 2023 (UTC)
- The Gmpy2 library converts numbers using the number theoretic transform. It can do fast arithmetic and exponents on numbers with thousands of digits, no problem. I want to take a much closer look at the GNFS and see if there's a way to improve upon it. I will take a look at your bio page if you have one. Jehochman Talk 20:07, 24 January 2023 (UTC)
- That name is from a Tom Hanks character in one of his films. If you decide that you'll list your email contact on your User Page, then I'll figure out the easiest way to communicate. My basic thought for this topic is to take the approach that it might be possible to prove some results on the distribution of possible factors to consider when factoring a large integer; the tighter the distribution then the more efficient the computational complexity. Possibly you have already thought about some of this. ErnestKrause (talk) 22:46, 25 January 2023 (UTC)
- The Gmpy2 library converts numbers using the number theoretic transform. It can do fast arithmetic and exponents on numbers with thousands of digits, no problem. I want to take a much closer look at the GNFS and see if there's a way to improve upon it. I will take a look at your bio page if you have one. Jehochman Talk 20:07, 24 January 2023 (UTC)
- Sounds ok. My own thoughts would be to try to do some preliminary theorem-proof studies and then to try to target something sub-quartic or even sub-cubic, to address the sixth order polynomial complexity currently found in the general number field sieve. I'm assuming that you have a fast algorithm for computing remainders for the division of one integer by another when the integers are over 200 or 300 digits long, and that you might be able to implement and test the theorem-proofs once I've set them up. My research is done mostly at Columbia which might make it easier to communicate results if this sounds like it might be interesting. ErnestKrause (talk) 17:13, 24 January 2023 (UTC)
- I know that the general number field sieve is an ugly algorithm that is sub-exponential, supra-polynomial. My suspicion is that there's something better, perhaps O(n^6) where n = log(N), but that's pure conjecture. Jehochman Talk 21:46, 23 January 2023 (UTC)
