Idle Thoughts About Pollard Rho | Hacker News Reader

Idle Thoughts About Pollard Rho

solipsys.co.uk

8 pointsColinWright10 comments

The asymptotic means for tails and cycles of random functions are in Theorem 3 of https://link.springer.com/content/pdf/10.1007/3-540-46885-4_...

Great catch - thank you! Now to find some time to read it properly.

Antoine Joux's book:

https://books.google.co.uk/books?id=buQajqt-_iUC

precis-es this paper in its sections 7.2 and 7.3 and highlights the fact that looking at "Pollard rho style" random functions with in-degree 0 or 2, merely changes the multiplicative constants of the tail and cycle statistics without changing the order.

That's pretty much what I was expecting, and it's great to see that someone's done the work. I never expected my idle musings to be in any way new or insightful, so it's nice to be able to see that at least I'm not completely off-track.

I'm now wondering about constructing fast-to-compute functions with in-degree (0,0,3) or (0,0,0,4), which should change the characteristics, but I need to read a bit first.

Again, thanks.

Do I have to speak TeX to understand this? What's it with all the dollar signs and periods?

I recognize the graphics, though. Iteration paths of a polynomial modulo N graphviz'ed. These seemingly simple constructs don't cease to fascinate me.

Edited ...

I thought something might have broken, but it's working for me. I don't know how the MathJax works, it might be that you need Javascript turned on. Certainly usually when I'm using Javascript there is no sensible "fall back" for times when it's not available, so it doesn't try.

I'm not a front-end person, so I can't do anything more about it now. If someone else can check it out and let me know the best course of action I'd be delighted to hear from them - contact details in my profile.

Edited again ...

OK, now looking at it from another browser and it is broken. The other browser must have something cached. I'll see if I can get it fixed soon.

We apologise for the inconveniece (and incoherence).

The problem is that your site is served through HTTPS, but the MathJax code is loaded via HTTP, and Chrome/Firefox refuse to load external JavaScript due to mixed content policy. The embedded images also produce a mixed content warning, but are still loaded because they are not a security risk.

Thanks ... So the link without the https should work, I'll get to fixing the proper site when I can back to my desk.

Cheers.

Edit: temporary fix in place - working on the rest of the site now 8-(

This is malformatted on my Android chrome--math is overlaying subsequent text :(

In the past I've tried repeatedly to get things to layout decently on a wide selection of web browsers, but I have simply given up completely. I try to get it to work on a reasonably broad selection, and there are days when I get time to work on it, but I don't have the front-end skills to cope with the utter crap-fest that the web has become with regards layout. To be honest, I'm on the verge of converting things like this to a PDF so I can get proper control of the formatting and stop pissing away time on something that really, really should be better.

I'm sorry it doesn't work well on Android/Chrome, but I've tried, and I have neither the time nor the skills. 8-(

And as a side-comment - kudos to those who work hard to get stuff to render well on the web. One day there'll be a way for numpties like me to produce something that looks good and doesn't require endless fiddling.

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