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posts about math.

over the last weeks, i’ve been starting to convert my blogs to nikola, a static blog generator named after nikola tesla. so far, i’ve finished my math blog and musikwiese. i also got rid of the fixed width layout. spielwiese itself will take a bit more work, mostly because of the wordpress plugins i wrote and heavily rely on throughout this blog.

to convert my blogs, i had to add some changes to nikola. most of the core changes are now contained in nikola itself or are close to be integrated (except xhtml support). i also worked a lot on improving its wordpess import, which so far wasn’t very helpful from my point of view. for that, i created a wordpress page compiler for nikola which essentially does the same to posts as wordpress’ formatter does. that part is still not completely done, and since it is a pure plugin, i haven’t released it yet. (that will happen later, hopefully still this year.)

the main disadvantage of the whole conversion process is currently that there’s no more possibility to add comments. all comments written so far are preserved, but currently there’s no support for adding new ones. i’ll try to figure out a good way to do that later. the “standard way” to do that, i.e. using something like disqus, is not acceptable for me, and even though there are free alternatives for self-hosting, i don’t like to rely on javascript for such things. for the moment, you have to send me an email if you want to add a comment to musikwiese or my math blog.

two days ago, alexander grothendieck, one of the greatest mathematicians of the 20th century, died. i’ve seen a small excerpt of his work in algebraic geometry and commutative algebra during my studies, phd and postdoc times. without his work and ideas, the theory of schemes wouldn’t be what it is today, and without it, the study of elliptic curves over rings might have taken quite a different road. (elliptic curves over rings are a topic i’ve been very interested in while working on my diplom thesis.) even though his active mathematical career stopped over 40 years ago, his work had an immense influence on generations of mathematicians.

rest in peace.

(a great obituary can be read at the telegraph.)

i’m very happy to announce that the lattice reduction library plll has finally been released as open source under the MIT license by the university of zurich. during my recent years at the university of zurich, i’ve been mainly working on this c++ library. it supports a wide range of lattice reduction algorithms and svp solvers, and makes heavy use of c++ templates and has support for c++11‘s move operations.

in 2011, i began implementing it since i wasn’t happy with some of the behavior of ntl‘s lattice reduction algorithms (mainly: in case of fatal numerical instability, they just terminate the program, and the library cannot be used in more than one thread at the same time). back then, ntl’s main competior fplll didn’t support bkz reduction, so i decided to try things out myself. after some time (years), my initial experiments grew into a full library supporting not only the more common lll and bkz algorithms as well as svp solving by enumeration, but also several different algorithms for lattice reduction and svp solving which are described in literature but for which it is sometimes quite hard to find a working implementation of. though the implementations of these algorithms are still more on the experimental side, the basic algorithms such as lll, bkz, potentially combined with deep insertions, and enumeration, are well-tested over the years. (in fact, some large-scale lattice reduction experiments i did for these algorithms yielded some results in the svp challenge’s hall of fame).

in case you’re interested in this library, feel free to play around with it! in case you have any questions, encounter problems, or want to give feedback, feel free to contact me by email.

already two and a half weeks ago, scott vanstone died at age of 66. scott intensively pushed, commercialized and invested in elliptic curve cryptography from its beginnings on. he also co-founded the ecc conference series, which i attended eight times.

rest in peace, scott.

posted in: daily life math

today i was in bad säckingen to give a talk at the kinderuni (children university) hochrhein, a eu-funded joint project between the two cities bad säckingen in germany and stein (ag) in switzerland. in the talk, i tried to explain kids, age 8 to 12, a bit about cryptography.

starting with caesar-type ciphers and more general substitution ciphers, i then continued to explained how to crack such ciphers using frequency analysis. this included a live demonstration, which was quite fun thanks to all the contributions from the audience. after shortly giving hints on how to improve on ciphers, i quickly presented the advanced encryption standard before continuing with the second part of the presentation: public key cryptography.

i began by explaining the situation: two cats want to communicate / exchange something (like cat food :-) ), while a third cat is watching / able to intercept (eat). after mentioning diffie and hellman, i continued with a more practical example: a simple massey-omura three-pass protocol type exchange using a box and two padlocks. this was another great thing, asking the kids how they think this could work after presenting the box and the padlocks. and the sudden murmur of understanding when the second lock got added to the box and the box was sent back.
afterwards i asked the kids how they think this system could be attacked, and they both came up with the bruteforce (crack the box open) and the more tricky (man-in-the-middle attack) variant. great!

the last slides on factoring-based crypto and elliptic curves were quite hard to comprehend, as i knew beforehand, but at least they now know that there’s more out there for which they have to learn more about mathematics :-)

if you’re interested, you can download the slides here.

on the weekend before easter we were in kaiserslautern. the main reason for our visit was to attend a team meeting for matheraum, but then we also visited rebekka and m. i haven’t seen rebekka for … i don’t know how many years now. (ignoring a “train incident” where she saw me, but i didn’t saw her while changing trains in mannhein or so.) definitely longer as this blog exists, i.e. before 2007. anyway. even though the weather wasn’t too great most of the weekend, we were lucky to get a glimpse of kaiserslautern with sun on both friday and sunday (on sunday we met rebekka and m.).

on saturday, we went to the japanese garden. while inside at least it didn’t snow (it waited until we left), but the weather wasn’t very great and also the cherry blossom didn’t bloom yet. still, it was a nice experience:

next time i’ll go there, there should better be sun and cherry blossoms :-)

today i discovered why sometimes, some of my latex output contains tildes (~) in the dvi/pdf version. usually, if you use a tilde in a tex file, it is interpreted as a non-breakable space (except in special circumstances, such as verbatim environments or in \url{…}). but thanks to a “bugfix” to texi2dvi/texi2pdf, which is a wonderful tool as it runs (pdf)latex often enough together with bibtex, makeindex etc., tildes appearing in tex files are now shown as tildes in the dvi/pdf output. which is absolutely inacceptable behaviour.
it seems that this already was reported (see here, here, here), but it is still around. i don’t really know what to think of this – is nobody responsible for working on texi2dvi/texi2pdf? or did people stop using it as it is broken?
anyway, i fixed my local installed version (/usr/bin/texi2dvi) by chaning the line catcode_special=true to catcode_special=false. a more sophisticated version would be nice, which only changes catcode_special for tex files (and not for texinfo files), but i don’t have time for that now.

someone just sent around this link:

[[for legal reasons, i do not want to include youtube videos here anymore. please click on this link to watch the video at youtube.]]

(theoretically) infinite pendulum fun with a period of 60 seconds (since gcd(51,52,…,65)=1)!

posted in: math

some time ago, a friend borrowed me his copy of logicomix, a comic on logic i heard a lot of good about from various friends. yesterday, i finally got around to start reading, finishing it today. i must admit, the idea of telling the quest for finding a foundation of logic, of mathematics, in a comic sounds somewhat strange, like a hopeless endeavor. but my friends were right: this comic is excellent! telling a story in a story in a story, sometimes with less layers, introducing all important characters of this quest, whose names are familiar to most people interested in mathematics, logic and philosophy, this comic manages to present the quest for foundation of logic and mathematics in a nice, easy accessable way. lots of explanations here and there, hidden as story elements, as well as an appendix containing more information on certain topics as well as the involved persons, hopefully help readers with less background than me.
if you get a chance, read it! even if you are no mathematician, logician or philosopher. it’s worth it.

posted in: math

one of the video/animation compo entries at revision was raum/zeit by subdream. it displays a lot of three-dimensional fractals and scored the second place. this was one of my favorite entries for that compo, and so here it is:

[[for legal reasons, i do not want to include youtube videos here anymore. please click on this link to watch the video at youtube.]]

another fractal based compo entry was electronenmultiplizierer by akronyme analogiker, which is a 4k intro, i.e. an executable of size four kilobytes (that is a very small amount!) which plays something in realtime. you can watch a low-quality recording here:

[[for legal reasons, i do not want to include youtube videos here anymore. please click on this link to watch the video at youtube.]]