>> >> I don't know if that is of any interest but someone around here might care >> about the fact that Sage was probably the most mentioned (and cited) >> mathematics software at the "First Conference for Symbolic Computation and >> Cryptography" (SCC 2008) in Beijing. >> >> Specifically, these authors/papers mentioned Sage: >> >> * Tobias Eibach and Gunnar Völkel: Optimising Gröbner Bases on Bivium (used >> Sage to implement attack) >> * Burçin Eröcal: SCrypt: Using Symbolic Computation to Bridge the Gap >> Between >> Algebra and Cryptography (module for Sage) >> * Ralf-Philipp Weinmann and Johannes Buchmann: Distributed Memory >> Computation >> of Row-Reduced Echelon Forms over Finite Fields (benchmarked against Sage) >> * Yours truly and Carlos Cid: Algebraic Techniques in Differential >> Cryptanalysis (used Sage to implement attack) >> >> (... yes, I know that 3 out of 4 are Sage developers, but still ...) >> >> Another thing:Two talks dealt with Braid group cryptography, namely: >> >> * Robert Gilman, Alex D. Miasnikov, Alexei G. Myasnikov and Alexander >> Ushakov: >> New Developments in Commutator Key Exchange >> * Alex D. Myasnikov and Alexander Ushakov: Cryptanalysis of the >> Anshel-Anshel-Goldfeld-Lemieux Key Agreement Protocol >> >> The group developed a C++ library CRAG: >> >> """ >> The Cryptography And Groups (CRAG) Library provides an environment to test >> cryptographic protocols constructed from non-commutative groups, for example >> the braid group. The Library is written in C++ and provides an interface and >> routines for computations. There are implementations of basic algebraic >> objects like words, maps and subgroups. We plan to continually expand the >> list of group-theoretic algorithms implemented in the library. In addition >> the Library will contain classes and routines implementing non-classical >> heuristic approaches and tools to perform statistical and exploratory >> analysis of algebraic data. Together with the C++ source code CRAG contains >> interface to Python scripting language. >> """ >> >> http://www.acc.stevens.edu/downloads.php >> >> I don't know much about group theory but still I figured someone might find >> it >> interesting and is able to evaluate if it could be a good addition to Sage. > >This is very interesting. I just have some general remarks. Alexi Myasnikov >(a good friend of mine knows him well and that is what he calls him - Alexi, >not >Alex. as on the website) is an extremely talented group theorist. I heard that >there was some discussion of him getting a Fields medal years ago when >he announced >his solution of the Tarski problem. That is his level. If he is behind >this library >then I think that it at least has the stamp of authority. BTW, both Alexi and >Gilbert Baumslag were behind MAGNUS, an infinite group theory package. I had >a few (off-list, I think) emails with William Stein and Gilbert >Baumslag, and I met >with Gilbert face-to-face a month or so ago about MAGNUS and SAGE. The >problem is that MAGNUS is designed in a way which makes its GUI front-end >difficult to separate from its group-computational engine at the back-end. As a >bit of background, Gilbert Baumslag is also a superstar in the field >of combinatorial >group theory and has just recently moved from the math dept at CUNY to the CS >dept. This graphic design was probably Gilbert's idea and very much in >line with some >other (computer science) projects he has worked on. Anyway, >MAGNUS->SAGE just didn't >work out. I think the design of CRAG is different and may be easier to >integrate >into SAGE. I do see that they have a free group and finitely presented group >(C++) class, which is good. These are also in GAP though. What GAP >does not have is >"Definition of equations over finitely presented group", nor does it >have any of the >crypto stuff. > >So, I vote +1 to include it at least as an optional package. Making it >a standard part of SAGE >should IMHO wait until a solid FreeGroup and FinitelyPresentedGroup >(Python) class >are created for SAGE. If I had more time I would do this myself. > >Thanks again Martin for pointing this out.
(disclaimer: I'm the person who set up the Magnus sourceforge site and I worked for Gilbert Baumslag at City College) I know that there is an existing Python wrapper around Magnus. I know that Magnus has a large number of C++ routines for group theory that exist nowhere else. I know that Magnus can be used without the frontend (we used it as a password mechanism for logging into linux using groups theory). I know that Magnus is designed to run procedures in parallel. (not algorithms since they may not terminate; in general, there are very few algorithms for this kind of work) Using the procedures in parallel enable you to try various approaches until one succeeds and then poison the others. I know that Magnus is GPL. I know that there are a large number of people who have collaborated with Gilbert Baumslag over the years. Gilbert is definitely in the superstar category (distinguished prof, 7 books, 150 papers, etc). Tim Daly --~--~---------~--~----~------------~-------~--~----~ To post to this group, send email to sage-devel@googlegroups.com To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/sage-devel URLs: http://www.sagemath.org -~----------~----~----~----~------~----~------~--~---
