On Wed, Apr 30, 2008 at 10:48 AM, Martin Albrecht <[EMAIL PROTECTED]> wrote: > > Hi, > > 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. > > Cheers, > Martin > > -- > name: Martin Albrecht > _pgp: http://pgp.mit.edu:11371/pks/lookup?op=get&search=0x8EF0DC99 > _www: http://www.informatik.uni-bremen.de/~malb > _jab: [EMAIL PROTECTED] > > > > > --~--~---------~--~----~------------~-------~--~----~ 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 -~----------~----~----~----~------~----~------~--~---
