CGC Bulletin 16
CONTENTS
- A new Heldermann-Verlag journal: Groups, Complexity, and Cryptology
- Computing twisted conjugacy classes in free groups using nilpotent quotients
- Finitely generated lattice-ordered groups with soluble word problem
- Finite index subgroups of R. Thompson's group F
- Towards generating secure keys for braid cryptography
EDITOR'S NOTE: Not every day a big brother is born (!). The CGC Bulletin welcomes his new big brother: The journal of Groups, Complexity, and Cryptology (GCC). Section 1 gives some details and a link to the detailed journal's webpage. We thank Gerhard Rosenberger and Vladimir Shpilrain for the initiative, and look forward for the first issue, scheduled to appear in 2008.
Your high-quality papers on CGC would be welcome there.
Boaz Tsaban
Bulletin's webpage: http://www.cs.biu.ac.il/~tsaban/CGC/cgc.html
1. A new Heldermann-Verlag journal: Groups, Complexity, and Cryptology
Call for papers
Managing Editors: G. Rosenberger, V. Shpilrain
Groups-Complexity-Cryptology is a journal for publication of articles in the areas of combinatorial and computational group theory, complexity theory, and cryptology. Preference is given to papers that touch upon at least two of these areas, but exceptional papers representing just one of the areas are considered, too.
Groups-Complexity-Cryptology primarily publishes research papers, but comprehensive and timely survey articles on a topic inside the scope of the journal are also welcome.
All submitted papers are peer-reviewed before publication.
Editorial Board:
- J.-C. Birget (Camden, U.S.A.)
- M. Conders (Auckland, New Zealand)
- P. Dehornoy (Caen, France)
- B. Fine (Fairfield, U.S.A.)
- R. Gilman (Hoboken, U.S.A.)
- D. Grigoriev (Rennes, France)
- G. Kern-Isberner (Dortmund, Germany)
- K. H. Ko (Daejeon, Korea)
- M. Kreuzer (Passau, Germany)
- A. Myasnikov (Montreal, Canada)
- R. Thomas (Leicester, England)
- B. Tsaban (Ramat Gan, Israel)
- E. Ventura (Barcelona, Spain)
- P. Weil (Bordeaux, France)
Instructions for submission are available at the Journal's homepage: http://www.heldermann.de/GCC/gcccover.htm
2. Computing twisted conjugacy classes in free groups using nilpotent quotients
P. Christopher Staecker
There currently exists no algebraic algorithm for computing twisted conjugacy classes in free groups. We propose a new technique for deciding twisted conjugacy relations using nilpotent quotients. Our technique is generalization of the common abelianization method, but admits significantly greater rates of success. We present experimental results demonstrating the efficacy of the technique, and detail how it can be applied the related settings of surface groups and doubly twisted conjugacy.
http://arxiv.org/abs/0709.4407
3. Finitely generated lattice-ordered groups with soluble word problem
A. M. W. Glass
William W. Boone and Graham Higman proved that a finitely generated group has soluble word problem if and only if it can be embedded in a simple group that can be embedded in a finitely presented group. We prove the exact analogue for lattice-ordered groups: Theorem: A finitely generated lattice-ordered group has soluble word problem if and only if it can be embedded in an simple lattice-ordered group that can be embedded in a finitely presented lattice-ordered group. The proof uses permutation groups and the ideas used to prove the lattice-ordered group analogue of Higman's Embedding Theorem.
http://arxiv.org/abs/0710.1699
4. Finite index subgroups of R. Thompson's group F
Collin Bleak and Bronlyn Wassink
The authors classify the finite index subgroups of R. Thompson's group F. All such groups that are not isomorphic to F are non-split extensions of finite cyclic groups by F. The classification describes precisely which finite index subgroups of F are isomorphic to F, and also separates the isomorphism classes of the finite index subgroups of F which are not isomorphic to F from each other; characterizing the structure of the extensions using properties of the structure of the finite index subgroups of ZxZ.
http://arxiv.org/abs/0711.1014
5. Towards generating secure keys for braid cryptography
Ki Hyoung Ko, Jang Won Lee, and Tony Thomas
Braid cryptosystem was proposed in CRYPTO 2000 as an alternate public-key cryptosystem. The security of this system is based upon the conjugacy problem in braid groups. Since then, there have been several attempts to break the braid cryptosystem by solving the conjugacy problem in braid groups. In this article, we ?rst survey all the major attacks on the braid cryptosystem and conclude that the attacks were successful because the current ways of random key generation almost always result in weaker instances of the conjugacy problem. We then propose several alternate ways of generating hard instances of the conjugacy problem for use braid cryptography.
Design, Codes, and Cryptography (2007) 45:317333
DOI 10.1007/s10623-007-9123-0
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