By Benjamin Fine, Gerhard Rosenberger, Dennis Spellman
This e-book is a festschrift in honor of Professor Anthony Gaglione's 60th birthday. This quantity provides an exceptional mixture of learn and expository articles on a variety of elements of countless staff concept. The papers provide a large assessment of current study in limitless crew conception more often than not, and combinatorial team conception and non-Abelian group-based cryptography specifically. in addition they pinpoint the interactions among combinatorial team conception and mathematical common sense, in particular version conception.
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Additional info for Aspects of Infinite Groups: A Festschrift in Honor of Anthony Gaglione (Algebra and Discrete Mathematics)
First of all the 43 unit group U(R) contains a free group via the Magnus representation. Further there is no factoring algorithm within H. Keeping the defining power d secret makes determining inverses open only to those who know d. Hence this ring provides an ideal algebraic platform for the ring theoretic DiffieHellman method described in the last section. The actual method goes as was described there which we briefly repeat. Suppose that Bob wants to send Alice the message T E Q[[Xl, '" xnll where x~ = 0 for all i.
Goldberg, B. H. H. W. Koblitz, Algebraic Methods of Cryptography, Springer, 1998 [MJ W. Magnus, Rational Representations of Fuchsian Groups and NonParabolic Subgroups of the Modular Group, Nachrichten der Akad Gottingen, 1973, 179-189 [MKS] W. Magnus, A. Karass and D. Solitar Combinatorial Group Theory, Wiley Interscience,New York, 1968 [StJ R. Steinwandt, Loopholes in two public key cryptosystems using the modular groups preprint Univ. D. Yamamura, Public Key cryptosystems using the modular group, Lecture Notes in Comput.
Akad. ) 111, pp. 528-530 (1956). 3. R. D. Blyth, P. Moravec and R. F. Morse, On the nonabelian tensor squares of free nilpotent groups of finite rank, in Computational Group Theory and the Theory of Groups, eds. -C. Kappe, A. Magidin and R. F. Morse (American Mathematical Society, Providence, RI, 2008) 4. R. -L. Loday, Van Kampen theorems for diagrams of spaces, Topology 26, pp. 311-335 (1987), With an appendix by M. Zisman. 5. R. K. Dennis, In Search of New "Homology" Functors having a Close Relationship to K-theory, Unpublished preprint.