156 research outputs found

    New Invariants for surfaces

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    We take the fundamental group of the complement of the branch curve of a generic projection induced from canonical embedding of a surface. This group is stable on connected components of moduli spaces of surfaces. Since for many classes of surfaces it is expected that the fundamental group has a polycyclic structure, we define a new invariant that comes from this structure. We compute this invariant for a few examples. Braid monodromy factorizations related to curves is a first step in computing the fundamental group of the complement of the curve, and thus we also indicate the possibility of using braid monodromy factorizations of branch curves as an invariant of a surface.Comment: 15 pages. To appear in Con. Math, AMS-TE

    Iterated LD-Problem in non-associative key establishment

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    We construct new non-associative key establishment protocols for all left self-distributive (LD), multi-LD-, and mutual LD-systems. The hardness of these protocols relies on variations of the (simultaneous) iterated LD-problem and its generalizations. We discuss instantiations of these protocols using generalized shifted conjugacy in braid groups and their quotients, LD-conjugacy and ff-symmetric conjugacy in groups. We suggest parameter choices for instantiations in braid groups, symmetric groups and several matrix groups.Comment: 30 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1305.440
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