5,945 research outputs found

    β-Nd2Mo4O15

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    The title compound, dineodymium(III) tetra­molybdate(VI), has been prepared by a flux technique and is the second polymorph of composition Nd2Mo4O15. The crystal structure is isotypic with those of Ce2Mo4O15 and Pr2Mo4O15. It features a three-dimensional network composed of distorted edge- and corner-sharing NdO7 polyhedra, NdO8 polyhedra, MoO4 tetra­hedra and MoO6 octa­hedra

    Self-pairings on Hyperelliptic Curves

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    A self-pairing is a pairing computation where both inputs are the same group element. Self-pairings are used in some cryptographic schemes and protocols. In this paper, we show how to compute the Tate-Lichtenbaum pairing (D,\phi(D)) on a curve more efficiently than the general case. The speedup is obtained by requiring a simpler final exponentiation. We also discuss how to use this pairing in cryptographic applications
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