6,441 research outputs found
Algebraic Geometric Secret Sharing Schemes over Large Fields Are Asymptotically Threshold
In Chen-Cramer Crypto 2006 paper \cite{cc} algebraic geometric secret sharing
schemes were proposed such that the "Fundamental Theorem in
Information-Theoretically Secure Multiparty Computation" by Ben-Or, Goldwasser
and Wigderson \cite{BGW88} and Chaum, Cr\'{e}peau and Damg{\aa}rd \cite{CCD88}
can be established over constant-size base finite fields. These algebraic
geometric secret sharing schemes defined by a curve of genus over a
constant size finite field is quasi-threshold in the following
sense, any subset of players (non qualified) has no information of
the secret and any subset of players (qualified) can reconstruct
the secret. It is natural to ask that how far from the threshold these
quasi-threshold secret sharing schemes are? How many subsets of players can recover the secret or have no information of the secret?
In this paper it is proved that almost all subsets of
players have no information of the secret and almost all subsets of players can reconstruct the secret when the size goes to the
infinity and the genus satisfies . Then algebraic
geometric secret sharing schemes over large finite fields are asymptotically
threshold in this case. We also analyze the case when the size of the base
field is fixed and the genus goes to the infinity
An Improvment of the Elliptic Net Algorithm
In this paper we propose a modified Elliptic Net algorithm to compute pairings. By reducing the number of the intermediate variables which should be updated in the iteration loop of the Elliptic Net algorithm, we speed up the computation of pairings. Experimental results show that the proposed method is about faster than the original Elliptic Net algorithm on certain supersingular elliptic curves with embedding degree
β-Nd2Mo4O15
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
- …