Verifiable Secret Sharing Scheme Based on the Plane Parametric Curve

Verifiable secret sharing is a special kind of secret sharing. In this paper, A secure and efficient threshold secret sharing scheme is proposed by using the plane parametric curve on the basis of the principle of secret sharing. And the performance of this threshold scheme is analyzed. The results reveal that the threshold scheme has its own advantage of one-parameter representation for a master key, and it is a perfect ideal secret sharing scheme. It can easily detect cheaters by single operation in the participants so that the probability of valid cheating is less than 1/p (where p is a large prime).

A Simple, Fast and Stabilized Flowing Finite Volume Method for Solving General Curve Evolution Equations

A new simple Lagrangian method with favorable stability and efficiencyproperties for computing general plane curve evolutions is presented. The methodis based on the flowing finite volume discretization of the intrinsic partial differentialequation for updating the position vector of evolving family of plane curves. A curvecan be evolved in the normal direction by a combination of fourth order terms relatedto the intrinsic Laplacian of the curvature, second order terms related to the curva-ture, first order terms related to anisotropy and by a given external velocity field. Theevolution is numerically stabilized by an asymptotically uniform tangential redistri-bution of grid points yielding the first order intrinsic advective terms in the governingsystem of equations. By using a semi-implicit in time discretization it can be numer-ically approximated by a solution to linear penta-diagonal systems of equations (inpresence of the fourth order terms) or tri-diagonal systems (in the case of the secondorder terms). Various numerical experiments of plane curve evolutions, including, inparticular, nonlinear, anisotropic and regularized backward curvature flows, surfacediffusion and Willmore flows, are presented and discussed.

A Class of Pseudo-Real Riemann Surfaces with Diagonal Automorphism Group

A Riemann surface S having field of moduli M,but not a field of definition,is called pseudo-real.This means that S has anticonformal automorphisms,but none of them is an involution.A Riemann surface is said to be plane if it can be described by a smooth plane model of some degree d≥4 in P^2/C.We characterize pseudo-real-plane Riemann surfaces»S,whose conformal automorphism group Aut+(S)is PGL3(C)-conjugate to a finite non-trivial group that leaves invariant infinitely many points of P^2/C.In particular,we show that such pseudo-real-plane Riemann surfaces exist only if Aut+(S)is cyclic of even order n dividing the degree d.Explicit families of pseudo-reai-plane Riemann surfaces are given for any degree d=2pm with m>1 odd,p prime and n=d/p.

Design and fabrication of silicon-tessellated structures for monocentric imagers

Compared with conventional planar optical image sensors,a curved focal plane array can simplify the lens design and improve the field of view.In this paper,we introduce the design and implementation of a segmented,hemispherical,CMOS-compatible silicon image plane for a 10-mm diameter spherical monocentric lens.To conform to the hemispherical focal plane of the lens,we use flexible gores that consist of arrays of spring-connected silicon hexagons.Mechanical functionality is demonstrated by assembling the 20-μm-thick silicon gores into a hemispherical test fixture.We have also fabricated and tested a photodiode array on a siliconon-insulator substrate for use with the curved imager.Optical testing shows that the fabricated photodiodes achieve good performance;the hemispherical imager enables a compact 160°field of view camera with >80% fill factor using a single spherical lens.