Research On Key Technologies In Rational Threshold Signature Protocol

Rational threshold signature regards the individuals which participate in thethreshold signature as rational people. Different utility function value depends on thedifferent protocol operation. Constructing different threshold structure on the basis ofsecret sharing, the signature private key is divided into different sub-key shadow, eachparticipant holds a different sub-key shadow, and the number of participants onlyreaches the threshold value to be able to restore the threshold signature private key.The collection which meets the threshold value is called permissive signaturecollection. Permissive signature collection has upward monotonic. The collectionwhich does not meet the threshold value is called non-permissive signature collection.Non-permissive signature collection has downward monotonic. If the order ofsignature sub-key space equal to the order of the threshold signature private key space,the threshold structure is called ideal threshold shared. When the number of internalstaff is more than or equal to the threshold value and joint strike system, thisphenomenon is called conspiracy attack. Prevent conspiracy attacks becomes a hottopic from the view of rational.The existing threshold structure mainly includes the method of computingintersections to solve equations in Euclidean space, the method of Chinese RemainderTheorem, the method of Lagrange interpolation polynomial, the method of OrdinaryDifferential Difference Equations, the method of RSA key segmentation techniques,the method of Circle Characteristics, the method of function field and so forth. Theinterpolation coefficients recalculate due to the interpolation node of change in themethod of Lagrange interpolation polynomial, and the efficiency problem in regard ofhigh curve order. Constructing super increasing sequence is inconvenience in themethod of Chinese Remainder Theorem. The efficiency of the Circle Characteristicsis low. The method of RSA key segmentation techniques is not the real thresholdstructure, can only be used in the field of group signature.Proposing new threshold structure has an important significance both in theoryand in practice. The main research results in this paper are as follows:1. Proposes two new threshold construction methods based on projectivegeometry. Using direct transformation and generalize projective transformation toconstruct threshold structure, achieves confusion and diffusion. Solves thecomputational efficiency reduce when the number of participants is growing problem.2. Based on bilinear mapping to improve a threshold signature scheme. Using the trace set to solve conspiracy attack problem. In addition, uses the idea of Gu Ke tosolve low efficiency problem.3. Based on homogeneous constant coefficient linear differential equation, thispaper proposes computable complete and perfect information dynamic gamet1t2elasticity equilibrium theory, using the time series, Feldman’s publicly verified,Pedersen’s bitstream commitment, Okamoto’s dual key signature, matrix thresholdand other technologies to construct a rational threshold signature model, solves fraudproblem.