A rational threshold signature protocol based on generalised projective transformation

摘要

The prevalence of threshold structures is mainly based on the Lagrange interpolation polynomial, Chinese Remainder Theorem, RSA key segmentation techniques, circular features and so forth. Combining with above-mentioned threshold structures, a series of threshold signature plans can be constructed. Because of the change of interpolation nodes the Lagrange interpolation polynomial causes the recalculation of interpolation coefficient. Moreover, the degree of algebraic curve sometimes is so high to cause an efficiency problem. Chinese Remainder Theorem is not easy to construct ultra-increment sequence. Circular features has with low performance. RSA key segmentation techniques is not the real threshold structure, so it can be used only by group signature. The paper aims at the drawbacks of the above-mentioned threshold structures, and constructs a new threshold structure based on generalised projective transformation. In order to put this into use, gives an ID-based rational threshold signature protocol. We analyse the threshold plan by using the crisp cooperative game theory, and the theorems show that this threshold structure scheme is ideal.