基于多项式插值的门限函数秘密分享方案

Threshold Function Secret Sharing Scheme Based on Polynomial Interpolation

针对现存的函数秘密分享方案在重构的过程中需要所有的参与者全部参与,不能灵活地适用于现实场景的问题,本文运用多项式技术构造了含有门限的函数秘密分享方案.按照函数秘密分享的安全模型证明了新构造的方案具有信息论意义下的安全性.此外本文分析了Yuan等学者提出的函数秘密分享方案,阐述了其方案不满足函数秘密分享方案安全性的原因.最后将本文构造的方案与现有的函数秘密分享方案进行了比较,发现其具有更高级别的安全性和更高的效率.

Since the existing function secret sharing schemes require all participants to join in the reconstruction phase.Therefore,it cannot be flexibly applied to real-world scenarios.A function secret sharing scheme with thresholds is constructed in this study using polynomial techniques.According to the security model of function secret sharing,we proved that the proposed scheme has security in the sense of information theory.In addition,this study analyzes the function secret sharing scheme proposed by Yuan et al.,and expounds the reason why their scheme does not satisfy the security of function secret sharing.Finally,a comprehensive comparison between the newly constructed scheme and the existing function secret sharing scheme is found.We note that the newly constructed scheme has higher level of security and higher efficiency through the comprehensive comparison.