密码学报2016，Vol.3Issue(3)：270-281,12.DOI:10.13868/j.cnki.jcr.000127
基于非齐次线性递归的门限多密钥共享方案的研究*
On the Construction of Threshold Multi-secret Sharing Scheme Based on Non-homogeneous Linear Recursions
摘要
Abstract
Secret sharing scheme is an important branch of modern cryptography. It is also an important tool for information security and data privacy, and has been widely used in digital signatures, secure multiparty computation schemes, error-correcting codes, and so on. In many existing schemes, the construction of secret sharing scheme is mostly based on the Lagrange interpolation polynomial, the secret share is selected and distributed by a dealer and can only be used once, hence a secret channel is needed to transmit the information, only one secret can be shared in one secret sharing process. In the recovery phase, the participants cannot check whether other participants provide the true secret shares. In this paper, two verifiable threshold multi-secret sharing schemes based on non-homogeneous linear recursions are proposed. In the initial phase, the secret share of each participant is selected by himself. In the distribution phase, each scheme can be divided into two cases according toktandkt,and thek multiple secrets are put in the equations of non-homogeneous linear recursions of degreet. In the verification phase, an improved verification algorithm is proposed which improves the Dehkordi-Mashhadi schemes by reducing the number of public values from 2n+k-t+4 ton+k+5. In the recovery phase, each participant just needs to provide a pseudo share instead of the secret share, which makes the reuse of secret share to be secure. The proposed schemes have the following features: verifiable, can share multiple secrets, the reuse of secret shares is possible, only public channels are needed, based on elliptic curves, and have better performance than some other typical schemes, such as less public values and reconstruction polynomial with lower degree.This makes the schemes more efficient and useful in practical applications.关键词
门限多密钥共享/非齐次线性递归/公开信道/重构多项式/公开参数Key words
threshold multi-secret sharing/non-homogeneous linear recursion/public channel/reconstruction polynomial/public value分类
信息技术与安全科学引用本文复制引用
张本慧,唐元生..基于非齐次线性递归的门限多密钥共享方案的研究*[J].密码学报,2016,3(3):270-281,12.基金项目
国家自然科学基金项目(61379004) （61379004）
安徽省教育厅自然科学研究重点项目(KJ2016A634) （KJ2016A634）
淮北师范大学青年科研项目(2014xq006) （2014xq006）
