一种可验证的(k,n)门限多秘密共享方案  

A verifiable(k,n)threshold multi-secret sharing scheme

作　　者：张宏图 胡航 李富林[1] ZHANG Hongtu;HU Hang;LI Fulin(School of Mathematics,Hefei University of Technology,Hefei 230601,China)

机构地区：[1]合肥工业大学数学学院,安徽合肥230601

出　　处：《合肥工业大学学报(自然科学版)》2025年第4期544-548,共5页Journal of Hefei University of Technology:Natural Science

基　　金：国家自然科学基金资助项目(12171134);国家自然科学基金联合基金资助项目(U21A20428)。

摘　　要：基于排列和Diffie-Hellman问题,文章提出一种可验证的(k,n)门限多秘密共享方案。该方案中排列的使用确保了计算生成的秘密份额的安全性,在Diffie-Hellman问题的假设下,各参与者的伪份额均由自己生成,基于相关等式是否成立实现了方案的可验证性。各参与者只需维护1个彼此不同的伪份额即可根据门限值k进行多个秘密的重构。结果表明,该方案不需要安全信道,各参与者的伪份额可重复使用,且可以抵抗合谋攻击和外部攻击。Based on the permutation and Diffie-Hellman problem,a verifiable(k,n)threshold multi-secret sharing scheme is proposed.In the scheme,the application of the permutation ensures the security of the secret shares generated by calculation.Under the assumption of the Diffie-Hellman problem,participants’pseudo-shares are generated by themselves.The verifiability of the scheme is achieved based on whether the relevant equation holds.Each participant only needs to maintain a pseudo-share that is different from each other to reconstruct multiple secrets according to the threshold value k.Further analysis shows that the scheme does not need a secure channel,the pseudo-share of each participant can be reused,and it can resist collusion and external attacks.

关 键 词：多秘密共享 门限恢复 可验证性 排列 DIFFIE-HELLMAN问题 

分 类 号：TN918.1[电子电信—通信与信息系统]