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J. Hefei Univ. Tech. (Nat. Sci.)

合肥工业大学学报(自然科学版)

JOURNAL OF HEFEI UNIVERSITY OF TECHNOLOGY (NATURAL SCIENCE)

Competent Authorities: Ministry of Education of the People's Republic of China

Sponsor by: Hefei University of Technology

ISSN 1000-1646, CN 34-1001/N

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

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一种可验证的 $ (k,n) $门限多秘密共享方案

Journal Information

J. Hefei Univ. Tech. (Nat. Sci.), Apr.2025, Vol.48 No.4: 544-548

DOI: 10.3969/j.issn.1003-5060.2025.04.018

Authors

ZHANG Hongtu, HU Hang, LI Fulin

(School of Mathematics, Hefei University of Technology, Hefei 230601, China)

Abstract and Keywords

Abstract: 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.

Keywords: multi-secret sharing; threshold recovery; verifiability; permutation; Diffie-Hellman problem

作者信息

张宏图，胡航，李富林

（合肥工业大学数学学院，安徽合肥230601）

摘要和关键词

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。

关键词: 多秘密共享；门限恢复；可验证性；排列；Diffie-Hellman问题

Funding

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）

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