一种安全的多使用门限多秘密共享方案

在多秘密共享方案中,通常会生成大量公开值来保障多个秘密安全正确地重构,同时参与者也需要保存大量信息.为减少公开值的个数以及参与者所需保存的信息量,本文基于中国剩余定理和Shamir(t,n)-门限秘密共享方案设计了一个子秘密可多使用的门限存取结构多秘密共享方案.根据中国剩余定理将多项式产生的子秘密信息进行聚合生成公开值,减少了公开值的个数;应用转换值的方法和离散对数对参与者子秘密信息进行保护.构造了具有以下特点的多秘密共享方案:可一次共享多个秘密;不同的秘密可对应不同门限的存取结构;参与者可验证所恢复秘密值的正确性;公开值个数更少;参与者存储一个子秘密且子秘密可以多次使用.

Secure Multi-Use Threshold Multi-Secret Sharing Scheme

In a multi-secret sharing scheme, a large number of public values are generated to ensure the secure and correct reconstruction of multi-secrets, and participants also need to keep a large amount of information. In order to reduce the number of public values and the information that participants should keep, this study designs a multi-secret sharing scheme based on the Chinese Remainder Theorem (CRT) and Shamir (t, n)-threshold secret sharing scheme in which shares can be used more than once. Specifically, the shares generated by polynomials are aggregated to generate public values by CRT, which reduces the number of public values. Transformed value and discrete logarithms are used to protect the shares of participants. In a multi-secret sharing scheme, multiple secrets can be shared at one time; different secrets can be shared in access structures with different thresholds; participants can verify the secrets recovered; the number of public values is fewer; each participant only needs to store one share which can be used repeatedly.